Consider the reaction 3CH4(g)= C3H8(g)+ 2H2(g).
Using data from Appendix C in the textbook, calculate delta G at 298 K.
Look in the Appendix C for delta Go at 25C. Then
dGorxn = (n*dGoproducts) - (n*dGoreactants)
To calculate ΔG (delta G) at 298 K for the given reaction, you will need to use the standard Gibbs free energy of formation (ΔGf°) values of the compounds involved in the reaction. These values can be found in Appendix C of your textbook.
Step 1: Write down the balanced chemical equation for the reaction:
3CH4(g) → C3H8(g) + 2H2(g)
Step 2: Find the standard Gibbs free energy of formation (ΔGf°) values for each compound involved in the reaction. These values represent the change in Gibbs free energy when one mole of the compound is formed from its elements, with all substances in their standard states (usually 1 atm pressure and 298 K temperature).
From Appendix C, the ΔGf° values are:
ΔGf° (CH4) = -74.8 kJ/mol
ΔGf° (C3H8) = -103.8 kJ/mol
ΔGf° (H2) = 0 kJ/mol
Step 3: Calculate the ΔG for the reaction using the equation:
ΔG = Σ(n ΔGf° products) - Σ(n ΔGf° reactants)
where n represents the stoichiometric coefficients from the balanced equation.
In this case, the reaction has:
- 3 moles of CH4 (reactant)
- 1 mole of C3H8 (product)
- 2 moles of H2 (product)
Substituting the values into the equation, we get:
ΔG = (1 ΔGf° C3H8 + 2 ΔGf° H2) - (3 ΔGf° CH4)
= (1 * -103.8 kJ/mol + 2 * 0 kJ/mol) - (3 * -74.8 kJ/mol)
= -103.8 kJ/mol + 0 kJ/mol + 224.4 kJ/mol
= 120.6 kJ/mol
So, the value of ΔG at 298 K for the given reaction is 120.6 kJ/mol.
To calculate delta G (Gibbs free energy) at 298 K for the reaction 3CH4(g) = C3H8(g) + 2H2(g) using data from Appendix C in the textbook, we need to use the following equation:
delta G = [ΣnGf(products)] - [ΣnGf(reactants)]
where ΣnGf is the sum of the standard Gibbs free energy of formation for each species in the reaction, with n representing the stoichiometric coefficient.
Let's look up the values for the standard Gibbs free energy of formation for each compound involved in the reaction in Appendix C:
ΔGf° (CH4) = -50.8 kJ/mol
ΔGf° (C3H8) = -103.8 kJ/mol
ΔGf° (H2) = 0 kJ/mol
Now we substitute these values into the equation:
delta G = [ΣnGf(products)] - [ΣnGf(reactants)]
= [1 * ΔGf° (C3H8) + 2 * ΔGf° (H2)] - [3 * ΔGf° (CH4)]
= [1 * (-103.8 kJ/mol) + 2 * 0 kJ/mol] - [3 * (-50.8 kJ/mol)]
= -103.8 kJ/mol + 0 kJ/mol + 152.4 kJ/mol
= 48.6 kJ/mol
Therefore, delta G at 298 K for the reaction 3CH4(g) = C3H8(g) + 2H2(g) is 48.6 kJ/mol.