Question

What will be the pressure of the gaseous mixture when $0.5L$ of $H_2$ at $0.8$ bar and $2.0L$ of dioxygen at $0.7$ bar are introduced in a $1L$ vessel at ${27}^{\circ }C$?

• A. $2.5bar$
• B. $2.1bar$
• C. $1.8bar$
• D. None of these

Answer 1

Answer: (C)

$1.8bar$

Use gaseous formula ,

$PV=nRT$

$n=\frac{PV}{RT}$

now,

moles of $H2=\frac{PV}{RT}$

for $H_2$, pressure ( P ) = 0.8 bar and volume ( V ) = 0.5 L ,

moles of $H_2=0.8\times \frac{0.5}{RT}=\frac{0.4}{RT}$

similarly for $O_2$,

pressure ( P ) = 0.7 bar , volume ( V ) = 2 L

moles of $O_2=\frac{PV}{RT}$

$=0.7\times \frac{2}{RT}=\frac{1.4}{RT}$

hence, total number of moles $=\frac{0.4}{RT}+\frac{1.4}{RT}$

$=\frac{1.8}{RT}$

now, Total pressure $==\frac{n^{\prime }RT}{V^{\prime }}$ [ by gas formula]

here, $n^{\prime }$ is Total moles $=\frac{1.8}{RT}$

$V^{\prime }$ is total volume $=1L$

now, total pressure $=\frac{1.8}{RT}\times \frac{RT}{1}=1.8$ $bar$

Hence, the correct option is $\text{C}$