`1.0 mol` of an ideal gas initially present in a `2.0L` insulated cylinder at `300K` is allowed to expand against vacuum to `8.0L`. Determine `w, DeltaU, Delta_("total")S`, and `DeltaG`.

Explanation

To solve the problem step by step, we will calculate the work done (w), change in internal energy (ΔU), change in total entropy (ΔS_total), and change in Gibbs free energy (ΔG) for the given expansion of an ideal gas.

### Step 1: Calculate Work Done (w)

The work done by the gas during expansion against vacuum is given by the formula:
\[ w = - P_{\text{external}} \Delta V \]
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