A closed vessel contains 8g of oxygen and 7g of nitrogen. The total pressure is 10 atm at a given temperature. If now oxygen is absorbed by introducing a suitable absorbent the pressure of the remaining gas in atm will be

The correct answer is 5.

To find the pressure of the remaining gas after oxygen is absorbed, we can apply Dalton's Law of Partial Pressures and the ideal gas equation. Let us break down the solution step-by-step.

Step 1: Calculate the number of moles of each gas present initially.
The molar mass of oxygen ($O_2$) is 32 g/mol, and the molar mass of nitrogen ($N_2$) is 28 g/mol.
For oxygen ($O_2$):

$n_{O_2}=\frac{8\text{g}}{32\text{g/mol}}=0.25\text{mol}$

For nitrogen ($N_2$):

$n_{N_2}=\frac{7\text{g}}{28\text{g/mol}}=0.25\text{mol}$

Step 2: Calculate the total number of moles of gas.

$n_{\text{total}}=n_{O_2}+n_{N_2}=0.25+0.25=0.50\text{mol}$

Step 3: Relate pressure to the number of moles.
According to the ideal gas law, at constant volume and temperature, the pressure is directly proportional to the number of moles of gas present:

$P\propto n$

When oxygen is completely absorbed by the absorbent, only nitrogen remains in the closed vessel. Therefore, the pressure of the remaining gas is simply the partial pressure exerted by the nitrogen gas.

Step 4: Calculate the pressure of the remaining nitrogen gas.
Using the mole fraction of nitrogen:

$P_{N_2}=\frac{n_{N_2}}{n_{\text{total}}}$

Substituting the values:

$P_{N_2}=\frac{0.25}{0.50}$

Thus, the pressure of the remaining gas in the vessel is 5 atm.