100 g of an ideal gas is kept in a cylinder of 416 L volume at 27°C under 1.5 bar pressure. The molar mass of the gas is ______ g mol$$^{-1}$$. (Nearest integer)
(Given: R = 0.083 L bar K$$^{-1}$$ mol$$^{-1}$$)

We need to find the molar mass of an ideal gas using the ideal gas equation. The mass of gas (w) is 100 g, the volume (V) is 416 L, the temperature (T) is 27°C = 300 K, the pressure (P) is 1.5 bar, and R = 0.083 L bar K$$^{-1}$$ mol$$^{-1}$$.

Using the ideal gas equation $$PV = nRT$$ with $$n = \frac{w}{M}$$ (w = mass, M = molar mass) gives $$PV = \frac{w}{M} \times RT$$. Solving for the molar mass yields $$M = \frac{wRT}{PV}$$, so $$M = \frac{100 \times 0.083 \times 300}{1.5 \times 416}$$.

The numerator is $$100 \times 0.083 \times 300 = 2490$$ and the denominator is $$1.5 \times 416 = 624$$, hence $$M = \frac{2490}{624} = 3.99 \approx 4 \text{ g mol}^{-1}$$. The molar mass is approximately 4 g mol$$^{-1}$$, which corresponds to helium (He).

Hence, the answer is 4.