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Kp and Kc are equilibrium constants for ideal gas mixtures under reversible processes, and they are defined as follows: Kp is an equilibrium constant written with respect to atmospheric pressure, whereas Kc is an equilibrium constant written with respect to concentrations expressed in molarity. The Kp- Kc relationship can be deduced by first understanding what Kp and Kc are :
Consider the following equation for general equilibrium:
A + B ⇌ C + D
According to the law of mass action,
The pace at which A reacts is denoted by the letter A.
The pace at which B reacts is denoted by the letter B.
∴ The rate at which A and B react together ∝AB
As a result, the rate of the forward reaction is equal to kf[A][B].
With respect to the forward reaction, kf denotes the velocity constant.
Now, the rate at which C and D react together ∝CD
As a result, the backward reaction rate is equal to kb[C][D].
For the reverse reaction, kb is the velocity constant (velocity constant).
The rate of the forward reaction equals the rate of the backward reaction when the system is in equilibrium.
kf[A][B] = kb[C][D]
[C][D]/[A][B]=kf/kb
At constant temperature, both kf and kb are constant; as a result, kf/kb=K is constant at constant temperature as well as at constant temperature.
In this case, K is referred to as the Equilibrium constant.
Equilibrium Constant Kc
Consider the following example of a general reversible reaction:
aA + bB ⇌ uU + vV
Applying the law of mass action in this situation: [U]u[V]v/[A]a[B]b=K or Kc
When it comes to the expressing of concentrations, the letter k is written as kc.
The law of chemical equilibrium is a mathematical expression that expresses this mathematical expression.
Equilibrium Constant Definition
A steady-state equilibrium constant at a constant temperature is the product of the molar concentrations of the products, each raised to the power equal to its stoichiometric coefficient, and the product of the molar concentrations of the reactants, each raised to the power equal to their stoichiometric coefficient.
Do you know how to calculate the equilibrium constant kp for a process like this?
Let’s look at how to get the equilibrium constant formula for gas-phase processes, which is:
The Equilibrium Constant kp for the Reaction
When both the reactants and the products are in a gaseous form, the equilibrium constant can be expressed in terms of concentration in moles per litre or partial pressures of the reactants and the products, depending on the situation.
Derivation:
The following straightforward deduction reveals the relationship between Kp and Kc: Consider the reversible process described below in order to obtain the relationship between Kp and Kc:
When ‘a’ mole of reactant A is reacted with ‘b’ mole of reactant B, ‘c’ moles of product C and ‘d’ moles of product D are formed, the reaction is said to be complete.
aA + bB ⇌ cC + dD
When A and B are the reactants, the Stoichiometric coefficients of C and D are used to calculate the reaction rate.
What exactly is kc?
Kc is the equilibrium constant for a reversible reaction and it may be calculated using the formula
Kc=[C]c.[D]d/[A]a.[B]b
C is the molar concentration of the product ‘C’ in the equation
D – The molar concentration of the product ‘D’ in the sample.
A is the molar concentration of the reactant ‘A’ in the solution.
B – The molar concentration of the reactant ‘B’ in the solution
Relation between Kp and Kc
Consider the ideal gas equation, PV = nRT, in order to develop a relationship between Kp and Kc.
Where P denotes the ideal gas’s pressure.
V represents the volume of the ideal gas.
n is the number of moles, while R is the universal gas constant.
T – TemperatureWhen the preceding equation is substituted for P, the result is
P = nRT/V
Due to our knowledge of the relationship between the number of moles per unit volume and the molar concentration of the material, we can express the pressure equation as:P = molar concentration RT.
Consider the following example of a general reversible reaction equation:
aA + bB ⇌ cC + dD
Substituting the values shown above into the equation and simplifying:
kp=CcDd.RTc+d/AaBbRTa+b
kp=kc∗RT(c+d)-(a+b)
As a result of eq Where,
c + d – Number of moles of product = np
a + b – Number of moles of reactant = nr
Therefore,
(c + d) – (a + b) = np – nr = Δng
As a result, we have a relationship between Kp and Kc.
Kp = Kc (RT)∆ng
Where,
∆ng= The change in the number of gaseous moles of product and reactant.
CONCLUSION
It has already been shown above that the amount of heat provided at constant pressure is used in two ways: to increase internal energy (and thus temperature; remember that internal energy is a function of temperature); and to do work. The amount of heat given at a fixed volume, on the other hand, is used solely for the purpose of raising the internal energy. Because of this, more heat at constant pressure is required to increase the temperature by a factor of one.
The internal energy of a gas is exactly proportional to the temperature of the gas in which it exists. In technical terms, it is the number of independent ways in which a gas molecule can move in space along three axes (x,y, and z), and this is referred to as the degrees of freedom [DOF] of a gas. As the number of atoms in a molecule rises, the freedom of the atoms to move in additional modes, such as vibrational and rotational modes, in addition to linear translational motion, increases as well. For the avoidance of doubt, monatomic gases have a DOF of 3, diatomic gases have a DOF of 5, and triatomic gases have a DOF of 6.
Each degree of freedom adds 1/2kT per atom to the total internal energy of the atom.
The total internal energy U of monatomic ideal gases with N atoms is given as U=3/2NkT for ideal gases with N atoms. In the case of diatomic gases, U=5/2NkT, where k is the Boltzmann constant.
Y [Gamma] = 1 + 2/[DOF]
The greater the depth of field (DOF), the smaller the Cp/Cv = Gamma ratio.
The Cp/Cv ratios for monoatomic, diatomic, and triatomic atoms are 1.67, 1.4, and 1.33, respectively, for the three types of atoms.
