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]

To answer the questions, you can use the following equations and concepts:

1. The standard entropy change (∆Sº) for the reaction can be related to the standard molar entropy (Sº) of C2H6 gas using the equation:

∆Sº = ΣnSº(products) - ΣmSº(reactants)

Where:
- ∆Sº is the standard entropy change.
- ΣnSº(products) is the total sum of the standard molar entropy of the products (in this case, C2H6 gas).
- ΣmSº(reactants) is the total sum of the standard molar entropy of the reactants (in this case, C2H2 gas and H2 gas).
- n and m are the stoichiometric coefficients of the products and reactants, respectively.

2. The standard free-energy change (∆Gº) can be calculated using the equation:

∆Gº = ∆Hº - T∆Sº

Where:
- ∆Gº is the standard free-energy change.
- ∆Hº is the standard enthalpy change (given as ∆Hºf in the tables).
- T is the temperature in Kelvin.
- ∆Sº is the standard entropy change.

3. The equilibrium constant (K) can be calculated using the equation:

K = e^(-∆Gº/RT)

Where:
- K is the equilibrium constant.
- ∆Gº is the standard free-energy change.
- R is the gas constant (8.314 J/mol∙K).
- T is the temperature in Kelvin.

4. The bond energy of a C-C triple bond (C≡C) in C2H2 can be estimated by subtracting the bond energies of C-C single bonds (C-C) and C=C double bonds (C=C) from each other.

Now, let's go through each question step by step:

1. To calculate the standard molar entropy (Sº) of C2H6 gas, you need to use the equation:

∆Sº = ΣnSº(products) - ΣmSº(reactants)

Here, ∆Sº = -232.7 J/mol∙K,
n = 1 (since C2H6 is the only product), and
m = 1 (since C2H2 and H2 are the only reactants with stoichiometric coefficients of 1 and 2, respectively).

Now, substitute the values into the equation:

-232.7 J/mol∙K = Sº(C2H6) - Sº(C2H2) - 2Sº(H2)

You have the given values for Sº(C2H2) and Sº(H2) from the table. Rearrange the equation to solve for Sº(C2H6):

Sº(C2H6) = Sº(C2H2) + 2Sº(H2) - 232.7 J/mol∙K

Substitute the values and calculate Sº(C2H6).

2. To calculate the standard free-energy change (∆Gº) for the reaction, you need to use the equation:

∆Gº = ∆Hº - T∆Sº

You have the given value for ∆Hº from the table. Substitute the values into the equation and calculate ∆Gº. The sign of ∆Gº indicates the direction of the reaction: if ∆Gº is negative, the reaction is spontaneous (favoring the forward reaction), and if ∆Gº is positive, the reaction is non-spontaneous (favoring the reverse reaction).

3. To calculate the equilibrium constant (K) for the reaction at 298 K, you need to use the equation:

K = e^(-∆Gº/RT)

You have the calculated value of ∆Gº from the previous step and the given temperature (298 K). Substitute the values into the equation and calculate K.

4. To estimate the bond energy of the C-C triple bond (C≡C) in C2H2, you need to subtract the bond energies of C-C single bonds (C-C) and C=C double bonds (C=C) from each other. Use the given values for the bond energies in the table and subtract them to find the bond energy of C-C triple bond (C≡C).

Following these steps, you will be able to answer the questions using the given information and the equations provided.