Question

An open flask contains air at ${{27}^{o}}C$. At what temperature should it be heated so that $1/{{3}^{rd}}$of air present in it goes out?
A. ${{177}^{o}}C$
B. ${{100}^{o}}C$
C. ${{300}^{o}}C$
D. ${{150}^{o}}C$

Answer 1

Hint: To solve this question, try to look at the parameters given to us in the question. Consider pressure, volume and real gas to be constant and relate the number of moles and temperature by using the ideal gas equation and you will get your answer.

Complete step by step solution:
According to the given question, there is an open flask that contains air at a temperature equal to ${{27}^{o}}C$ i.e. equal to $(27+273)K=300K$ and it is being asked to find out the temperature of the air so that $1/{{3}^{rd}}$ amount is escaped.
So, we can say that there is a change in the number of moles of the air.
Thus, let us consider the initial number of moles of the air be ${{N}_{1}}$ and the number of moles after one-third of the air goes out be ${{N}_{2}}$.
The initial temperature be ${{T}_{1}}$ i.e. $300K$and the temperature at which one-third of the gas goes out be ${{T}_{2}}$.
So, ${{N}_{1}}=1\text{ mole}$
Then, ${{N}_{2}}={{N}_{1}}-\dfrac{1}{3}=1-\dfrac{1}{3}=\dfrac{2}{3}$
Considering volume($V$), pressure($P$) and real gas constant ($R$) to be constant and relating to the ideal gas equation i.e. $PV=nRT$, we can relate the number of moles($n$) and temperature($T$) as:
$nT=\text{Constant}$
So, here ${{N}_{1}}{{T}_{1}}={{N}_{2}}{{T}_{2}}$.
Now, putting the values of moles and temperature, we will get:
$1\times 300=\dfrac{2}{3}\times {{T}_{2}}$
So, ${{T}_{2}}=\dfrac{300\times 3}{2}=450K$
Now, convert the temperature to Celsius.
So, ${{T}_{2}}={{(450-273)}^{o}}C={{177}^{o}}C$
Therefore, the temperature should be heated at ${{177}^{o}}C$ so that one-third of air present will go out.

Hence, the correct option is A.

Note: Ideal gas equation is the equation of state of an ideal gas (hypothetical). It is an approximation of the behaviour of gases under ideal conditions. It is a combination of empirical laws like Boyle’s law, Charles’ law, Gay-Lussac’s law and Avogadro’s law.