Calculate ΔG∘ at 298 K for the following reactions.
Ca(s)+CO2(g)+12O2(g)→CaCO3(s)
2KClO3(s)→2KCl(s)+3O2(g)
CO(g)+H2O(g)→H2(g)+CO2(g)
dGorxn = (n*dGo formation products) = (n*dGo formation reactants)
could you set this up for the first one for me please
then i can do the other two
In order to calculate ΔG∘ at 298 K for the given reactions, we will use the equation:
ΔG∘ = ΔH∘ - TΔS∘
where ΔG∘ is the standard Gibbs free energy change, ΔH∘ is the standard enthalpy change, ΔS∘ is the standard entropy change, and T is the temperature in Kelvin.
Let's calculate the values for each reaction:
1. Ca(s) + CO2(g) + 1/2O2(g) → CaCO3(s)
First, we need to find the values for ΔH∘ and ΔS∘. We can look up these values in a reference table or use Hess's law.
- ΔH∘ (standard enthalpy change): -1206 kJ/mol
- ΔS∘ (standard entropy change): 160.5 J/mol·K
Now, let's calculate ΔG∘:
ΔG∘ = ΔH∘ - TΔS∘
= -1206 kJ/mol - (298 K)(160.5 J/mol·K) (Note: units for temperature should be consistent)
= -1206 kJ/mol - 47.769 kJ/mol
= -1253.769 kJ/mol
Therefore, ΔG∘ for the first reaction is -1253.769 kJ/mol at 298 K.
2. 2KClO3(s) → 2KCl(s) + 3O2(g)
Again, we need to find the values for ΔH∘ and ΔS∘:
- ΔH∘ (standard enthalpy change): 89.9 kJ/mol
- ΔS∘ (standard entropy change): 193.8 J/mol·K
Calculate ΔG∘:
ΔG∘ = ΔH∘ - TΔS∘
= 89.9 kJ/mol - (298 K)(193.8 J/mol·K) (Note: units for temperature should be consistent)
= 89.9 kJ/mol - 57.773 kJ/mol
= 32.127 kJ/mol
So, ΔG∘ for the second reaction is 32.127 kJ/mol at 298 K.
3. CO(g) + H2O(g) → H2(g) + CO2(g)
Let's find the values for ΔH∘ and ΔS∘:
- ΔH∘ (standard enthalpy change): +41.2 kJ/mol
- ΔS∘ (standard entropy change): -222.2 J/mol·K
Calculate ΔG∘:
ΔG∘ = ΔH∘ - TΔS∘
= 41.2 kJ/mol - (298 K)(-222.2 J/mol·K) (Note: units for temperature should be consistent)
= 41.2 kJ/mol + 66.1956 kJ/mol
= 107.3956 kJ/mol
Hence, ΔG∘ for the third reaction is 107.3956 kJ/mol at 298 K.
To calculate ΔG∘ (standard Gibbs free energy change) at 298 K for each reaction, follow these steps:
Step 1: Write the balanced chemical equation for each reaction.
Step 2: Determine the standard Gibbs free energy change, ΔG∘f, for each compound involved in the reaction.
Step 3: Use the ΔG∘f values to calculate ΔG∘ for the overall reaction.
Let's go through each reaction one by one:
Reaction 1: Ca(s) + CO2(g) + 1/2 O2(g) → CaCO3(s)
Step 1: The balanced chemical equation is already given.
Step 2: Find the standard Gibbs free energy change, ΔG∘f, for each compound involved. You can obtain these values from a standard thermodynamic data table or use a reliable software.
ΔG∘f(Ca(s)) = 0 (since standard state for element/compound in its most stable form is zero)
ΔG∘f(CO2(g)) = -394.36 kJ/mol (standard Gibbs free energy of formation of CO2)
ΔG∘f(CaCO3(s)) = -1128.19 kJ/mol (standard Gibbs free energy of formation of CaCO3)
ΔG∘f(O2(g)) = 0 (since O2 is the most stable form of oxygen under standard conditions)
Step 3: Calculate ΔG∘ for the overall reaction by subtracting the sum of ΔG∘f of reactants from the sum of ΔG∘f of products.
ΔG∘ = [ΔG∘f(CaCO3) - ΔG∘f(Ca) - ΔG∘f(CO2) - (1/2)ΔG∘f(O2)]
= [-1128.19 - 0 - (-394.36) - (1/2)(0)]
= -733.83 kJ/mol
Therefore, ΔG∘ at 298 K for the reaction Ca(s) + CO2(g) + 1/2 O2(g) → CaCO3(s) is -733.83 kJ/mol.
Now, let's move on to the next reaction.
Reaction 2: 2KClO3(s) → 2KCl(s) + 3O2(g)
Repeat the same steps as above to calculate ΔG∘ for this reaction. Determine the values of ΔG∘f for each compound involved and use them in the ΔG∘ calculation.
Finally, for the third reaction:
Reaction 3: CO(g) + H2O(g) → H2(g) + CO2(g)
Once again, follow the same steps outlined above to calculate ΔG∘ for this reaction.
Remember to use the appropriate ΔG∘f values for each compound when calculating the ΔG∘ for the overall reaction.