Using data in table below and S °(NaCl(s))= 72.38 J·mol-1·K-1, calculate ÄfS° for NaCl(s) in J·mol-1·K-1.
Compound S °, J·mol-1·K-1 Compound S °, J·mol-1·K-1
C(s) 5.69 H2(g) 130.6
N2(g) 191.5 O2(g) 205.0
Na(s) 51.0 Cl2(g) 223.0
Ca(s) 154.8 S(s) 31.8
To calculate the standard molar entropy change (ΔfS°) for NaCl(s), you need to use the formula:
ΔfS° = ΣnS°(products) - ΣmS°(reactants)
where ΣnS°(products) is the sum of the standard molar entropies of the products and ΣmS°(reactants) is the sum of the standard molar entropies of the reactants in the balanced chemical equation.
The balanced chemical equation for the formation of NaCl(s) is:
Na(s) + 0.5Cl2(g) -> NaCl(s)
Now, let's calculate the ΔfS° for NaCl(s) step by step:
1. Identify the standard molar entropies of the reactants and products from the given table:
Na(s): 51.0 J·mol-1·K-1 (from the table)
Cl2(g): 223.0 J·mol-1·K-1 (from the table)
NaCl(s): unknown (to be determined)
2. Substitute the values into the formula:
ΔfS° = ΣnS°(products) - ΣmS°(reactants)
ΔfS° = [1 * S°(NaCl(s))] - [1 * S°(Na(s)) + 0.5 * S°(Cl2(g))]
3. Convert the units of the standard molar entropies to J·mol-1·K-1:
Note: The given standard molar entropy values are already in J·mol-1·K-1, so no conversion is needed.
4. Substitute the known values into the formula:
ΔfS° = [1 * S°(NaCl(s))] - [1 * 51.0 + 0.5 * 223.0]
5. Calculate the value:
ΔfS° = S°(NaCl(s)) - 51.0 - (0.5 * 223.0)
6. Substitute the standard molar entropy value for NaCl(s) from the given data:
ΔfS° = 72.38 - 51.0 - (0.5 * 223.0)
7. Calculate the value:
ΔfS° = 72.38 - 51.0 - 111.5
ΔfS° = - 90.12 J·mol-1·K-1
Therefore, the standard molar entropy change (ΔfS°) for NaCl(s) is -90.12 J·mol-1·K-1.