Three bulbs are filled with CH 4 , CO 2 and Ne as shown in the...

The total number of moles remains constant.

${n}_{1} + {n}_{2} + {n}_{3} = {n}_{f}$

${n}_{1}, {n}_{2}, {n}_{3}$ moles of gases in the individual containers. ${n}_{f}$ is resultant moles.

Using ideal gas equation $PV = nRT$, we van write as

$\dfrac{{P}_{1}{V}_{1}}{RT} + \dfrac{{P}_{2}{V}_{2}}{RT} + \dfrac{{P}_{3}{V}_{3}}{RT} = \dfrac{{P}_{f}{V}_{f}}{RT}$

${P}_{1}{V}_{1} + {P}_{2}{V}_{2} + {P}_{3}{V}_{3} = {P}_{f}{V}_{f}$

$2 \times 2 + 4 \times 3 + 3 \times 4 = {P}_{f} \times 9$

${P}_{f} = \dfrac{28}{9} \approx 3$