Answer - Given,
Temperature = 25C or 298 K [0°C + 273 = 273K]
Pressure = 1 bar
1 kJ = 1000 J
S°rxn = ?
Some useful information,
Species | Hf°(kJ/mol) | Gf°(kJ/mol) |
---|---|---|
C (s) | 0 | 0 |
O2 (g) | 0 | 0 |
CO2 (g) | -110.525 | -137.168 |
CH4 (g) | -74.81 | -50.72 |
C2H2 (g) | 226.73 | 209.2 |
H2 (g) | 0 | 0 |
H2O (l) | -285.83 | -237.129 |
C2H4 (g) | 52.26 | 68.15 |
A)
C (s) + O2 (g) CO2 (g)
We know that,
Grxn = n * Gf(products) - n * Gf(reactants)
where, n = stiochiometric coefficient
Grxn = 1 * Gf(CO2 (g)) - 1 * Gf(O2 (g)) - 1 *Gf(C (s))
Grxn = [1 * (-137.168 kJ/mol)] - [1 * (0 kJ/mol)] - [1 * (0 kJ/mol)]
Grxn = -137.168 kJ/mol
Also,
Hrxn = n * Hf(products) - n * Hf(reactants)
where, n = stiochiometric coefficient
Hrxn = 1 * Hf(CO2 (g)) - 1 * Hf(O2 (g)) - 1 *Hf(C (s))
Hrxn = [1 * (-110.525 kJ/mol)] - [1 * (0 kJ/mol)] - [1 * (0 kJ/mol)]
Hrxn = -110.525 kJ/mol
Now,
We know that,
Grxn = Hrxn - T Srxn
Put the values,
-137.168 kJ/mol = -110.525 kJ/mol - 298 K * Srxn
So,Srxn = (137.168 kJ/mol - 110.525 kJ/mol )/ 298 K
Srxn = 0.0894 kJ/mol.K or 89.4 J/mol.K [Answer]
B)
CH4 (g) + 2 O2 (g) CO2 (g) + 2 H2O (l)
We know that,
Grxn = n * Gf(products) - n * Gf(reactants)
where, n = stiochiometric coefficient
Grxn = 2 * Gf(H2O (l)) + 1 * Gf(CO2 (g)) - 1 *Gf(CH4 (g)) - 2 *Gf(O2 (g))
Grxn = [2 * (-237.129 kJ/mol)] + [1 * (-137.168 kJ/mol)] - [1 * (-50.72 kJ/mol)] - [2 * (0 kJ/mol)]
Grxn = -560.706 kJ/mol
Also,
Hrxn = n * Hf(products) - n * Hf(reactants)
where, n = stiochiometric coefficient
Hrxn = 2 * Hf(H2O (l)) + 1 * Hf(CO2 (g)) - 1 *Hf(CH4 (g)) - 2 *Hf(O2 (g))
Hrxn = [2 * (-285.83 kJ/mol)] + [1 * (-110.525 kJ/mol)] - [1 * (-74.81 kJ/mol)] - [2 * (0 kJ/mol)]
Hrxn = -607.375 kJ/mol
Now,
We know that,
Grxn = Hrxn - T Srxn
Put the values,
-560.706 kJ/mol = -607.375 kJ/mol - 298 K * Srxn
So,Srxn = (560.706 kJ/mol - 607.375 kJ/mol)/ 298 K
Srxn = -0.15661 kJ/mol.K or -156.61 J/mol.K [Answer]
C)
C2H2 (g) + H2 (g) C2H4 (g)
We know that,
Grxn = n * Gf(products) - n * Gf(reactants)
where, n = stiochiometric coefficient
Grxn = 1 * Gf(C2H4 (g)) - 1 * Gf(C2H2 (g)) - 1 *Gf(H2 (g))
Grxn = [1 * (68.15 kJ/mol)] - [1 * (209.2 kJ/mol)] - [1 * (0 kJ/mol)]
Grxn = -141.05 kJ/mol
Also,
Hrxn = n * Hf(products) - n * Hf(reactants)
where, n = stiochiometric coefficient
Hrxn = 1 * Hf(C2H4 (g)) - 1 * Hf(C2H2 (g)) - 1 *Hf(H2 (g))
Hrxn = [1 * (52.26 kJ/mol)] - [1 * (226.73 kJ/mol)] - [1 * (0 kJ/mol)]
Hrxn = -174.47 kJ/mol
Now,
We know that,
Grxn = Hrxn - T Srxn
Put the values,
-141.05 kJ/mol = -174.47 kJ/mol - 298 K * Srxn
So,Srxn = (141.05 kJ/mol - 174.47 kJ/mol)/ 298 K
Srxn = -0.11215 kJ/mol.K or -112.14 J/mol.K [Answer]
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