At $$300$$ K, a sample of $$3.0$$ g of gas A occupies the same volume as $$0.2$$ g of hydrogen at $$200$$ K at the same pressure. The molar mass of gas A is ______ g mol$$^{-1}$$. (nearest integer) Assume that the behaviour of gases as ideal.
(Given: The molar mass of hydrogen ($$H_2$$) gas is $$2.0$$ g mol$$^{-1}$$.)

We are given that at the same pressure, 3.0 g of gas A at 300 K occupies the same volume as 0.2 g of hydrogen at 200 K.

For an ideal gas: $$PV = nRT$$. Since both gases occupy the same volume at the same pressure: $$V_A = V_{H_2}$$, which implies $$\frac{n_A R T_A}{P} = \frac{n_{H_2} R T_{H_2}}{P}$$ and hence $$n_A \times T_A = n_{H_2} \times T_{H_2}$$.

Expressing moles in terms of mass and molar mass, $$n_A = \frac{3.0}{M_A}$$ and $$n_{H_2} = \frac{0.2}{2.0} = 0.1$$ mol. Substituting into the relation gives $$\frac{3.0}{M_A} \times 300 = 0.1 \times 200$$, so $$\frac{900}{M_A} = 20$$ and thus $$M_A = \frac{900}{20} = 45 \text{ g mol}^{-1}$$.

The molar mass of gas A is 45 g mol$$^{-1}$$.