Consider the following reaction:
CaCO3(s)→CaO(s)+CO2(g).
Estimate ΔG∘ for this reaction at each of the following temperatures. (Assume that ΔH∘ and ΔS∘ do not change too much within the given temperature range.)
A) 310K and is it spontaneous
B) 1070K and is it spontaneous
C) 1470K and is it spontaneous
To estimate ΔG∘ for the given reaction at different temperatures, we can use the equation:
ΔG∘ = ΔH∘ - TΔS∘
where ΔH∘ is the standard enthalpy change of the reaction and ΔS∘ is the standard entropy change of the reaction.
A) For the temperature 310K:
To estimate ΔG∘ at this temperature, we need to know the values of ΔH∘ and ΔS∘ for the reaction. Assuming ΔH∘ and ΔS∘ do not change significantly within the given temperature range, we can use the standard values at 298K.
The standard enthalpy change, ΔH∘ = ΔH∘(products) - ΔH∘(reactants)
ΔH∘ = [ΔH∘(CaO) + ΔH∘(CO2)] - ΔH∘(CaCO3)
The standard entropy change, ΔS∘ = ΔS∘(products) - ΔS∘(reactants)
ΔS∘ = [ΔS∘(CaO) + ΔS∘(CO2)] - ΔS∘(CaCO3)
Now, substitute the calculated values of ΔH∘ and ΔS∘ into the equation:
ΔG∘ = ΔH∘ - TΔS∘
Calculate the value of ΔG∘ using the given equation, and if ΔG∘ is negative, it indicates the reaction is spontaneous.
B) For the temperature 1070K:
Follow the same procedure as in part A, but this time using the given temperature value of 1070K instead of 310K to calculate the value of ΔG∘. Again, check if ΔG∘ is negative to determine if the reaction is spontaneous.
C) For the temperature 1470K:
Repeat the procedure as before, but now using the given temperature of 1470K. Calculate the value of ΔG∘ and determine if the reaction is spontaneous by checking if ΔG∘ is negative.
Please note that you'll need the values of ΔH∘ and ΔS∘ at 298K for this estimation.
Look up dHo formation and dSo formation.
Then dHo rxn = (n*dHo products) - (dHo reactants)
dSo rxn = (n*dSo products) - (n*dSo reactants)
Then dG = dH - TdS for each temperature
dG = - number is spontaneous
dG = + number is not spontaneous.