Using data in table below and S °(CaSO4·H2O(s))= 194.0 J·mol-1·K-1, calculate ÄfS° for CaSO4·H2O(s) in 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
Anyone help me please
To calculate ∆fS° for CaSO4·H2O(s), we need to use the following equation:
∆fS° = ∑(n × S°(products)) - ∑(n × S°(reactants))
The stoichiometric coefficients (n) for the reactants and products can be obtained from the balanced equation. In this case, the balanced equation for the formation of CaSO4·H2O(s) is:
Ca(s) + SO4^2-(aq) + H2O(l) → CaSO4·H2O(s)
Reactants:
Ca(s) → Stoichiometric coefficient (n) = 1
SO4^2-(aq) → Stoichiometric coefficient (n) = 1
H2O(l) → Stoichiometric coefficient (n) = 1
Products:
CaSO4·H2O(s) → Stoichiometric coefficient (n) = 1
Now, let's calculate ∆fS° for CaSO4·H2O(s) using the given data:
∆fS° = (1 × S°(CaSO4·H2O(s))) - (1 × S°(Ca(s))) - (1 × S°(SO4^2-(aq))) - (1 × S°(H2O(l)))
From the table:
S°(CaSO4·H2O(s)) = 194.0 J·mol^-1·K^-1
S°(Ca(s)) = 154.8 J·mol^-1·K^-1
S°(SO4^2-(aq)) = S°(S(s)) + 4 × S°(O2(g)) = 31.8 J·mol^-1·K^-1 + 4 × 205.0 J·mol^-1·K^-1 = 860.8 J·mol^-1·K^-1
S°(H2O(l)) = 130.6 J·mol^-1·K^-1
Substituting the values into the equation:
∆fS° = (1 × 194.0) - (1 × 154.8) - (1 × 860.8) - (1 × 130.6)
∆fS° = 194.0 - 154.8 - 860.8 - 130.6
∆fS° = -951.2 J·mol^-1·K^-1
Therefore, the ∆fS° for CaSO4·H2O(s) is -951.2 J·mol^-1·K^-1.
To calculate ΔfS° for CaSO4·H2O(s), you need to use the standard entropy values for the compounds involved in the reaction and apply the stoichiometric coefficients.
First, let's write the balanced equation for the formation of CaSO4·H2O(s):
Ca(s) + SO4^2-(aq) + H2O(l) → CaSO4·H2O(s)
ΔfS° is the standard molar entropy change for the formation of 1 mole of the compound from its elements in their standard states at 298 K and 1 atm.
Now, we need to determine the standard molar entropy of each compound involved:
CaSO4·H2O(s) - Given: S°(CaSO4·H2O(s)) = 194.0 J·mol-1·K-1
Ca(s) - S°(Ca(s)) = 154.8 J·mol-1·K-1
SO4^2-(aq) - Since it is an ion, its value is determined from tables. In this case, it is most likely not provided in the given data. You may need to refer to a reliable source or database for the standard molar entropy of SO4^2-(aq) at 298 K.
H2O(l) - S°(H2O(l)) = 69.9 J·mol-1·K-1 (This is another value that may vary slightly depending on the source, so make sure you are using the appropriate value.)
Now, calculate the ΔfS° for CaSO4·H2O(s) using the stoichiometric coefficients:
ΔfS°(CaSO4·H2O(s)) = S°(CaSO4·H2O(s)) - [S°(Ca(s)) + S°(SO4^2-(aq)) + S°(H2O(l))]
Complete the calculation with the provided standard entropy values for CaSO4·H2O(s), Ca(s), and H2O(l), and substitute a reliable value for the standard molar entropy of SO4^2-(aq).
Remember to pay attention to the units and follow proper mathematical operations (addition/subtraction).
Unfortunately, the value for SO4^2-(aq) standard molar entropy is not provided in the given data, so you'll need to refer to other sources to find the necessary value to complete the calculation accurately.