C2H2(g) + 2 H2(g)--> C2H6(g)
Information about the substances involved in the reaction represented above is summarized in the following tables.
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
1.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.
2.Calculate the value of the standard free-energy change, ∆Gº, for the
reaction. What does the sign of ∆Gº indicate about the reaction above?
3.Calculate the value of the equilibrium constant for the reaction at 298 K.
4.Calculate the value of the C C(triple bond) bond energy in C2H2 in kJ/mole.
C C= [ C triple bond C]
1. The standard molar entropy of C2H6 gas is 200.9 J/mol∙K.
2. The standard free-energy change, ∆Gº, for the reaction is -111.4 kJ/mol. The sign of ∆Gº indicates that the reaction is exothermic.
3. The equilibrium constant for the reaction at 298 K is 0.0014.
4. The C C(triple bond) bond energy in C2H2 is 822 kJ/mol.
To answer these questions, we need to use the given information about the standard entropies and enthalpies of formation, as well as bond energies. Let's solve each question step-by-step:
1. To calculate the standard molar entropy, Sº, of C2H6 gas, we need to use the equation:
ΔSº = Σ(Sº(products)) - Σ(Sº(reactants))
Considering that the reaction involves only one product (C2H6) and three reactants (C2H2, H2), we can rewrite the equation as:
ΔSº = Sº(C2H6) - Sº(C2H2) - 2 × Sº(H2)
From the given table, we are missing the value for Sº(C2H6). Therefore, we cannot calculate ΔSº.
2. To calculate the standard free-energy change, ΔGº, for the reaction, we need to use the equation:
ΔGº = ΔHº - TΔSº
Where ΔHº is the standard enthalpy change and T is the temperature in Kelvin. Given that we have ΔHºf values, we need to calculate ΔHº for the reaction:
ΔHº = Σ(ΔHºf(products)) - Σ(ΔHºf(reactants))
ΔHº = ΔHºf(C2H6) - ΔHºf(C2H2) - 2 × ΔHºf(H2)
Using the given values from the table:
ΔHº = -84.7 kJ/mol - 226.7 kJ/mol - 2 × 0 kJ/mol
ΔHº = -84.7 kJ/mol - 226.7 kJ/mol = -311.4 kJ/mol
Now we can substitute the values into the equation for ΔGº:
ΔGº = -311.4 kJ/mol - (298 K) × (-232.7 J/mol·K × (1 kJ/1000 J))
ΔGº = -311.4 kJ/mol - (298 K) × (-0.2327 kJ/K)
ΔGº = -311.4 kJ/mol + 69.8 kJ/mol
ΔGº = -241.6 kJ/mol
The negative value of ΔGº indicates that the reaction is spontaneous in the forward direction.
3. To calculate the equilibrium constant for the reaction at 298 K, we can use the equation:
ΔGº = -RT ln(K)
Where R is the ideal gas constant (8.314 J/mol·K), T is the temperature in Kelvin, and K is the equilibrium constant.
-241600 J/mol = -(8.314 J/mol·K) × (298 K) × ln(K)
-241600 J/mol = -2474.292 J·K/mol × ln(K)
ln(K) = -241600 J/mol / -2474.292 J·K/mol
ln(K) = 97.70
Therefore, the value of the equilibrium constant, K, is e^97.70 ≈ 1.76 × 10^42.
4. To calculate the value of the C-C triple bond energy in C2H2, we need to consider the given bond energies. The C-C bond energy can be calculated by subtracting the energy of the C=C bond and two times the energy of the C-H bond from the energy of the C≡C bond:
C≡C = C=C - 2 × C-H
C≡C = 611 kJ/mol - 2 × 414 kJ/mol
C≡C = 611 kJ/mol - 828 kJ/mol
C≡C = -217 kJ/mol
Therefore, the value of the C-C (triple bond) bond energy in C2H2 is -217 kJ/mol.
1. To calculate the standard molar entropy (Sº) of C2H6 gas, you need to use the information about the standard entropy change (∆Sº) and the stoichiometric coefficients of the reaction.
Given that the reaction is:
C2H2(g) + 2 H2(g) --> C2H6(g)
The stoichiometric coefficient of C2H6 in the balanced equation is 1. This means that the change in the number of moles of C2H6 during the reaction is 1 mole.
Using the equation ∆Sº = ΣnSº(products) - ΣnSº(reactants), where n is the stoichiometric coefficient and Sº is the standard molar entropy, you can calculate the standard molar entropy of C2H6.
∆Sº = (1 mol)Sº(C2H6) - [ (1 mol)Sº(C2H2) + (2 mol)Sº(H2) ]
Plugging in the values given for ∆Sº and Sº(C2H2) and Sº(H2), you can solve for Sº(C2H6):
-232.7 J/(mol·K) = Sº(C2H6) - [ (1 mol)(200.9 J/(mol·K)) + (2 mol)(130.7 J/(mol·K)) ]
2. To calculate the standard free-energy change (∆Gº) for the reaction, you need to use the equation ∆Gº = ∆Hº - T∆Sº, where ∆Hº is the standard enthalpy change and T is the temperature in Kelvin.
Given that ∆Hºf for C2H6 is -84.7 kJ/mol, you can use the equation ∆Hº = ∆Hºf(products) - Σn∆Hºf(reactants) to calculate ∆Hº for the reaction:
∆Hº = ∆Hºf(C2H6) - [ (1 mol)∆Hºf(C2H2) + (2 mol)∆Hºf(H2) ]
Then, plug in the values for ∆Hº and ∆Sº into the equation ∆Gº = ∆Hº - T∆Sº to calculate ∆Gº for the reaction.
The sign of ∆Gº indicates the spontaneity of the reaction. If ∆Gº is negative, it means that the reaction is spontaneous and product-favored. If ∆Gº is positive, it means that the reaction is non-spontaneous and reactant-favored. If ∆Gº is zero, it means the reaction is at equilibrium.
3. To calculate the value of the equilibrium constant for the reaction at 298 K, you can use the equation ∆Gº = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin.
Given that ∆Gº for the reaction can be calculated from the previous step, you can rearrange the equation to solve for K:
K = e^(-∆Gº / (RT))
Rearrange the equation to solve for K.
4. To calculate the value of the C-C(triple bond) bond energy in C2H2, you need to subtract the bond energies of the other bonds involved in C2H2 from the total bond energy of C2H2.
Given that the bond energy for C-C bond is 347 kJ/mol, and the bond energy for C=C is 611 kJ/mol, you can calculate the C-C(triple bond) bond energy as follows:
C C(triple bond) = Total bond energy of C2H2 - [ (2 mol)C-H bond energy + (1 mol)C=C bond energy ]