Relationship between solubility (S) and solubility product (Ksp)
Consider MqAr a sparingly soluble salt.
Where
q = Number of cations (Mr+) and
r = Number of anions (Aq-)
That is we have in dissolved state
MqAr ↔ qMr+ + r Aq-
Then
Ksp = [Mr+]q [Aq-]r
If solubility is S, according to the definition of solubility product
We have
[Mr+]q = q.S mol/dm³
[Aq-]r = r.S mol/dm³
Hence Ksp = [q.S] q [r.S] r
= Sq+r. qq.rr
For example for the salt, calcium Phophate, Ca3(PO4)2
Ca3(PO4)2 ↔ 3Caaq2+ + 2PO4(aq)3-
Ksp = [Ca2+] 3 [PO43-]2
= S3+2.33.22
= 108S5
Past JEE Question
For a sparingly soluble salt ApBq, the relationship of its solubility product (Ksp) with its solubility (s) is
a. Ksp = sp+q.pp.qq
b. Ksp = sp+q.pq.qp
c. Ksp = spq.pp.qq
d. Ksp = spq.(pq)p+q)
(2001)
Answer: a
Saturday, August 30, 2008
Friday, August 29, 2008
Solubility Product - July Dec Revision
Solubility product of a salt at a given temperature is equal to the product of the concentrations of its ions in the saturated solution, with each concentration term raised to the power equal to the number of moles of ions produced on dissociation of one mole of the substance.
Law of Mass Action - July-Dec Revision
Law of Mass Action
For the reaction
2 NO2 = N2O4
in a sealed tube the ratio
[N2O4]
-------
[NO2]²
is a constant. This phenomenon is known as chemical equilibrium. The ratio is called equilibrium constant (K).
[N2O4] and [NO2] are molar concentrations of N2O4 and NO2.
Such a law of nature is called the law of mass action or mass action law.
Of course, when conditions, such as pressure and temperature, change, a period of time is required for the system to establish an equilibrium.
For systems that are not at equilibrium yet, the ratio calculated from the mass action law is called a reaction quotient Q. The Q values of a closed system have a tendency to reach a limiting value called equilibrium constant K over time. A system has a tendency to reach an equilibrium state.
The law of mass action may be written as:
The rate of a chemical reaction at any particular temperature is proportional to the product of the molar concentrations of reactants with each concentration term raised to the power equal to the number of molecules of the respective reactants taking part in the reaction.
In the chemical kinetics chapter we come to know that chemical reactions can be elementary reactions or complex reactions having number of elementary reactions.
Law of mass action is valid for elementary reactions.
For the reaction
2 NO2 = N2O4
in a sealed tube the ratio
[N2O4]
-------
[NO2]²
is a constant. This phenomenon is known as chemical equilibrium. The ratio is called equilibrium constant (K).
[N2O4] and [NO2] are molar concentrations of N2O4 and NO2.
Such a law of nature is called the law of mass action or mass action law.
Of course, when conditions, such as pressure and temperature, change, a period of time is required for the system to establish an equilibrium.
For systems that are not at equilibrium yet, the ratio calculated from the mass action law is called a reaction quotient Q. The Q values of a closed system have a tendency to reach a limiting value called equilibrium constant K over time. A system has a tendency to reach an equilibrium state.
The law of mass action may be written as:
The rate of a chemical reaction at any particular temperature is proportional to the product of the molar concentrations of reactants with each concentration term raised to the power equal to the number of molecules of the respective reactants taking part in the reaction.
In the chemical kinetics chapter we come to know that chemical reactions can be elementary reactions or complex reactions having number of elementary reactions.
Law of mass action is valid for elementary reactions.
JEE 2010 Study Plan Blog
Readers can subscribe to this blog to read it in their google readers etc.
www.iit-jee-2010.blogspot.com
www.iit-jee-2010.blogspot.com
Chemical Equilibrium - July Dec Revision
In most of the reaction carried out in closed vessels, reaction does not go to completion under given set of conditions of temperature and pressure. Initially, in the vessel, only reactants are present, and as the reaction proceeds, the concetration of reactants will decrease and that of products will increase.
After some time a stage is reached when no further change in concetrations of reactants and products is observed. This state is called equilibrium state and some of the important questions regarding this phenomenon are:
1. why do reactions seem to stop before they reach completion?
2. What is the extent to which a reaction proceed?
3. Can we modify the conditions to improve the yield of products?
Equilibrium - The phenomenon
Equilibrium is the state at which the concentrations of reactants and products do not change with time.
It is important to remember that equilibrium is achieved in closed vessel reactions only.
The important aspect of reaction equilibrium is the reversibility. The products combine and form reactants. At equilibrium, both the forward and backward reactions are taking place. The rates of forward and backward reactions are same or equal at the equilibrium. As a result, the concentration of each species becomes constant.
The equilibrium is termed as dynamic reaction equilibrium. Dynamic means at a microscopic level, the system is in motion. But at macroscopic level, concentrations are not changing.
Chemical reactions may be classified as reversible reactions and irreversible reactions.
Example of irrereversible reaction
Decomposition of potassium chlorate into potassium chloride and oxygen. Even in a closed vessel this reaction is not reversible.
Example of reversible reaction
1. Decompositon of calcium carbonate. When solid calcium carbonate is heated in a closed vessel at 1073 K, it decomposes into solid calcium oxide and gaseous carbon dioxide. Due to gaseous CO2 there is pressure of gas in the vessel which can be measured. At a constant temperature it can be observed that pressure becomes constant after some time, which means no further CO2 is being produced even though calcium carbonate is still there in the vessel. The constant pressure indicates to us that reaction equilibrium is reached.
Characteristics of chemical equilibrium
1. Chemical equilibrium is dynamic in nature (already explained).
2. the properites of the system become constant at equilibrium and remain unchanged thereafter unless external or internal conditions are changed.
3. The equilibrium is attained only if the system is closed one.
4. As the reactions are reversible and happen under the same conditions, equilibrium can be attained from either direction.
5. A catalyst does not alter the equilibrium point. The catalyst increases the rate of reaction, and at equilibrium it increases both forward and backward reaction rates. But it does not alter equilibrium point, the concentrations of products and reactants at a given set of conditions. But the equilibrium is reached earlier in the presence of a catalyst.
After some time a stage is reached when no further change in concetrations of reactants and products is observed. This state is called equilibrium state and some of the important questions regarding this phenomenon are:
1. why do reactions seem to stop before they reach completion?
2. What is the extent to which a reaction proceed?
3. Can we modify the conditions to improve the yield of products?
Equilibrium - The phenomenon
Equilibrium is the state at which the concentrations of reactants and products do not change with time.
It is important to remember that equilibrium is achieved in closed vessel reactions only.
The important aspect of reaction equilibrium is the reversibility. The products combine and form reactants. At equilibrium, both the forward and backward reactions are taking place. The rates of forward and backward reactions are same or equal at the equilibrium. As a result, the concentration of each species becomes constant.
The equilibrium is termed as dynamic reaction equilibrium. Dynamic means at a microscopic level, the system is in motion. But at macroscopic level, concentrations are not changing.
Chemical reactions may be classified as reversible reactions and irreversible reactions.
Example of irrereversible reaction
Decomposition of potassium chlorate into potassium chloride and oxygen. Even in a closed vessel this reaction is not reversible.
Example of reversible reaction
1. Decompositon of calcium carbonate. When solid calcium carbonate is heated in a closed vessel at 1073 K, it decomposes into solid calcium oxide and gaseous carbon dioxide. Due to gaseous CO2 there is pressure of gas in the vessel which can be measured. At a constant temperature it can be observed that pressure becomes constant after some time, which means no further CO2 is being produced even though calcium carbonate is still there in the vessel. The constant pressure indicates to us that reaction equilibrium is reached.
Characteristics of chemical equilibrium
1. Chemical equilibrium is dynamic in nature (already explained).
2. the properites of the system become constant at equilibrium and remain unchanged thereafter unless external or internal conditions are changed.
3. The equilibrium is attained only if the system is closed one.
4. As the reactions are reversible and happen under the same conditions, equilibrium can be attained from either direction.
5. A catalyst does not alter the equilibrium point. The catalyst increases the rate of reaction, and at equilibrium it increases both forward and backward reaction rates. But it does not alter equilibrium point, the concentrations of products and reactants at a given set of conditions. But the equilibrium is reached earlier in the presence of a catalyst.
Thursday, August 28, 2008
IIT JEE 2010 Study Plan
iit-jee-2010.blogspot.com
Trying to develop topic wise study plan for exam through this blog
Join Orkut Community
IIT-JEE-ACADEMY
http://www.orkut.co.in/Community.aspx?cmm=39291603
Trying to develop topic wise study plan for exam through this blog
Join Orkut Community
IIT-JEE-ACADEMY
http://www.orkut.co.in/Community.aspx?cmm=39291603
Wednesday, August 27, 2008
Chemical Kinetics - July December Revision
Jee Syllabus
Chemical kinetics:
Rates of chemical reactions;
Order of reactions;
Rate constant;
First order reactions;
Temperature dependence of rate constant (Arrhenius equation).
--------------------------
The topic "Chemical kinetics" consists of reaction rate and reaction mechanism.
Reaction rate is the speed with which a reaction takes place. This shows the rate or speed at which the reactants are consumed and products are formed.
Reaction mechanism is the path by which a reaction takes place.
Rate of reaction
The rate of reaction is a quantity that tells how the concentration of reactants or product changes with time.
So this can be expressed as Δ concentration/Δ time. That is change in concentration divided by time taken for the change.
Molar concentration i.e., moles per liter (M), is used in these equations.
The brackets, [ ] are always used to to indicate molar concentrations.
Rate law
The rate for a reaction is a mathematical expression that relates the rate of reaction to the concentrations of the reactants.
For the reaction aA + bB → products
The rate law is expressed as, rate of reaction is proportional to [A]^x[B]^y.
x and y are determined experimentally. These values can be whole or fractional numbers or zero.
Law of Mass Action
In 1867, Cato Guldberg, and Peter Waage, proposed this law. According to this law, for the rate determining step in a reaction, the rate of reaction is proportional to the product of the concentrations of the reactants, each raised to the power of its coefficient in the balanced equation.
For the reaction aA + bB → cC (when it is a rate determining step)
Rate of reaction is proportional to [A]^a[B]^b
The above proportionality can be written as an equation, by putting in a proportionality constant k.
Rate = k *[A]^a[B]^b
K is called the specific rate constant
Order of Reaction
From the rate law for a reaction order of reaction can be determined.
For a particular species or reactant, the order is equal to the exponent for that species in the rate law.
For example for Rate = k *[A][B]^2
for B the order of reaction is 2. For A it is 1.
The overall order of reaction is equal to the sum of all the individual orders of reactants.
Temperature
As temperature increases, the average kinetic energy increases. So there are more molecules with activation energy and hence reaction rate increases.
As a general approximation, the rate roughly doubles for each 10°C rise in temperature.
-----------
Molecularity
I recently read the lesson in NCERT Book Part I for Class XII.
There is a section on Molecularity of a Reaction
The number of reacting species which much collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction.
In the case of reaction
NH4NO2 --> N2 + 2H20
Only one molecule of the reactant decomposes. It is a unimolecular reaction. Its molecularity is one.
In case of the reaction
2HI --> H2 + I2
Two molecules of HI are involved in the reaction. It is a bimolecular reaction and its molecularity is two.
In case of the reaction
2NO + O2 --> 2NO2
2 molecules of NO and one molecule of O2 are involved. Hence it is a trimolecular reaction. The probability that more than three molecules can collide and react simultaneously is very small.
Molecularity above three is not observed. Hence reactions involving many molecules take place in steps.
Hence rate determining step will be there. Law of mass action is applicable to that step.
Chemical kinetics:
Rates of chemical reactions;
Order of reactions;
Rate constant;
First order reactions;
Temperature dependence of rate constant (Arrhenius equation).
--------------------------
The topic "Chemical kinetics" consists of reaction rate and reaction mechanism.
Reaction rate is the speed with which a reaction takes place. This shows the rate or speed at which the reactants are consumed and products are formed.
Reaction mechanism is the path by which a reaction takes place.
Rate of reaction
The rate of reaction is a quantity that tells how the concentration of reactants or product changes with time.
So this can be expressed as Δ concentration/Δ time. That is change in concentration divided by time taken for the change.
Molar concentration i.e., moles per liter (M), is used in these equations.
The brackets, [ ] are always used to to indicate molar concentrations.
Rate law
The rate for a reaction is a mathematical expression that relates the rate of reaction to the concentrations of the reactants.
For the reaction aA + bB → products
The rate law is expressed as, rate of reaction is proportional to [A]^x[B]^y.
x and y are determined experimentally. These values can be whole or fractional numbers or zero.
Law of Mass Action
In 1867, Cato Guldberg, and Peter Waage, proposed this law. According to this law, for the rate determining step in a reaction, the rate of reaction is proportional to the product of the concentrations of the reactants, each raised to the power of its coefficient in the balanced equation.
For the reaction aA + bB → cC (when it is a rate determining step)
Rate of reaction is proportional to [A]^a[B]^b
The above proportionality can be written as an equation, by putting in a proportionality constant k.
Rate = k *[A]^a[B]^b
K is called the specific rate constant
Order of Reaction
From the rate law for a reaction order of reaction can be determined.
For a particular species or reactant, the order is equal to the exponent for that species in the rate law.
For example for Rate = k *[A][B]^2
for B the order of reaction is 2. For A it is 1.
The overall order of reaction is equal to the sum of all the individual orders of reactants.
Temperature
As temperature increases, the average kinetic energy increases. So there are more molecules with activation energy and hence reaction rate increases.
As a general approximation, the rate roughly doubles for each 10°C rise in temperature.
-----------
Molecularity
I recently read the lesson in NCERT Book Part I for Class XII.
There is a section on Molecularity of a Reaction
The number of reacting species which much collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction.
In the case of reaction
NH4NO2 --> N2 + 2H20
Only one molecule of the reactant decomposes. It is a unimolecular reaction. Its molecularity is one.
In case of the reaction
2HI --> H2 + I2
Two molecules of HI are involved in the reaction. It is a bimolecular reaction and its molecularity is two.
In case of the reaction
2NO + O2 --> 2NO2
2 molecules of NO and one molecule of O2 are involved. Hence it is a trimolecular reaction. The probability that more than three molecules can collide and react simultaneously is very small.
Molecularity above three is not observed. Hence reactions involving many molecules take place in steps.
Hence rate determining step will be there. Law of mass action is applicable to that step.
Monday, August 25, 2008
Lwas of Thermodynamics - July Dec Revision
Zeroth Law of Thermodynamics
If a system A is in thermal equilibrium with a system C and if B is also in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other whatever the composition of the systems.
First law of thermodynamics;
Energy cannot be created or destroyed.
Energy can neither be created or nor destroyed although it can be converted from one form into another.
The energy of a system that isolated from its surroundings is constant.
Mathematical expresson for the first law
ΔU = q + w
q = heat added to the sytem
w = work done on the system
Sign conventions for heat and work
When w and q are positive, the internal energy increases. It means that energy is supplied to the system.
When w and q are negative, the internal energy decreases. It means that energy has left the system.
If a system A is in thermal equilibrium with a system C and if B is also in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other whatever the composition of the systems.
First law of thermodynamics;
Energy cannot be created or destroyed.
Energy can neither be created or nor destroyed although it can be converted from one form into another.
The energy of a system that isolated from its surroundings is constant.
Mathematical expresson for the first law
ΔU = q + w
q = heat added to the sytem
w = work done on the system
Sign conventions for heat and work
When w and q are positive, the internal energy increases. It means that energy is supplied to the system.
When w and q are negative, the internal energy decreases. It means that energy has left the system.
Chemical Energetics - Basic Terms - July Dec Revision
System
a specified part of universe which is under observation is called the system.
A system is homogeneous system if physical properties nad chemical composition are identical throughout the system. It is heterogeneous if it consists of parts each of which has different physical and chemical properties.
surroundings
The remaining portion of the universe which is not part of the system is termed the surroundings.
Open system: A system which can exchange matter as well as energy with the surroundings is called an open system.
Closed system: A system which can exchange energy but not matter with the surroundings is called a closed system.
Isolated system: A system which can neither exchange matter nor energy with the surroundings is called an isolated system.
Macroscopic properties
Pressure, Volume etc. are related to the behavior of the bulk of the material. These properties are called macroscopic properties.
the macroscopic properties are divided into types.
1. Intensive properties 2. Extensive properties
1. Intensive properties: These properties have no relation to the amount of substance present in a system. Examples: temperature, pressure, viscosity, surface tension, refractive index etc.
2. Extensive properties: The value of these properties depends upon the amount of substance present in the system.
Examples: Mass, volume, surface area, energy, enthalpy, entropy, free energy, heat capacity
State Variables and State Functions
The state of a system is described by macroscopic properties when they are stable and have definite values. If any of the macroscopic properties of the system changes, the state of the system changes.
We describe a system by its state variables. A system having ideal gas can be described by three state variables. These three variables are : temperature (T), pressure (p) and volume (V). Once these three variables are specified all the other variables will be definite and can be easily calculated.
State function is a property of the system whose value depends only upon the state of the system and is independent of the path or manner by which the state is reached.
A system is said to be in thermodynamic equilibrium when the macroscopic properties do not change with time.
Processes
Isothermal: Temperature of the system is constant.
Adiabatic: No heat flows into or out of the system.
Isochoric: volume of the system remains the same.
Isobaric: Pressure of the sytem remains the same.
Reversible: The system changes in infinitesimal steps and they can be reversed.
Irrevesible: Real life systems do not satisfy the reverbility criterion and hence irreversible.
Cyclic: a process in which the system undergoes a series of changes and ultimately returns to its original state is called a cyclic process.
Modes of transfer of energy between system and surroundings
1. Heat (Q): Energy is exchanged between the system and the surroundings as heat if they are at different temperatures.
2. Another modes of transfer of energy is work. Work is said to be performed if th point of application of a force is displaced in the direction of the force.
Pressure volume work
Pressure volume work is mechanical work. It is the work done when the gas expands or contracts against external pressure.
It is equal to force multiplied by distance moved or pressured mulitiplied by change in volume.
Units of Heat and Work
S.I. unit of heat is joule or kilojoule
S.I. unit of work is also joule or kilojoule
Joule and calories are related by the relation
1 cal = 4.184 J
1 kcal = 4.184 kJ
a specified part of universe which is under observation is called the system.
A system is homogeneous system if physical properties nad chemical composition are identical throughout the system. It is heterogeneous if it consists of parts each of which has different physical and chemical properties.
surroundings
The remaining portion of the universe which is not part of the system is termed the surroundings.
Open system: A system which can exchange matter as well as energy with the surroundings is called an open system.
Closed system: A system which can exchange energy but not matter with the surroundings is called a closed system.
Isolated system: A system which can neither exchange matter nor energy with the surroundings is called an isolated system.
Macroscopic properties
Pressure, Volume etc. are related to the behavior of the bulk of the material. These properties are called macroscopic properties.
the macroscopic properties are divided into types.
1. Intensive properties 2. Extensive properties
1. Intensive properties: These properties have no relation to the amount of substance present in a system. Examples: temperature, pressure, viscosity, surface tension, refractive index etc.
2. Extensive properties: The value of these properties depends upon the amount of substance present in the system.
Examples: Mass, volume, surface area, energy, enthalpy, entropy, free energy, heat capacity
State Variables and State Functions
The state of a system is described by macroscopic properties when they are stable and have definite values. If any of the macroscopic properties of the system changes, the state of the system changes.
We describe a system by its state variables. A system having ideal gas can be described by three state variables. These three variables are : temperature (T), pressure (p) and volume (V). Once these three variables are specified all the other variables will be definite and can be easily calculated.
State function is a property of the system whose value depends only upon the state of the system and is independent of the path or manner by which the state is reached.
A system is said to be in thermodynamic equilibrium when the macroscopic properties do not change with time.
Processes
Isothermal: Temperature of the system is constant.
Adiabatic: No heat flows into or out of the system.
Isochoric: volume of the system remains the same.
Isobaric: Pressure of the sytem remains the same.
Reversible: The system changes in infinitesimal steps and they can be reversed.
Irrevesible: Real life systems do not satisfy the reverbility criterion and hence irreversible.
Cyclic: a process in which the system undergoes a series of changes and ultimately returns to its original state is called a cyclic process.
Modes of transfer of energy between system and surroundings
1. Heat (Q): Energy is exchanged between the system and the surroundings as heat if they are at different temperatures.
2. Another modes of transfer of energy is work. Work is said to be performed if th point of application of a force is displaced in the direction of the force.
Pressure volume work
Pressure volume work is mechanical work. It is the work done when the gas expands or contracts against external pressure.
It is equal to force multiplied by distance moved or pressured mulitiplied by change in volume.
Units of Heat and Work
S.I. unit of heat is joule or kilojoule
S.I. unit of work is also joule or kilojoule
Joule and calories are related by the relation
1 cal = 4.184 J
1 kcal = 4.184 kJ
Wednesday, August 20, 2008
Kinetic theory of gases - July-Dec 2008 revision
Kinetc theory of gases is also called kinetic molecular theory of gases.
The model takes into account molecular concept and the kinetic concept of gas molecules.
The theory was put forward by Bernoulli and was further developed and extended by Clausius, Maxwell, Boltzmann and others.
Postulates of the theory
1. All gases are made up of large number of minute particles called molecules.
2. The molecules are separated from one another by large distances.
3. The molecules are in a state of ceaseless and random motion in all directions. They keep colliding with other molecules and walls of the container and change their directions.
4. Molecular collissions are perfectly elastic (See physics for concept of elastic collisions)
5. There are no forces of interaction (attrative or repulsive) between molecules.
6. The pressure exerted by the gas is due to the collisions of the its molecules on the walls of the container per unit area.
7. Teh average kinetc engery of the gas molecules is directly proportional to the absolute temperature.
Kinetic gas equation
From the postulates of kinetic molecular theory, an equation was derived for the pressure of the gas. This equation is known as kinetic gas equation and is
pV = 1/3 mNu²
where
m = mass of a molecule
N = the number of molecules in the volume V
u = root mean square velocity of the molecules. u² is the mean square velocity of molecules. The velociytof each molecule is first squared and then its average is taken.
Averge Kinetic Energy of Molecules of a gas
The average translational kinetic energy of a molecule is
1/2 mu²
where
m = mass of a molecule
u = root mean square velocity of the molecules. u² is the mean square velocity of molecules. The velociytof each molecule is first squared and then its average is taken.
The total kinetic energy of the whole gas is
Ek = 1/2 mNu²
From the formulas for pV and Ek we can get
pV = 2/3 Ek
If we take one mole of gas and define Ek as total kinetic energy of one mole of gas
pV = RT = 2/3 Ek
=> Ek = 3/2RT for one mole of gas
For n moles of gas
Ek = 3/2 nRT.
If we want averge kinetic energy of one molecule, we divide Ek of one mole by Avogadros' number NA(6.022*1023).
averge kinetic energy of one molecule = (3/2) RT/NA = 3/2kbT
Where kb = R/NA is called Boltzmann constant.
Thus Ek α T
As Kinetic energy is proportional to u²
u² α T
u α √T
Molecular velocity of any gas is directly proportional to the square root of the absolute temperature.
This molecular motion is also referred to as thermal motion of the molecules. It will be zero when T = 0.
Past IIT JEE Questions
1. Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetic energy of a helium atom is
a. same as that of a hydrogen molecule
b. two times that of a hydrogen molecule
c. four times that of a hydrogen molecule
d. half that of a hydrogen molecule
(JEE 1982)
Answer: (a)
2. State whether the statement is True or False.
Kinetic energy of molecules is zero at 0°C. (JEE 1985)
Ans: False
The equation relating energy of molecules to temperature is in absolute temperature and not centigrade temperature.
3. the average velocity of an ideal gas molecule at 27°C is 0.3 m/s. the average speed at 927°C will be:
a. 0.6 m/s
b. 0.3 m/s
c. 0.9 m/s
d. 3.0 m/s
(JEE 1986)
Answer: (a)
4. Eight grams of oxygen and hydrogen at 27°C will have the total kinetic energy in the ratio of __________________.
(JEE 1989)
Answer: 1:16
Reason: For a mixture of gases, in thermal equilibrium, average kinetic energy of all molecules is same.
(½)*m1* v1² = (1/2)*(m2*v2²
Oxygen’s molecular weight is 32 and hence 8 grams will have 8/32 = ¼ moles.
Hydrogen’s molecular weight is 2 and hence 8 grams will have 8/2 = 4 mols
Total kinetic energy of oxygen moleculues = (¼ )* (½)*m1* v1²
Total kinetic energy of hydrogen molecules = 4*(1/2)*(m2*v2²
The ratio will be (1/4)/4 = 1/16 as remaining terms or equal in both cases.
The model takes into account molecular concept and the kinetic concept of gas molecules.
The theory was put forward by Bernoulli and was further developed and extended by Clausius, Maxwell, Boltzmann and others.
Postulates of the theory
1. All gases are made up of large number of minute particles called molecules.
2. The molecules are separated from one another by large distances.
3. The molecules are in a state of ceaseless and random motion in all directions. They keep colliding with other molecules and walls of the container and change their directions.
4. Molecular collissions are perfectly elastic (See physics for concept of elastic collisions)
5. There are no forces of interaction (attrative or repulsive) between molecules.
6. The pressure exerted by the gas is due to the collisions of the its molecules on the walls of the container per unit area.
7. Teh average kinetc engery of the gas molecules is directly proportional to the absolute temperature.
Kinetic gas equation
From the postulates of kinetic molecular theory, an equation was derived for the pressure of the gas. This equation is known as kinetic gas equation and is
pV = 1/3 mNu²
where
m = mass of a molecule
N = the number of molecules in the volume V
u = root mean square velocity of the molecules. u² is the mean square velocity of molecules. The velociytof each molecule is first squared and then its average is taken.
Averge Kinetic Energy of Molecules of a gas
The average translational kinetic energy of a molecule is
1/2 mu²
where
m = mass of a molecule
u = root mean square velocity of the molecules. u² is the mean square velocity of molecules. The velociytof each molecule is first squared and then its average is taken.
The total kinetic energy of the whole gas is
Ek = 1/2 mNu²
From the formulas for pV and Ek we can get
pV = 2/3 Ek
If we take one mole of gas and define Ek as total kinetic energy of one mole of gas
pV = RT = 2/3 Ek
=> Ek = 3/2RT for one mole of gas
For n moles of gas
Ek = 3/2 nRT.
If we want averge kinetic energy of one molecule, we divide Ek of one mole by Avogadros' number NA(6.022*1023).
averge kinetic energy of one molecule = (3/2) RT/NA = 3/2kbT
Where kb = R/NA is called Boltzmann constant.
Thus Ek α T
As Kinetic energy is proportional to u²
u² α T
u α √T
Molecular velocity of any gas is directly proportional to the square root of the absolute temperature.
This molecular motion is also referred to as thermal motion of the molecules. It will be zero when T = 0.
Past IIT JEE Questions
1. Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetic energy of a helium atom is
a. same as that of a hydrogen molecule
b. two times that of a hydrogen molecule
c. four times that of a hydrogen molecule
d. half that of a hydrogen molecule
(JEE 1982)
Answer: (a)
2. State whether the statement is True or False.
Kinetic energy of molecules is zero at 0°C. (JEE 1985)
Ans: False
The equation relating energy of molecules to temperature is in absolute temperature and not centigrade temperature.
3. the average velocity of an ideal gas molecule at 27°C is 0.3 m/s. the average speed at 927°C will be:
a. 0.6 m/s
b. 0.3 m/s
c. 0.9 m/s
d. 3.0 m/s
(JEE 1986)
Answer: (a)
4. Eight grams of oxygen and hydrogen at 27°C will have the total kinetic energy in the ratio of __________________.
(JEE 1989)
Answer: 1:16
Reason: For a mixture of gases, in thermal equilibrium, average kinetic energy of all molecules is same.
(½)*m1* v1² = (1/2)*(m2*v2²
Oxygen’s molecular weight is 32 and hence 8 grams will have 8/32 = ¼ moles.
Hydrogen’s molecular weight is 2 and hence 8 grams will have 8/2 = 4 mols
Total kinetic energy of oxygen moleculues = (¼ )* (½)*m1* v1²
Total kinetic energy of hydrogen molecules = 4*(1/2)*(m2*v2²
The ratio will be (1/4)/4 = 1/16 as remaining terms or equal in both cases.
Tuesday, August 12, 2008
Criterion of Spontaneity and Free Energy
July-December Revision
The flow of heat takes from a body at high temperature to a body at low temperature through conduction, convection or radiation. Similarly a liquid at higher level flows to a lower level. In both these cases the action occurs without any additional support. But if a liquid at lower level has to go higher level additional supporting activity is required.
Similarly in chemical reactions some reactions take place if the reactants are in contact. Some reactions will not take place through contact but require additional inputs like heat, catalysts etc. Reactions that take place due to contact alone are called spontaneous reactions. The rate of reaction is not the issue here. Even if the rate of reaction is very slow, if the reaction is taking place, it is a spontaneous reaction.
What determines the spontaneity of a chemical reaction?
Is decrease in enthalpy in the reaction a criterion for spontaneity?
In exothermic reactions, enthalpy of products is less than that of reactants. Thus some persons postulated that a spontaneous chemical reaction may be due to decrease in energy of the products. It sounds reasonable. But some scientists found that some endothermic reactions are also spontaneous. Therefore it is concluded that enthalpy may be a contributory factor for spontaneity, but it is not the complete explanation.
Is entropy a criterion for spontaneity?
Entropy is a thermodynamic function. It can be interpreted as measuring disorder in the system. A gas is more disordered than a liquid and a liquid is more disordered than a solid. In a chemical reaction, if the disorder in products is more than that of reactants, entropy increases. It is found in examples like diffusion of gases etc. that in spontaneous activities disorder increases.
As heat is added to the system, solids become liquids and liquids become gases. Hence heat increases entropy. Entropy is defined as
ΔS = qrev/T for a reversible reaction.
The criterion of spontaneity is defined by the total entropy change of system and surrounding. The total entropy change (ΔStotal) for the system and surroundings of a spontaneous process is given by
ΔStotal = ΔSsystem + ΔSsurrounding > 0
Gibbs energy of Free energy
Gibbs energy or Gibbs function is a thermodynamic functions defined by
G = H-TS
For a constant temperature reaction
ΔGsys = ΔHsys -T ΔSsys
Criterion for spontaneity in terms of Gibbs energy or function is that
If ΔG is negative or< 0, the reaction will be spontaneous.
This condition comes from the condition that was given above only. That is
ΔStotal = ΔSsystem + ΔSsurrounding > 0
ΔSsurr = ΔHsurr/T = -ΔHsys/T (because what system loses surrounding gains and vice versa)
Hence
ΔStotal = ΔSsystem - ΔHsys/T
=> TΔStotal = TΔSsystem - ΔHsys
As spontaneity criterion is ΔStotal > 0
RHS must be greater than 0.
=> TΔSsystem - ΔHsys > 0
=> -( ΔHsys - TΔSsystem) > 0
=> ( ΔHsys - TΔSsystem) < 0
The flow of heat takes from a body at high temperature to a body at low temperature through conduction, convection or radiation. Similarly a liquid at higher level flows to a lower level. In both these cases the action occurs without any additional support. But if a liquid at lower level has to go higher level additional supporting activity is required.
Similarly in chemical reactions some reactions take place if the reactants are in contact. Some reactions will not take place through contact but require additional inputs like heat, catalysts etc. Reactions that take place due to contact alone are called spontaneous reactions. The rate of reaction is not the issue here. Even if the rate of reaction is very slow, if the reaction is taking place, it is a spontaneous reaction.
What determines the spontaneity of a chemical reaction?
Is decrease in enthalpy in the reaction a criterion for spontaneity?
In exothermic reactions, enthalpy of products is less than that of reactants. Thus some persons postulated that a spontaneous chemical reaction may be due to decrease in energy of the products. It sounds reasonable. But some scientists found that some endothermic reactions are also spontaneous. Therefore it is concluded that enthalpy may be a contributory factor for spontaneity, but it is not the complete explanation.
Is entropy a criterion for spontaneity?
Entropy is a thermodynamic function. It can be interpreted as measuring disorder in the system. A gas is more disordered than a liquid and a liquid is more disordered than a solid. In a chemical reaction, if the disorder in products is more than that of reactants, entropy increases. It is found in examples like diffusion of gases etc. that in spontaneous activities disorder increases.
As heat is added to the system, solids become liquids and liquids become gases. Hence heat increases entropy. Entropy is defined as
ΔS = qrev/T for a reversible reaction.
The criterion of spontaneity is defined by the total entropy change of system and surrounding. The total entropy change (ΔStotal) for the system and surroundings of a spontaneous process is given by
ΔStotal = ΔSsystem + ΔSsurrounding > 0
Gibbs energy of Free energy
Gibbs energy or Gibbs function is a thermodynamic functions defined by
G = H-TS
For a constant temperature reaction
ΔGsys = ΔHsys -T ΔSsys
Criterion for spontaneity in terms of Gibbs energy or function is that
If ΔG is negative or< 0, the reaction will be spontaneous.
This condition comes from the condition that was given above only. That is
ΔStotal = ΔSsystem + ΔSsurrounding > 0
ΔSsurr = ΔHsurr/T = -ΔHsys/T (because what system loses surrounding gains and vice versa)
Hence
ΔStotal = ΔSsystem - ΔHsys/T
=> TΔStotal = TΔSsystem - ΔHsys
As spontaneity criterion is ΔStotal > 0
RHS must be greater than 0.
=> TΔSsystem - ΔHsys > 0
=> -( ΔHsys - TΔSsystem) > 0
=> ( ΔHsys - TΔSsystem) < 0
Subscribe to:
Posts (Atom)