Question

steam reforming of methane (ch₄) produces \synthesis gas,\ a mixture of carbon monoxide gas and hydrogen gas, which is the starting point for many important industrial chemical syntheses. an industrial chemist studying this reaction fills a 200. ml flask with 1.3 atm of methane gas and 4.6 atm of water vapor, and when the mixture has come to equilibrium measures the partial pressure of hydrogen gas to be 2.7 atm.
calculate the pressure equilibrium constant for the steam reforming of methane at the final temperature of the mixture. round your answer to 2 significant digits.
kₚ = □

Explanation:

Step1: Write the balanced chemical equation

The steam - reforming of methane is \(CH_{4}(g)+H_{2}O(g)
ightleftharpoons CO(g) + 3H_{2}(g)\)

Step2: Set up the ICE table

	\(P_{CH_{4}}\)	\(P_{H_{2}O}\)	\(P_{CO}\)	\(P_{H_{2}}\)
Change (\(atm\))	\(-x\)	\(-x\)	\(+x\)	\(+3x\)
Equilibrium (\(atm\))	\(1.3 - x\)	\(4.6 - x\)	\(x\)	\(3x\)

We know that \(P_{H_{2}}=3x = 2.7\ atm\), so \(x=\frac{2.7}{3}=0.9\ atm\)

Step3: Calculate the equilibrium partial pressures

\(P_{CH_{4}}=1.3 - 0.9=0.4\ atm\)
\(P_{H_{2}O}=4.6 - 0.9 = 3.7\ atm\)
\(P_{CO}=x = 0.9\ atm\)
\(P_{H_{2}}=2.7\ atm\)

Step4: Calculate \(K_{p}\)

The formula for \(K_{p}\) is \(K_{p}=\frac{P_{CO}\times P_{H_{2}}^{3}}{P_{CH_{4}}\times P_{H_{2}O}}\)
Substitute the values: \(K_{p}=\frac{0.9\times(2.7)^{3}}{0.4\times3.7}\)
First, calculate \((2.7)^{3}=2.7\times2.7\times2.7 = 19.683\)
Then, \(0.9\times19.683 = 17.7147\)
And \(0.4\times3.7=1.48\)
\(K_{p}=\frac{17.7147}{1.48}\approx12\)

Answer:

\(12\)