Two vessels $$A$$ and $$B$$ are of the same size and are at same temperature. $$A$$ contains $$1$$ g of hydrogen and $$B$$ contains $$1$$ g of oxygen. $$P_A$$ and $$P_B$$ are the pressures of the gases in $$A$$ and $$B$$ respectively, then $$\frac{P_A}{P_B}$$ is :

We need to find the ratio of pressures $$P_A/P_B$$ where vessel A contains 1 g of hydrogen and vessel B contains 1 g of oxygen, with both vessels being the same size and at the same temperature.

$$PV = nRT$$

Since both vessels have the same volume ($$V$$) and temperature ($$T$$), and $$R$$ is a constant:

$$P \propto n$$

Therefore:

$$\frac{P_A}{P_B} = \frac{n_A}{n_B}$$

The number of moles is given by $$n = \frac{\text{mass}}{\text{molar mass}}$$.

For hydrogen ($$H_2$$), molar mass = 2 g/mol:

$$n_A = \frac{1}{2} = 0.5 \text{ mol}$$

For oxygen ($$O_2$$), molar mass = 32 g/mol:

$$n_B = \frac{1}{32} \text{ mol}$$

$$\frac{P_A}{P_B} = \frac{n_A}{n_B} = \frac{0.5}{1/32} = 0.5 \times 32 = 16$$

The correct answer is Option (1): 16.