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

We start by restating the problem to ensure clarity: the reaction CH4(g) + CO2(g) ⇌ 2 CO(g) + 2 H2(g) has Kp = 4.5 × 10^2 atm^2 at 825 K. We are asked for Kc at the same temperature.

First, recall the relationship between Kp and Kc for gas-phase reactions: Kp = Kc (RT)^(Δn). Here Δn is the change in moles of gas on the product side minus the reactant side. For this reaction, acquire the counts: reactants have 1 CH4 + 1 CO2 = 2 moles of gas; products have 2 CO + 2 H2 = 4 moles of gas. Therefore Δn = 4 − 2 = 2.

Next, compute RT at 825 K using R = 0.082057 L·atm/(mol·K): RT = 0.082057 × 825 ≈ 67.7 L·atm/mol. Then (RT)^2 ≈ (67.7)^2 ≈ 4580 (L^2·atm^2)/(mol^2).

Now solve for Kc: Kc = Kp / (RT)^(Δn) = (4.5 × 10^2 atm^2) / 4580 L^2·atm^2/mol^2 ≈ 450 / 4580 mol^2/L^2 ≈ 0.098 mol^2/L^2, i.e., 0.098 M^2.

Examine each option:
- Option: 2.1 × 10^6 M^2. This is vastly larger than the calculated 0.098 M^2; it would imply an enormous equilibrium concentration of products, which contradicts the given Kp value and the small Kc we computed. It shows a misunderstanding of units or the relation Kp = Kc (RT)^(Δn).
- Option: 4.5 × 10^−2 M^2 (i.e., 0.045 M^2). This is of the same order of magnitude as the correct result but off by about a factor of 2–3; the precise (RT)^2 factor at 825 K does not yield 0.045 M^2 when Kp = 450 atm^2, so this is too small.
- Option: 6.6 M^2. This value lacks the proper scale given Kp and RT; it’s much larger than the correct result and does not reflect the (RT)^2 division by Kp.
- Option: 0.098 M^2. This matches the calculation Kc = Kp / (RT)^2 with Δn = 2 at T = 825 K using R = 0.082057 and the provided Kp. The units M^2 are consistent with a reaction where Δn ≠ 0 and the stoichiometric changes lead to squared concentration terms in Kc.

In summary, the correct reasoning applies the Δn = 2 adjustment to relate Kp and Kc, uses the appropriate R and T to compute (RT)^2, and yields Kc ≈ 0.098 M^2. The other options deviate either by incorrect magnitude or by ignoring the (RT)^(Δn) factor required to convert Kp to Kc at the given temperature.

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?单项选择题

类似问题

If the equilibrium constants for the two reactions 2 HCl(g) ⇔H2(g) + Cl2(g) and I2(g) + Cl2(g) ⇔ 2 ICl(g) are denoted K1 and K2 respectively, then the equilibrium constant for the reaction 2 HCl(g) + I2(g) ⇔ 2 ICl(g) + H2(g) equals

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?

The equilibrium constant is given for one of the reactions below. Determine the value of the missing equilibrium constant. Show your work for full credits.

Which of the following statements concerning equilibrium constants is true?

If the equilibrium constants for the two reactions 2 HCl(g) H2(g) + Cl2(g) and I2(g) + Cl2(g) 2 ICl(g) are denoted K1 and K2 respectively, then the equilibrium constant for the reaction 2 HCl(g) + I2(g) 2 ICl(g) + H2(g) equals

If the equilibrium constants for the two reactions 2 HCl(g) ⇔ H2(g) + Cl2(g) and I2(g) + Cl2(g) ⇔ 2 ICl(g) are denoted K1 and K2 respectively, then the equilibrium constant for the reaction 2 HCl(g) + I2(g) ⇔ 2 ICl(g) + H2(g) equals

Question at position 4 Which of the following is the value of the equilibrium constant for the following reaction, given the equilibrium constants K1 and K2? 1 x 10-51 x 1001 x 1051 x 10-1

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)

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单