Please also, help me set up this problem.
Acetylene, C2H2, can be converted to ethane, C2H6, by a process known as hydrogenation. The reaction is C2H2(g)+2H2(g)⇌C2H6(g). Given the following data at standard conditions (all pressures equal to 1 atm and the common reference temperature 298 K), what is the value of Kp for this reaction? Substance/delta G: C2H2(g)/delta G 209.2 kj/mol; H2 (g)/delta G 0 kj/mol, C2H6(g)/-32.89 kj/mol
What is Kp?
If you will type in your work I'll find the error.
Femember
dGrxn = (n*dGf products) - (n*dGf reactants).
Then dG = -RT*ln*K
2.7*10^42
Kp is the equilibrium constant for a chemical reaction expressed in terms of partial pressures. It represents the ratio of the product of the partial pressures of the products raised to their stoichiometric coefficients divided by the product of the partial pressures of the reactants raised to their stoichiometric coefficients, each raised to the power equal to its stoichiometric coefficient.
For the given reaction:
C2H2(g) + 2H2(g) ⇌ C2H6(g)
The Kp expression is:
Kp = (P(C2H6)^1) / (P(C2H2)^1 x P(H2)^2)
where P(C2H6), P(C2H2), and P(H2) are the partial pressures of C2H6, C2H2, and H2 respectively at equilibrium.
Please note that the values given for delta G are not directly relevant for calculating Kp. Delta G refers to the standard change in Gibbs free energy for a reaction and is not used in the calculation of Kp.
Kp, also known as the equilibrium constant in terms of partial pressures, is a measure of the extent to which a reaction proceeds to form products at a given temperature and pressure. It is calculated using the partial pressures of reactants and products at equilibrium.
To determine the value of Kp for the given reaction, we need to use the Gibbs free energy (ΔG) values provided for each substance. The ΔG values give us information about the spontaneity of the reaction and can be used to calculate the equilibrium constant.
The general equation relating Gibbs free energy to equilibrium constant for a reaction is:
ΔG = -RT ln(Kp)
Here, R is the ideal gas constant (8.314 J/(mol·K)) and T is the temperature in Kelvin. We are given the ΔG values at standard conditions, which means the temperature is 298 K.
Let's plug in the given values into the equation and solve for Kp:
ΔG(C2H2) = 209.2 kJ/mol
ΔG(H2) = 0 kJ/mol
ΔG(C2H6) = -32.89 kJ/mol
R = 8.314 J/(mol·K)
T = 298 K
First, we need to convert the given ΔG values from kJ/mol to J/mol:
ΔG(C2H2) = 209.2 kJ/mol × 1000 J/1 kJ = 209200 J/mol
ΔG(C2H6) = -32.89 kJ/mol × 1000 J/1 kJ = -32890 J/mol
Now, we can rearrange the equation to solve for Kp:
Kp = e^(-ΔG / (RT))
Substituting in the given values, we get:
Kp = e^(-(209200 J/mol + 2(0 J/mol) - (-32890 J/mol)) / (8.314 J/(mol·K) × 298 K))
Simplifying further:
Kp = e^(-209200 J/mol / 2490.172 J/(mol·K))
Using a calculator or a mathematical software, calculate the exponent and obtain the value of Kp.
Note: In the given equation, the stoichiometric coefficients (-2 and +1) for the reactants and product are used as the exponents of the concentration terms in Kp.