Question

$K_p$ is related to $K_c$ as ____.

• A. $K_c=K_p(RT{)}^{\Delta n}$
• B. $K_p=K_c(RT{)}^{\Delta n}$
• C. $K_p=K_c(RT{)}^3$
• D. $K_p=K_c(RT{)}^{}$

Answer 1

The correct option is B $K_p=K_c(RT{)}^{\Delta n}$

$K_p=K_c(RT{)}^{\Delta n}$

General derivation is following:

For the reaction:

aA(g) + bB(g) + ...cC(g) + dD(g) + ...

The equilibrium constant based on partial pressures is

From the ideal gas law:

$P_{Ae}V=n_{A}RT$

$n_A$ is the number of moles of A

R is the ideal gas constant = 0.0821 L•atm/mol•K

T the absolute temperature in K

P is the pressure in atm

V the system volume in L

Similar expressions can be written for each gas phase component.

Rearranging gives

but n_A/V is just the molar concentration = [A]_e

Substituting into the expression for K_p (for each gas phase component) gives

Collecting terms gives

The left part of the fraction is $K_C$, so

K_p = K_c × (RT)^{(c+d+...)–(a+b+...)}

The exponent in RT is the sum of the stoichiometric coefficients for the reactants subtracted from the sum of the stoichiometric coefficients for the products, defined as $\Delta n$.

$K_p=K_c\times (RT{)}^{\Delta n}$