The value of Kp for the reaction,

CH4(g) + CO2(g) ⇌ 2CO(g) + 2H2(g)

is 4.5 102 atm2 at 825 K. What is Kc for the reaction at this temperature?

Question

The value of Kp for the reaction,

CH4(g) + CO2(g) ⇌ 2CO(g) + 2H2(g)

is 4.5  102 atm2 at 825 K. What is Kc for the reaction at this temperature?

BlackTom AI · Accepted Answer

To relate Kp and Kc for a gas-phase reaction, use the equation Kp = Kc (RT)^{Δn}, where Δn is the change in moles of gas during the reaction.

First, write the reaction and determine Δn:
CH4(g) + CO2(g) ⇌ 2CO(g) + 2H2(g)
Reactants: 1 CH4 + 1 CO2 → total 2 moles of gas
Products: 2 CO + 2 H2 → total 4 moles of gas
Thus Δn = moles of gas products − moles of gas reactants = 4 − 2 = 2.

Next, solve for Kc using the given Kp and Δn:
Kp = 4.5 × 10^2 atm^2 (note: Kp has units of atm^Δn since pressure is involved; here it is atm^2).
R = 0.082057 L·atm·mol^−1·K^−1 and T = 825 K, so RT = 0.082057 × 825 ≈ 67.7 L·atm·mol^−1.

Compute (RT)^{Δn} = (RT)^2 ≈ (67.7)^2 ≈ 4580 (L^2·atm^2·mol^−2).

Now rearrange the relation: Kc = Kp / (RT)^{Δn}.
Plug in the values: Kc ≈ (4.5 × 10^2) / 4580 ≈ 0.098 M^2.

Therefore, the calculated Kc for the reaction at 825 K is approximately 9.8 × 10^−2 M^2. Note about units: since Δn = 2, Kc has units of (mol·L^−1)^2 = M^2, which matches the given unit in the answer.

If there were multiple answer choices, this is the reasoning you would apply to select the option closest to 0.098 M^2. If no options are provided, you can report the numerical value with the appropriate units and show the calculation steps as above.

Chem 1C General Chemis... Self Assessment Quiz 7

The value of Kp for the reaction, CH4(g) + CO2(g) ⇌ 2CO(g) + 2H2(g) is 4.5 102 atm2 at 825 K. What is Kc for the reaction at this temperature?

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