Two vessels A and B are of the same size and are at the same temperature. A contains 1 g of hydrogen and B contains 1 g

Question

Two vessels A and B are of the same size and are at the same temperature. A contains 1 g of hydrogen and B contains 1 g of oxygen. PA and PB are the pressures of the gases in A and B respectively,…

Accepted Answer

Given: Two vessels have the same volume and are at the same temperature. Vessel A contains $1 \, \text{g}$ of hydrogen and vessel B contains $1 \, \text{g}$ of oxygen.

Find: The ratio $P_A/P_B$ .

Using the ideal gas equation, for fixed volume and temperature, pressure is directly proportional to the number of moles.

P \propto n

So,

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

For hydrogen,

n_A = \frac{1}{2}

because the molar mass of hydrogen gas is $2 \, \text{g mol}^{-1}$ .

For oxygen,

n_B = \frac{1}{32}

because the molar mass of oxygen gas is $32 \, \text{g mol}^{-1}$ .

Therefore,

\frac{P_A}{P_B} = \frac{1/2}{1/32} = 16

The ratio of their pressures is $16$ . Hence, the correct option is A.

Given: Equal volume and equal temperature for both gases.

Find: $P_A/P_B$ .

At the same temperature and volume, pressure depends only on moles. For equal mass samples, moles are inversely proportional to molar mass.

\frac{P_A}{P_B} = \frac{n_A}{n_B} = \frac{M_B}{M_A}

Now use molar masses:

M_{H_2} = 2, \qquad M_{O_2} = 32

So,

\frac{P_A}{P_B} = \frac{32}{2} = 16

This works because both gases have the same mass, so the gas with smaller molar mass has more moles and therefore greater pressure. The correct option is A.

Answer

Step-by-step solution

Common mistakes

Practice more Equation of State of Ideal Gas questions

Related questions