Question

Use the data below to calculate ΔG°rxn for the reaction: A+3B ---> C+2D Data: Reaction 1:3C ---> A+3B ΔG°rxn​ 1​ = −414.0 kJ/mol Reaction 2:C ---> D ΔG°rxn​ 2​ = 380.0 kJ/mol

Answer 1

The ΔG°rxn for the given reaction A + 3B → C + 2D is -34.0 kJ/mol.

Step-by-step explanation:

The Gibbs free energy change (ΔG°rxn) for a reaction is determined by the difference between the sum of the ΔG°rxn values for the products and the sum of the ΔG°rxn values for the reactants. We can use the given data for Reaction 1 and Reaction 2 to calculate ΔG°rxn for the desired reaction.

First, let's consider Reaction 1: 3C → A + 3B with ΔG°rxn 1 = -414.0 kJ/mol. This reaction is the reverse of the desired reaction, so we need to change the sign to use it for our calculation. Therefore, ΔG°rxn 1 = 414.0 kJ/mol.

Next, Reaction 2: C → D with ΔG°rxn 2 = 380.0 kJ/mol. To make it consistent with the desired reaction, we multiply the coefficients by 2 to get C + 2D. Thus, ΔG°rxn 2 = 2 * 380.0 kJ/mol = 760.0 kJ/mol.

Now, we add these two values to find the ΔG°rxn for the overall reaction:

`\[ \Delta G°_(rxn) = \Delta G°_(rxn1) + \Delta G°_(rxn2) \]\[ \Delta G°_(rxn) = 414.0 \, \text{kJ/mol} + 760.0 \, \text{kJ/mol} = 1174.0 \, \text{kJ/mol} \]`

Finally, since the desired reaction involves the consumption of reactants, we invert the sign to get the final answer:

`\[ \Delta G°_(rxn) = -1174.0 \, \text{kJ/mol} \]`

Therefore, the ΔG°rxn for the reaction A + 3B → C + 2D is -34.0 kJ/mol. The negative sign indicates that the reaction is thermodynamically favorable under standard conditions.

Answer 2

ΔG°rxn for the reaction A + 3B → C + 2D is 1174.0 kJ/mol

To calculate ΔG°rxn for the reaction A + 3B → C + 2D using the given data, you can use Hess's Law, which states that the change in Gibbs free energy for a reaction is the sum of the changes in Gibbs free energy for the individual reactions that make up the overall reaction. Here are the steps:

Step 1: Write the balanced chemical equation for the overall reaction:

A + 3B → C + 2D

Step 2: Determine the change in Gibbs free energy for the overall reaction using the given data for the individual reactions. To do this, we'll manipulate the given reactions to match the overall reaction:

a) Reverse Reaction 1: C + 3B → A + 3B

ΔG°rxn1 = -(-414.0 kJ/mol) = 414.0 kJ/mol (because we reversed the reaction, we change the sign of ΔG°)

b) Multiply Reaction 2 by 2 to match the coefficient of D in the overall reaction: 2C → 2D

ΔG°rxn2 = 2(380.0 kJ/mol) = 760.0 kJ/mol

Step 3: Now, add the ΔG° values of the modified reactions to calculate ΔG°rxn for the overall reaction:

ΔG°rxn (overall) = ΔG°rxn1 + ΔG°rxn2

ΔG°rxn (overall) = 414.0 kJ/mol + 760.0 kJ/mol

ΔG°rxn (overall) = 1174.0 kJ/mol

So, ΔG°rxn for the reaction A + 3B → C + 2D is 1174.0 kJ/mol.