Determine Kc at 298 K for the reaction 2 CH4(g) reverse reaction arrow C2H2(g) + 3 H2(g), given the following data at 298 K. (Hint: How are Kc and Kp for the reaction related?)
CH4(g) + H2O(g) reverse reaction arrow CO(g) + 3 H2(g) Kp = 1.2 multiplied by 10-25
2 C2H2(g) + 3 O2(g) reverse reaction arrow 4 CO(g) + 2 H2O(g) Kp = 1.1 multiplied by 102
H2(g) + 1/2 O2(g) reverse reaction arrow H2O(g) Kp = 1.1 multiplied by 1040
To determine Kc for the reaction 2 CH4(g) ⇌ C2H2(g) + 3 H2(g) at 298 K, we can use the equilibrium constant expression:
Kc = ([C2H2] * [H2]^3) / ([CH4]^2)
However, we need the equilibrium concentrations of the reactants and products in the reaction. We can find these concentrations by using the given data and the relationship between Kp and Kc.
The relationship between Kp and Kc is given by the equation:
Kp = Kc(RT)^(Δn)
Where:
- Kp is the equilibrium constant in terms of partial pressures.
- Kc is the equilibrium constant in terms of molar concentrations.
- R is the gas constant (0.0821 L * atm / K * mol).
- T is the temperature in Kelvin.
- Δn is the difference in the number of moles of gaseous products and reactants.
Let's calculate the value of Kc for the given reaction using the provided data:
Step 1: Find Kp values for the given reactions
For the reaction: CH4(g) + H2O(g) ⇌ CO(g) + 3 H2(g)
Given Kp = 1.2 * 10^(-25)
For the reaction: 2 C2H2(g) + 3 O2(g) ⇌ 4 CO(g) + 2 H2O(g)
Given Kp = 1.1 * 10^(2)
For the reaction: H2(g) + 1/2 O2(g) ⇌ H2O(g)
Given Kp = 1.1 * 10^(40)
Step 2: Determine the relationship between the reactions
By comparing the stoichiometric coefficients, we can determine the relationship between the reactions.
Coefficients of CH4(g) and C2H2(g) are both 2, and no common product appears in the reactions. This suggests that we can multiply the first reaction by 2 to obtain the desired reaction.
Step 3: Calculate Kp for the desired reaction
Multiply the Kp value for the first reaction by 2, as we are doubling the reaction:
Kp1 = 1.2 * 10^(-25)
Kp_desired = (Kp1 * Kp1) / (Kp2 * Kp3^3)
Step 4: Convert Kp to Kc
To convert Kp to Kc, we use the equation Kp = Kc(RT)^(Δn).
Since the reaction involves gases, Δn is given by the sum of the stoichiometric coefficients of the gaseous products minus the sum of the stoichiometric coefficients of the gaseous reactants:
Δn = (4 + 2) - (2 + 3) = 1
Substituting the values into the equation and solving for Kc, we have:
Kp_desired = Kc(RT)^(Δn)
1.1 * 10^(2) = Kc(0.0821 * 298)^(1)
Kc = (1.1 * 10^(2)) / (0.0821 * 298)
Now, you can calculate the value of Kc by substituting the values for Kp, R, and T into the equation and performing the calculations.