Question

Find out the value of \(K_c\) for each of the following equilibria from the value of \(K_p\): 

1. \(2NOCl (g) ⇋ 2NO (g) + Cl_2 (g); \ K_p= 1.8 × 10^{–2}\  at \ 500\ K\)
2. \(CaCO_3 (s) ⇋ CaO(s) + CO_2(g); \ K_p= 167 \ at \ 1073\  K\)

Answer 1

Relation between K_p and K_c:

K_p = K_c(RT)^Δn

where Δn = (moles of gaseous products − moles of gaseous reactants)

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(i) 2NOCl(g) ⇋ 2NO(g) + Cl₂(g)

Given:

K_p = 1.8 × 10⁻²
Temperature, T = 500 K

Step 1: Calculate Δn

Δn = (2 + 1) − 2 = 1

Step 2: Use K_p–K_c relation

K_p = K_c(RT)

K_c = K_p / (RT)

R = 0.0831 L bar mol⁻¹ K⁻¹

K_c = (1.8 × 10⁻²) / (0.0831 × 500)

K_c = 4.33 × 10⁻⁴

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(ii) CaCO₃(s) ⇋ CaO(s) + CO₂(g)

Given:

K_p = 167
Temperature, T = 1073 K

Step 1: Calculate Δn

Only gaseous species is CO₂

Δn = 1 − 0 = 1

Step 2: Use K_p–K_c relation

K_p = K_c(RT)

K_c = K_p / (RT)

K_c = 167 / (0.0831 × 1073)

K_c = 1.87

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Final Answers:

(i) K_c = 4.33 × 10⁻⁴
(ii) K_c = 1.87