At 500 °C, the equilibrium constant, Kp, for the reaction,

2HCN(g) ⇌ H2(g) + C2N2(g)

is 4.0
×
10–4. What is Kp for the following reaction at 500 °C?

1
2
H2(g) +
1
2
C2N2(g) ⇌ HCN(g)

Question

At 500 °C, the equilibrium constant, Kp, for the reaction,

2HCN(g) ⇌ H2(g) + C2N2(g)

is 4.0 
×
 10–4.  What is Kp for the following reaction at 500 °C?

1
2
H2(g) + 
1
2
C2N2(g) ⇌ HCN(g)

BlackTom AI · Accepted Answer

First, restate the given information: the equilibrium constant at 500 °C for the reaction 2HCN(g) ⇌ H2(g) + C2N2(g) is Kp_full = 4.0 × 10^−4.

Now, consider the target reaction: (1/2) H2(g) + (1/2) C2N2(g) ⇌ HCN(g). This is the half-reaction obtained by taking the reverse of the original reaction and then scaling by a factor of 1/2. To relate the equilibrium constants across scaled reactions, remember that if you multiply all stoichiometric coefficients by a factor t, the new Kp is the old Kp raised to the power t.

Step 1: Find the Kp for the reverse of the original reaction. The reverse of 2HCN ⇌ H2 + C2N2 is H2 + C2N2 ⇌ 2HCN, whose Kp is the reciprocal of the original: Kp_reverse = 1 / Kp_full = 1 / (4.0 × 10^−4) = 2.5 × 10^3.

Step 2: Relate the half-reaction to the reverse reaction. The half-reaction H2 + C2N2 ⇌ 2HCN, when scaled by a factor t = 1/2, becomes (1/2)H2 + (1/2)C2N2 ⇌ HCN. Therefore, the equilibrium constant for the half-reaction, Kp_half, is Kp_reverse raised to the power t: Kp_half = (Kp_reverse)^{1/2} = (2.5 × 10^3)^{1/2} = √2500 = 50.

Step 3: Convert 50 into scientific notation as in the answer choices. 50 = 5.0 × 10^1.

Evaluation of the answer choice: The provided option is 5.0 × 101, which is equivalent to 5.0 × 10^1 = 50. This matches the calculated value.

Common pitfalls to avoid: Mixing up forward/reverse equilibria or forgetting to adjust the exponent when scaling stoichiometry. Also ensure to apply the square root correctly when the reaction coefficients are halved.

At 500 °C, the equilibrium constant, Kp, for the reaction, 2HCN(g) ⇌ H2(g) + C2N2(g) is 4.0 × 10–4. What is Kp for the following reaction at 500 °C? 1 2 H2(g) + 1 2 C2N2(g) ⇌ HCN(g)

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