Please show step by step with answer
The equilibrium constant for the reaction C (s) + H2O (g) <---> CO(g) + H2 (g) is 0.20 at 1000 degrees Celsius.
If an equilibruim mixture contains solid carbon, H20 = 0.40 M, and CO = 0.41 M, what is the H2?
To find the concentration of H2 (H2) in the equilibrium mixture, we will use the expression for the equilibrium constant (Kc). The equilibrium constant expression for this reaction is:
Kc = [CO][H2]/[C][H2O]
Given:
Kc = 0.20
[H2O] = 0.40 M
[CO] = 0.41 M
We need to find [H2] in the equilibrium mixture.
Step 1: Write the equilibrium constant expression using the given concentrations:
0.20 = [CO][H2]/[C][H2O]
Step 2: Plug in the values of the concentrations:
0.20 = (0.41 M)[H2]/[C](0.40 M)
Step 3: Determine the concentration of [C]:
Since carbon (C) is a solid and is not included in the expression for equilibrium concentrations, we assume its concentration is 1. Therefore, [C] = 1.
0.20 = (0.41 M)[H2]/(1)(0.40 M)
Step 4: Simplify the equation:
0.20 = (0.41 M)[H2]/0.40 M
Step 5: Cross-multiply to isolate [H2]:
(0.20)(0.40 M) = (0.41 M)[H2]
0.08 M = (0.41 M)[H2]
Step 6: Solve for [H2]:
[H2] = 0.08 M / 0.41 M
[H2] = 0.195 M
Therefore, the concentration of H2 in the equilibrium mixture is 0.195 M.