Calculate ΔG∘ at 298 K for the following reactions.
A) Ca(s)+CO2(g)+12O2(g)→CaCO3(s)
B) 2KClO3(s)→2KCl(s)+3O2(g)
C) CO(g)+H2O(g)→H2(g)+CO2(g)
dGorxn = (n*dGoproducts) - (n*dGoreactants)
To calculate ΔG∘ (standard Gibbs free energy change) at 298 K for the given reactions, we need to use the standard Gibbs free energy of formation (ΔG∘f) values for the reactants and products.
For reaction A:
Ca(s) + CO2(g) + 1/2O2(g) -> CaCO3(s)
The standard Gibbs free energy change can be calculated using the formula:
ΔG∘ = ΣΔG∘f(products) - ΣΔG∘f(reactants)
The standard Gibbs free energy of formation values (ΔG∘f) for the reactants and products are:
ΔG∘f(CaCO3) = -1128.9 kJ/mol
ΔG∘f(CO2) = -394.4 kJ/mol
ΔG∘f(O2) = 0 kJ/mol
ΔG∘f(Ca) = 0 kJ/mol
Using these values, we can calculate the standard Gibbs free energy change ΔG∘ for reaction A.
ΔG∘ = [ΔG∘f(CaCO3)] - [ΔG∘f(Ca) + ΔG∘f(CO2) + (1/2)ΔG∘f(O2)]
ΔG∘ = [-1128.9 kJ/mol] - [(0 kJ/mol) + (-394.4 kJ/mol) + (1/2)*(0 kJ/mol)]
ΔG∘ = -1128.9 kJ/mol + 394.4 kJ/mol
ΔG∘ ≈ -734.5 kJ/mol
Therefore, the standard Gibbs free energy change ΔG∘ at 298 K for reaction A is approximately -734.5 kJ/mol.
Now let's move on to the other reactions.
For reaction B:
2KClO3(s) -> 2KCl(s) + 3O2(g)
We can apply the same formula with the appropriate ΔG∘f values.
ΔG∘ = [ΔG∘f(KCl) + 3ΔG∘f(O2)] - [2ΔG∘f(KClO3)]
ΔG∘ = [(0 kJ/mol) + 3(0 kJ/mol)] - [2(0 kJ/mol)]
ΔG∘ = 0 kJ/mol - 0 kJ/mol
ΔG∘ = 0 kJ/mol
Therefore, the standard Gibbs free energy change ΔG∘ at 298 K for reaction B is 0 kJ/mol.
Moving on to reaction C:
CO(g) + H2O(g) -> H2(g) + CO2(g)
Using the same formula:
ΔG∘ = [ΔG∘f(H2) + ΔG∘f(CO2)] - [ΔG∘f(CO) + ΔG∘f(H2O)]
ΔG∘ = [(0 kJ/mol) + (-394.4 kJ/mol)] - [(0 kJ/mol) + (0 kJ/mol)]
ΔG∘ = -394.4 kJ/mol
Therefore, the standard Gibbs free energy change ΔG∘ at 298 K for reaction C is -394.4 kJ/mol.
To calculate ΔG∘ (standard Gibbs free energy change) at 298 K for a reaction, we need to use the following equation:
ΔG∘ = ΔH∘ - TΔS∘
where ΔH∘ is the standard enthalpy change and ΔS∘ is the standard entropy change.
A) Ca(s) + CO2(g) + 12O2(g) → CaCO3(s)
To calculate ΔG∘ for this reaction, we need to know the standard enthalpy change (ΔH∘) and the standard entropy change (ΔS∘) for the reaction.
1. Find the standard enthalpy change (ΔH∘):
Look up the standard enthalpies of formation (ΔH∘f) for each of the reactants and products from a reliable source. The standard enthalpy change for the reaction can be calculated using the following equation:
ΔH∘ = ΣnΔH∘f(products) - ΣmΔH∘f(reactants)
where n and m are coefficients in the balanced equation, and ΔH∘f represents the standard enthalpy of formation.
2. Find the standard entropy change (ΔS∘):
Calculate the sum of the standard entropies of the products (ΣS∘(products)) and the sum of the standard entropies of the reactants (ΣS∘(reactants)). Then, subtract the sum of the reactant entropies from the sum of the product entropies:
ΔS∘ = ΣS∘(products) - ΣS∘(reactants)
3. Calculate ΔG∘:
Substitute the values of ΔH∘ and ΔS∘ into the equation:
ΔG∘ = ΔH∘ - TΔS∘
where T is the temperature in kelvins (298 K in this case).
Follow similar steps to calculate ΔG∘ for the remaining reactions B and C.