(a) Calculate `DeltaG^(@)` for the following reaction at `25^(@)C`
`Au(s)+Ca^(2+)(aq 1 M)rarr Au^(3+)(aq 1 M)+Ca(s)`
Given`" "E_(Au^(3+)//Au)^(@)=+1.50 V, E_(Ca^(2+)//Ca)^(@)=-2.87 V`
(b) Predict whether the reaction will be spontaneous or not.

Explanation

To solve the problem step-by-step, we will first calculate the standard Gibbs free energy change (ΔG°) for the given electrochemical reaction and then determine if the reaction is spontaneous.

### Step 1: Identify the half-reactions
The given reaction is:
\[ \text{Au(s)} + \text{Ca}^{2+}(aq \, 1 \, M) \rightarrow \text{Au}^{3+}(aq \, 1 \, M) + \text{Ca(s)} \]

We can break this down into two half-reactions:
1. Oxidation half-reaction (at the anode):
...