Using data in table below and S °(CaSO4·H2O(s))= 194.0 J·mol-1·K-1, calculate Delta fS° for CaSO4·H2O(s) in J·mol-1·K-1.
CompoundS °, 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 CaSO4·H2O(s), we need to consider the difference in standard molar entropies between the products (CaSO4·H2O(s)) and the reactants (Ca(s) + SO4(s) + H2O(g)).
The equation is:
Ca(s) + SO4(s) + H2O(g) → CaSO4·H2O(s)
The standard molar entropy change (ΔfS°) can be calculated using the following formula:
ΔfS° = ΣνS°(products) - ΣνS°(reactants)
where ΣνS° represents the summation of stoichiometric coefficients (ν) multiplied by standard molar entropies (S°).
From the given data:
CaSO4·H2O(s): S° = 194.0 J·mol-1·K-1
Ca(s): S° = 154.8 J·mol-1·K-1
SO4(s): S° = 31.8 J·mol-1·K-1
H2O(g): S° = ?
We need to find the standard molar entropy of H2O(g). Unfortunately, it is not given in the table. We can assume it to be zero for this calculation, as it is a common assumption to use the entropy of an ideal gas at 0 K as a reference point. Therefore, we assume S°(H2O(g)) = 0 J·mol-1·K-1.
Using the formula, we can calculate ΔfS°:
ΔfS° = S°(CaSO4·H2O(s)) - [S°(Ca(s)) + S°(SO4(s)) + S°(H2O(g))]
ΔfS° = 194.0 J·mol-1·K-1 - [154.8 J·mol-1·K-1 + 31.8 J·mol-1·K-1 + 0 J·mol-1·K-1]
ΔfS° = 194.0 J·mol-1·K-1 - 186.6 J·mol-1·K-1
ΔfS° = 7.4 J·mol-1·K-1
Therefore, the standard molar entropy change (ΔfS°) for CaSO4·H2O(s) is 7.4 J·mol-1·K-1.
To calculate ΔfS° for CaSO4·H2O(s), we need to use the equation:
ΔfS° = Σ(nS°products) - Σ(mS°reactants)
Where n is the stoichiometric coefficient of the product and m is the stoichiometric coefficient of the reactant.
For CaSO4·H2O(s), the coefficients are:
CaSO4·H2O(s): 1
Using the given data:
ΔfS° for CaSO4·H2O(s) = (1 * 194.0 J·mol-1·K-1) - (1 * 154.8 J·mol-1·K-1 + 1 * 31.8 J·mol-1·K-1 + 2 * 205.0 J·mol-1·K-1 + 1 * 130.6 J·mol-1·K-1)
Simplifying the equation:
ΔfS° for CaSO4·H2O(s) = 194.0 J·mol-1·K-1 - 154.8 J·mol-1·K-1 - 31.8 J·mol-1·K-1 - 410.0 J·mol-1·K-1 - 130.6 J·mol-1·K-1
ΔfS° for CaSO4·H2O(s) = -132.2 J·mol-1·K-1
Therefore, ΔfS° for CaSO4·H2O(s) is -132.2 J·mol-1·K-1.