Question

An open vessel at ${27}^{0}C$ is heated until $(3/5{)}^{th}$ of the air in it has been expelled. Assuming that the volume of the vessel remains constant then:

• A. the air escaped out if vessel is heated to $900K$
• B. temperature at which half of the air escapes out
• C. the air escaped out if vessel is heated to $750K$
  
• D. none of these

Answer 1

Answer: (C)

the air escaped out if vessel is heated to $750K$

Given the vessel is open, its volume remains constant. Therefore, the pressure will also be constant.

We have the following two general gas equation:

$PV=n_{1}R{T}_1$

$PV=n_{2}R{T}_2$

where $n_1$, $n_2$ are the numbers of moles and $T_1$, $T_2$ are the temperatures.

Thus, $n_{1}R{T}_1=n_{2}R{T}_2$ or $n_1{T}_1=n_2{T}_2$

Let the initial number of moles be $1$.

Number of moles remaining $=1-3/5=2/5=0.4$ $T_1=27+273=300K$,

$T_2=?$

Putting the values in above equation, we get $1\times 300=0.4\times T_2$

$T_2=300\times \frac{1}{0.4}=750K$

Thus, the required temperature is $750-273={477}^{o}C$.