Question

K_p = K_c is TRUE for which of the following reactions?
1. N₂ (g) + 3 H₂(g) = 2 NH₃ (g)
2. 2NOCI(g) = 2NO (g) + Cl₂ (g)
3. H₂ (g) + Cl₂(g) = 2HCI (g)
4. H₂ (g) + I₂(s) = 2HI (g)

Answer 1

Correct Answer - Option 3 : H₂ (g) + Cl₂(g) = 2HCI (g)

Concept:

Equilibrium Law or Law of Chemical Equilibrium:

• At a given temperature, the product of concentrations of the reaction products raised to the respective stoichiometric coefficient in the balanced chemical equation divided by the product of concentrations of the reactants raised to their individual stoichiometric coefficients has a constant value.
• This is known as the Equilibrium Law or Law of Chemical Equilibrium.
• The equilibrium constant for a general reaction \(aA{\text{ }} + {\text{ }}bB{\text{ }}\overset {} \leftrightarrows cC{\text{ }} + {\text{ }}d{\text{ }}D\) is expressed as, 

\({K_c}{\text{ }} = {\text{ }}\frac{{{{\left[ C \right]}^c}{{\left[ D \right]}^d}{\text{ }}}}{{{{\left[ A \right]}^a}{{\left[ B \right]}^b}}}{\text{ }}\;\)
where [A], [B], [C], and [D] are the equilibrium concentrations of the reactants and products.

• If the equilibrium involves gaseous species, then the concentrations may be replaced by partial pressures, since at a given temperature the partial pressure of a gaseous component is proportional to its concentration. 
• Thus for the equilibrium, \(aA{\text{ }} + {\text{ }}bB{\text{ }}\overset {} \leftrightarrows cC{\text{ }} + {\text{ }}d{\text{ }}D\)

\({K_p} = \frac{{{{[{p_C}]}^c}{{[{p_D}]}^d}}}{{{{[{p_A}]}^a}{{[{p_B}]}^b}}}\)

Relationship between K_p and K_c :

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

Where Δn = no. of moles of gaseous products - no. of moles of gaseous reactants; R=gas constant; T=Kelvin temperature.

Explanation:

We know that \({K_p} = {K_c}{\left( {RT} \right)^{\Delta n}}\)

If Δn=0, then K_p​=K_c​

If Δn>0, then K_p​>K_c​

If Δn<0, then K_p​<K_c​

Consider the given reactions:

1) N2 (g) + 3 H2(g) ⇌ 2 NH3 (g)

Δn=no. of moles of gaseous products - no. of moles of gaseous reactants

For this reaction, No: of gaseous products=2 moles; No: of gaseous reactants= 4 moles.

⇒ Δn=2-(1+3)=-2

∴ Kp​<Kc​

2) 2NOCI(g) ⇌ 2NO (g) + Cl2 (g)

For  this reaction, No: of gaseous products=3 moles; No: of gaseous reactants= 2 moles.

⇒ Δn=(2+1)-2=1

∴ Kp​>Kc

3) H₂​(g)+Cl₂​(g) ⇌ 2HCl(​g)

For this reaction, No: of gaseous products=2 moles; No: of gaseous reactants= 2 moles.

⇒  Δn=2-(1+1)=0​

∴Kp​=Kc​

4) H2 (g) + I2(s) = 2HI (g)

• This reaction is an example of heterogeneous equilibria in which the substances involved are present in different phases.
• The concentration of all solids is taken as unity. So, [I2] = 1.

⇒ \({K_c}{\text{ }} = {\text{ }}\frac{{{{\left[ {HI} \right]}^2}{\text{ }}}}{{{{\left[ {{H_2}} \right]}^1}{{\left[ {{I_2}} \right]}^1}}}{\text{ }}\;\)i.e., \({K_c}{\text{ }} = {\text{ }}\frac{{{{\left[ {HI} \right]}^2}{\text{ }}}}{{\left[ {{H_2}} \right]}}{\text{ }}\;\)

For this reaction, No: of gaseous products=2 moles; No: of gaseous reactants= 1 moles

⇒ Δn=2-(1)=1

∴ Kp​>Kc

Hence, Kp = Kc is TRUE for the reaction, H2​(g)+Cl2​(g) ⇌ 2HCl(​g).

The relationship between K_p and K_c is \({K_p} = {K_c}{\left( {RT} \right)^{\Delta n}}\) 

If Δn=0, then Kp​=Kc​

If Δn>0, then Kp​>Kc​

If Δn<0, then Kp​<Kc​