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.)
for 310K,1070,1470
this is what i did
dH (kJ/mol)dS (J/moleK)
CO2(g) (-393.51) (213.6)
CaCO3(s) (-1206.9)(92.9)
CaO(s) (-635.1)(39.8)
CO2(g) +CaO(s) -CaCO3(s)
dH = -393.51 + (-635.1) - (-1206.9) = 178.29
dS = 213.6 + (39.8) - (92.9) = 160.5
dG = dH - TdS =
dG = 178.29 - 310 x 0.1605 = 130
dG = 178.29 - 1070 x 0.1605 = 6.55
dG = 178.29 - 1470 x 0.1605 = -57.65
However only 310 is correct i don't know what i am doing wrong for the other two
Well, it seems that you're calculating the change in free energy incorrectly for the other two temperatures. Let's try it again:
For 1070 K:
ΔG = ΔH - TΔS
ΔG = 178.29 - 1070 * (0.1605/1000) (notice that the units of ΔS should be in J/molK)
For 1470 K:
ΔG = ΔH - TΔS
ΔG = 178.29 - 1470 * (0.1605/1000)
Remember to convert the units correctly and ensure that the signs of your values are correct. Give it another try!
To calculate ΔG∘ at each temperature, you need to use the equations:
ΔG∘ = ΔH∘ - TΔS∘
Let's go through the calculations for each temperature:
For 310 K:
ΔG∘ = ΔH∘ - TΔS∘
ΔG∘ = 178.29 kJ/mol - (310 K)(0.1605 kJ/mol K)
ΔG∘ = 178.29 kJ/mol - 49.865 kJ/mol
ΔG∘ = 128.43 kJ/mol (rounded to two decimal places)
For 1070 K:
ΔG∘ = ΔH∘ - TΔS∘
ΔG∘ = 178.29 kJ/mol - (1070 K)(0.1605 kJ/mol K)
ΔG∘ = 178.29 kJ/mol - 171.635 kJ/mol
ΔG∘ = 6.65 kJ/mol (rounded to two decimal places)
For 1470 K:
ΔG∘ = ΔH∘ - TΔS∘
ΔG∘ = 178.29 kJ/mol - (1470 K)(0.1605 kJ/mol K)
ΔG∘ = 178.29 kJ/mol - 235.335 kJ/mol
ΔG∘ = -57.05 kJ/mol (rounded to two decimal places)
Therefore, the correct values of ΔG∘ are as follows:
For 310 K: ΔG∘ = 128.43 kJ/mol
For 1070 K: ΔG∘ = 6.65 kJ/mol
For 1470 K: ΔG∘ = -57.05 kJ/mol
To calculate ΔG∘ for the given reaction at different temperatures, you need to use the equation ΔG∘ = ΔH∘ - TΔS∘, where ΔH∘ is the standard enthalpy change and ΔS∘ is the standard entropy change.
Let's calculate it step by step.
Given values:
ΔH∘ (kJ/mol):
CO2(g) = -393.51
CaCO3(s) = -1206.9
CaO(s) = -635.1
ΔS∘ (J/(mol·K)):
CO2(g) = 213.6
CaCO3(s) = 92.9
CaO(s) = 39.8
For 310K:
ΔH∘ = -393.51 + (-635.1) - (-1206.9) = 178.29 kJ/mol
ΔS∘ = 213.6 + 39.8 - 92.9 = 160.5 J/(mol·K)
ΔG∘ = ΔH∘ - TΔS∘
ΔG∘ = 178.29 - 310K × (160.5 J/(mol·K) / 1000 J/kJ) = 178.29 - 50.055 = 128.235 kJ/mol
So, the estimated ΔG∘ at 310K is 128.235 kJ/mol.
Now let's calculate for 1070K:
ΔH∘ = -393.51 + (-635.1) - (-1206.9) = 178.29 kJ/mol
ΔS∘ = 213.6 + 39.8 - 92.9 = 160.5 J/(mol·K)
ΔG∘ = ΔH∘ - TΔS∘
ΔG∘ = 178.29 - 1070K × (160.5 J/(mol·K) / 1000 J/kJ) = 178.29 - 172.035 = 6.255 kJ/mol
So, the estimated ΔG∘ at 1070K is 6.255 kJ/mol.
Finally, let's calculate for 1470K:
ΔH∘ = -393.51 + (-635.1) - (-1206.9) = 178.29 kJ/mol
ΔS∘ = 213.6 + 39.8 - 92.9 = 160.5 J/(mol·K)
ΔG∘ = ΔH∘ - TΔS∘
ΔG∘ = 178.29 - 1470K × (160.5 J/(mol·K) / 1000 J/kJ) = 178.29 - 237.135 = -58.845 kJ/mol
So, the estimated ΔG∘ at 1470K is -58.845 kJ/mol.
By following these steps, you should be able to calculate the correct ΔG∘ values for each temperature.
I don't know. I looked up the numbers in my text. Although they are slightly different I obtained essentially the same values you did; i.e., 128.2, 6.05, and -58.2 all in kJ/mol.
I also looked up dGo in the same text and it was 130.4 at T = 298 and using
dG = dH - TdS I obtained 130.1 which tells me the formula is ok.
In previous instances like this, where it seems everything is ok but the data base says you're wrong, it has been a case of significant figures (too many or too few). I suggest you look at that closely.