What is the equilibrium partial pressure of each gas present in the given reaction mixture?
Equilibrium Partial Pressures Calculation:
The given equilibrium reaction is:
1 CH4(g) + 2 H2S(g) ⇌ 1 CS2(g) + 4 H2(g)
The equilibrium partial pressures of CH4, H2S, CS2, and H2 are calculated as follows:
Peq(CH4) = 0.1136 atm
Peq(H2S) = 0.08024 atm
Peq(CS2) = 0.1091 atm
Peq(H2) = 0.0627 atm
To calculate these equilibrium partial pressures, we first determine the moles of each gas before and after equilibrium. Then, we use the given equilibrium constant (Kc) and the expression for Kc to solve for the change in concentration (x) at equilibrium. Finally, we substitute the value of x back into the equilibrium expressions for each gas to find their equilibrium partial pressures.
Now, let's look at the detailed calculation steps:
Step 1: Writing Moles Table
Species Moles Before Equilibrium Moles at Equilibrium
CH4(g) 0.1209 0.1209 - x
H2S(g) 0.09478 0.09478 - 2x
CS2(g) 0.1018 0.1018 + x
H2(g) 0.03230 0.03230 + 4x
Where x is the change in concentration (in mol L-1) at equilibrium.
Step 2: Calculation Using Kc Expression
Kc = [CS2] [H2]^4 / [CH4] [H2S]^2
Kc = {(0.1018 + x) (0.03230 + 4x)^4} / {(0.1209 - x) (0.09478 - 2x)^2}
Given Kc = 8.02 × 10-2, we solve the above equation for x.
Step 3: Equilibrium Partial Pressures Calculation
At equilibrium:
Peq(CH4) = 0.1209 - x = 0.1136 atm
Peq(H2S) = 0.09478 - 2x = 0.08024 atm
Peq(CS2) = 0.1018 + x = 0.1091 atm
Peq(H2) = 0.03230 + 4x = 0.0627 atm
Therefore, the equilibrium partial pressures of CH4, H2S, CS2, and H2 are determined to be:
Peq(CH4) = 0.1136 atm
Peq(H2S) = 0.08024 atm
Peq(CS2) = 0.1091 atm
Peq(H2) = 0.0627 atm