Answer
From the ideal gas equation i.e.:
$$
p \cdot V=n \cdot R \cdot T \quad\quad\quad\quad(1)
$$
We can calculate the values of the universal gas constant from each of scenarios provided in the question.
$$
\begin{aligned} p \cdot V &=n \cdot R \cdot T \\ R &=p \cdot\left(\frac{V}{n}\right) \cdot\left(\frac{1}{T}\right) \\ &=p \cdot\left(V_{m}\right) \cdot\left(\frac{1}{T}\right) \end{aligned}
$$
Now substituting the values provided in each of the scenarios we have
i)
$$
\begin{aligned} R &=\frac{0.750 \times 29.8649}{273.15} \\ &=0.082001 \frac{\text { litre atm }}{\mathrm{K} \cdot \text { mol }} \end{aligned}
$$
ii)
$$
\begin{aligned} R &=\frac{0.50 \times 44.8090}{273.15} \\ &=0.082022 \frac{\text { litre } \cdot \mathrm{atm}}{\mathrm{K} \cdot \mathrm{mol}} \end{aligned}
$$
iii)
$$
\begin{aligned} R &=\frac{0.25 \times 89.6384}{273.15} \\ &=0.082041 \frac{\text { litre } \cdot \mathrm{atm}}{\mathrm{K} \cdot \mathrm{mol}} \end{aligned}
$$
The closest value to the actual universal gas constant is provided by the values provided in the scenario i
Work Step by Step
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