1. To calculate the standard molar entropy, Sº, of C2H6 gas, we can use the equation ∆Sº = Sº(products) - Sº(reactants). We know the values of ∆Sº and Sº for C2H2 and H2, so we can solve for the Sº of C2H6.
∆Sº = -232.7 J/mol∙K = [(1)(Sº_C2H6)] - [(1)(200.9 J/mol∙K) + (2)(130.7 J/mol∙K)]
Solving for Sº_C2H6, we get:
Sº_C2H6 = -232.7 + 200.9 + 2(130.7)
Sº_C2H6 = 229.6 J/mol∙K
2. To determine the standard free-energy change, ∆Gº, we use the equation:
∆Gº = ∆Hº - T∆Sº, where T is the temperature in Kelvin.
First, we must find ∆Hº for the reaction. Using the given ∆Hºf values:
∆Hº = ∆Hºf(products) - ∆Hºf(reactants)
∆Hº = [(1)(-84.7 kJ/mol)] - [(1)(226.7 kJ/mol) + (2)(0 kJ/mol)]
∆Hº = -84.7 - 226.7 = -311.4 kJ/mol
Now, we can find ∆Gº using the equation above with T = 298 K:
∆Gº = -311.4 kJ/mol - ((298 K)(-232.7 J/mol∙K)(1 kJ/1000 J))
∆Gº = -311.4 kJ/mol + 69.4 kJ/mol
∆Gº = -242.0 kJ/mol
The negative sign of ∆Gº indicates that the reaction is spontaneous under standard conditions.
3. We can find the equilibrium constant, K, using the equation:
∆Gº = -RT ln(K), where R is the gas constant (8.314 J/mol∙K).
Solving for K:
K = e^(-∆Gº / RT)
K = e^(242000 J/mol / (8.314 J/mol∙K * 298 K))
K = 2.37 × 10^20
4. To find the C≡C bond energy in C2H2, we can use the given bond energies for the other bonds in the reaction and the values of ∆Hºf for the reaction:
∆Hº = Bonds broken - Bonds formed
∆Hº = (1 C≡C + 2 H-H) - (1 C-C + 3 C-H)
We already found ∆Hº as -311.4 kJ/mol. The bond energies for H-H and C-C are given as 436 kJ/mol and 347 kJ/mol, respectively. The bond energy for C-H is given as 414 kJ/mol. We can now write the equation as:
-311.4 kJ/mol = (1 C≡C + 2 * 436) - (347 + 3 * 414)
Now we can solve for the C≡C bond energy:
C≡C = -311.4 + 347 + 3 * 414 - 2 * 436
C≡C = 812 kJ/mol
Thus, the value of the C≡C triple bond energy in C2H2 is 812 kJ/mol.
C2H2(g) + 2 H2(g)--> C2H6(g)
Substance So (J/mol∙K) ∆Hºf (kJ/mol)
C2H2(g 200.9 226.7
H2(g) 130.7 0
C2H6(g) -- -84.7
Bond Bond Energy (kJ/mol)
C-C 347
C=C 611
C-H 414
H-H 436
If the value of the standard entropy change, ∆Sº for the reaction is -232.7 joules per mole∙Kelvin, calculate the standard molar entropy, Sº, of C2H6
gas.
Calculate the value of the standard free-energy change, ∆Gº, for the reaction. What does the sign of ∆Gº indicate about the reaction above?
Calculate the value of the equilibrium constant for the reaction at 298 K.
Calculate the value of the C C (triple bond) bond energy in C2H2 in kJ/mole.
1 answer