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 triple bond C]
To answer those questions, we'll consider the following equations:
1. The standard entropy change (∆Sº) can be calculated using the equation:
∆Sº = ∑Sº(products) - ∑Sº(reactants)
2. The standard free-energy change (∆Gº) can be calculated using the equation:
∆Gº = ∑∆Gº(products) - ∑∆Gº(reactants)
3. The equilibrium constant (K) can be calculated using the equation:
∆Gº = -RTln(K), where R is the gas constant (8.314 J/mol·K), and T is the temperature in Kelvin.
4. The bond energy for C≡C can be determined by subtracting the bond energies of the individual bonds in C2H2 from the energy change (∆Hºf) for C2H2.
Now, let's solve the questions step by step:
1. Calculate the standard molar entropy (Sº) of C2H6 gas.
To calculate Sº, we need to know the stoichiometric coefficients of the reactants and products. Here, we have:
Reactants:
C2H2(g) - Sº = 200.9 J/mol∙K
H2(g) - Sº = 2 × 130.7 J/mol∙K
Products:
C2H6(g) - Sº = ? J/mol∙K
Using the equation ∆Sº = ∑Sº(products) - ∑Sº(reactants):
-232.7 = Sº(C2H6) - 200.9 - 2 × 130.7
Sº(C2H6) = -232.7 + 200.9 + 2 × 130.7
Sº(C2H6) = 199.5 J/mol∙K
Therefore, the standard molar entropy (Sº) of C2H6 gas is 199.5 J/mol∙K.
2. Calculate the value of the standard free-energy change (∆Gº) for the reaction and determine what the sign of ∆Gº indicates about the reaction.
To calculate ∆Gº, we need to know the standard free-energy changes (∆Gº) of the reactants and products. Here, we have:
Reactants:
C2H2(g) - ∆Gºf = 226.7 kJ/mol
H2(g) - ∆Gºf = 2 × 0 kJ/mol
Products:
C2H6(g) - ∆Gºf = -84.7 kJ/mol
Using the equation ∆Gº = ∑∆Gº(products) - ∑∆Gº(reactants):
∆Gº = -84.7 - 226.7 + 2 × 0
∆Gº = -311.4 kJ/mol
The negative value of ∆Gº indicates that the reaction is spontaneous and exothermic.
3. Calculate the value of the equilibrium constant (K) for the reaction at 298 K.
To calculate K, we can use the equation ∆Gº = -RTln(K).
Here, ∆Gº = -311.4 kJ/mol, R = 8.314 J/mol·K, and T = 298 K.
Converting ∆Gº to J/mol:
∆Gº = -311.4 × 1000 J/mol
Calculating K:
-∆Gº = RTln(K)
(K) = e^(-∆Gº/RT)
Therefore,
K = e^(-(-311.4 × 1000 J/mol) / (8.314 J/mol·K × 298 K))
Calculating this value will give us the equilibrium constant for the reaction at 298 K.
4. Calculate the value of the C≡C bond energy in C2H2.
To calculate the C≡C bond energy, we need to subtract the bond energies of the individual bonds in C2H2 from the energy change (∆Hºf) for C2H2.
Energy change (∆Hºf) for C2H2 = 226.7 kJ/mol
C-C bond energy = 347 kJ/mol
H-H bond energy = 436 kJ/mol
Therefore, the C≡C bond energy can be calculated as follows:
C≡C bond energy = ∆Hºf - 2 × C-H bond energy - C-C bond energy
Substituting the values:
C≡C bond energy = 226.7 - 2 × 414 - 347
Calculating this expression will give us the value of the C≡C bond energy in kJ/mol.
1. To calculate the standard molar entropy (Sº) of C2H6 gas, we need to use the equation:
∆Sº = Σ(Sº Products) - Σ(Sº Reactants)
Given the value of the standard entropy change (∆Sº) for the reaction (-232.7 J/mol∙K), we have:
∆Sº = Sº(C2H6) - [2 × Sº(H2) + Sº(C2H2)]
We can rearrange the equation to solve for Sº(C2H6):
Sº(C2H6) = ∆Sº + [2 × Sº(H2) + Sº(C2H2)]
Now, let's substitute the given values:
Sº(C2H6) = -232.7 J/mol∙K + [2 × 130.7 J/mol∙K + 200.9 J/mol∙K]
Sº(C2H6) = -232.7 J/mol∙K + 392.3 J/mol∙K
Sº(C2H6) = 159.6 J/mol∙K
Therefore, the standard molar entropy of C2H6 gas is 159.6 J/mol∙K.
2. To calculate the standard free-energy change (∆Gº) for the reaction, we use the equation:
∆Gº = ∆Hº - T∆Sº
Given the values of ∆Hºf for the reactants and products, and the standard entropy change ∆Sº, we have:
∆Gº = [∆Hºf(C2H6) - ∆Hºf(C2H2) - 2 × ∆Hºf(H2)] - T(∆Sº)
Substituting the values, we have:
∆Gº = [-84.7 kJ/mol - 226.7 kJ/mol - 2 × 0 kJ/mol] - (298 K)(-232.7 J/mol∙K)
Simplifying the equation:
∆Gº = -311.4 kJ/mol + 69.3636 kJ/mol
∆Gº = -242.0364 kJ/mol
The negative sign indicates that the reaction is exergonic (releases energy) under standard conditions.
3. The equilibrium constant (K) represents the ratio of product concentrations to reactant concentrations at equilibrium. It can be calculated using the equation:
K = e^(-∆Gº/RT)
Given the value of ∆Gº, the ideal gas constant (R = 8.314 J/mol∙K), and the temperature (298 K), we have:
K = e^(-(-242.0364 kJ/mol)/(8.314 J/mol∙K × 298 K))
Simplifying the equation and converting kJ to J:
K = e^(292610.47/2478.772 J)
K = e^118.0125
K ≈ 3.26 × 10^51
Therefore, the value of the equilibrium constant for the reaction at 298 K is approximately 3.26 × 10^51.
4. The bond energy of a specific bond can be calculated by subtracting the sum of the bond energies of the products from the sum of the bond energies of the reactants.
Given the equation:
C2H2(g) + 2 H2(g) → C2H6(g)
We are interested in the C-C triple bond energy in C2H2. To calculate it, we need to subtract the bond energy of the reactant C-C triple bond from the bond energies of the products C-C, C-H, and H-H bonds.
C-C triple bond energy = Σ(Bond energies products) - Σ(Bond energies reactants)
Substituting the given bond energies:
C-C triple bond energy = [2 × C-C] - [C-C + 6 × C-H + 2 × H-H]
C-C triple bond energy = [2 × 347 kJ/mol] - [611 kJ/mol + 6 × 414 kJ/mol + 2 × 436 kJ/mol]
C-C triple bond energy = [694 kJ/mol] - [611 kJ/mol + 2484 kJ/mol + 872 kJ/mol]
C-C triple bond energy = 694 kJ/mol - 3967 kJ/mol
C-C triple bond energy ≈ -3273 kJ/mol
Therefore, the value of the C-C triple bond energy in C2H2 is approximately -3273 kJ/mol.