Question

Consider the following reaction: $A(g) + B(g) \rightleftharpoons C(g) + D(g)$. Which one of the following is zero for this reaction at 298 K?

• A. $\Delta_r H^\ominus$
• B. $\Delta_r S^\ominus$
• C. $\Delta_r G$
• D. $\Delta_r G^\ominus$

Hint:

Equilibrium = minimum Gibbs energy, so $\Delta G = 0$.

Answer 1

The Correct Option is C

Step 1: Recall the key Gibbs energy relation.
For any reaction, the actual free energy change is $\Delta_r G = \Delta_r G^\ominus + RT \ln Q$, where $Q$ is the reaction quotient at that moment.

Step 2: Understand equilibrium.
When a reaction reaches equilibrium, there is no net push in either direction. At that point the system has the lowest free energy it can reach.

Step 3: Translate that into maths.
At equilibrium $Q$ equals the equilibrium constant $K$, and the system has no further drive to change, so the actual free energy change becomes zero: \[ \Delta_r G = 0. \]

Step 4: Check the standard quantities.
The standard values $\Delta_r H^\ominus$ and $\Delta_r S^\ominus$ are fixed properties of the reaction and are generally not zero here.

Step 5: Check the standard free energy.
$\Delta_r G^\ominus$ would be zero only if $K = 1$, which we are not told, so it is not the zero quantity.

Step 6: Pick the zero term.
The quantity that is zero at equilibrium is the actual free energy change.
\[ \boxed{\Delta_r G} \]