Calculate the standard free energy change for the formation of methane at `300K`:
`C("graphite") +2H_(2) (g) rarr CH_(4)(g)`
The following data are given:
`Delta_(f)H^(Theta) (kJ mol^(-1)): CH_(4)(g) =- 74.81`
`Delta_(f)S^(Theta)(JK^-1 mol^(-1)): C("graphite") = 5.70, H_(2)(g) = 130.7, CH_(4)(g) = 186.3`

Explanation

To calculate the standard free energy change (ΔG°) for the formation of methane (CH₄) at 300 K, we will follow these steps:

### Step 1: Write the Reaction
The reaction for the formation of methane from graphite and hydrogen is:
\[ \text{C (graphite)} + 2 \text{H}_2(g) \rightarrow \text{CH}_4(g) \]

### Step 2: Calculate the Enthalpy Change (ΔH°)
The enthalpy change for the reaction can be calculated using the formula:
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