Choose the correct option for the total pressure (in atm.) in a mixture of 4 g O₂ and 2 g H₂ confined in a total volume of one litre at 0⁰C is : [Given R=0.082 L atm mol−1K−1, T=273 K]

The correct option is 25.18.

To find the total pressure of the gas mixture, we can use Dalton's law of partial pressures and the ideal gas equation:
$PV=n_{\text{total}}RT$
where:
• $P$ is the total pressure of the mixture,
• $V$ is the volume of the container ($1\text{L}$),
• $n_{\text{total}}$ is the total number of moles of gas present,
• $R$ is the universal gas constant ($0.082{\text{L atm mol}}^{-1}{\text{K}}^{-1}$),
• $T$ is the absolute temperature ($273\text{K}$).

Step 1: Calculate the number of moles of each gas
The molar mass of Oxygen gas (${\text{O}}_2$) is $32{\text{g mol}}^{-1}$.
The number of moles of ${\text{O}}_2$ ($n_{{\text{O}}_2}$) is calculated as:
$n_{{\text{O}}_2}=\frac{\text{Mass}}{\text{Molar Mass}}=\frac{4\text{g}}{32{\text{g mol}}^{-1}}=0.125\text{mol}$

The molar mass of Hydrogen gas (${\text{H}}_2$) is $2{\text{g mol}}^{-1}$.
The number of moles of ${\text{H}}_2$ ($n_{{\text{H}}_2}$) is calculated as:
$n_{{\text{H}}_2}=\frac{\text{Mass}}{\text{Molar Mass}}=\frac{2\text{g}}{2{\text{g mol}}^{-1}}=1.000\text{mol}$

Step 2: Calculate the total number of moles in the mixture
$n_{\text{total}}=n_{{\text{O}}_2}+n_{{\text{H}}_2}=0.125\text{mol}+1.000\text{mol}=1.125\text{mol}$

Step 3: Calculate the total pressure using the ideal gas equation
Rearranging the ideal gas equation to solve for total pressure ($P$):
$P=\frac{n_{\text{total}}RT}{V}$

Substitute the given and calculated values into the formula:
$P=\frac{1.125\text{mol}\times 0.082{\text{L atm mol}}^{-1}{\text{K}}^{-1}\times 273\text{K}}{1\text{L}}$

Performing the multiplication:
$P=1.125\times 22.386\text{atm}$
$P=25.18425\text{atm}\approx 25.18\text{atm}$

Thus, the total pressure in the container is approximately 25.18 atm.