Two vessels \(A\) and \(B\) contain oxygen. The volume of \(B\) is twice that of \(A\), the pressure of…
Two vessels \(A\) and \(B\) contain oxygen. The volume of \(B\) is twice that of \(A\), the pressure of \(B\) is thrice that of \(A\) and the temperature of \(B\) is half of that of \(A\). Then, find the ratio of number of molecules of oxygen in vessels \(A\) and \(B\).
1:3
\(1: 12\)
\(3: 4\)
\(1: 6\)
Solution
For vessels \(A\) and \(B\),
\(\begin{aligned}
V_B & =2 V_A \\
p_B & =3 p_A \\
T_B & =\frac{T_A}{2}
\end{aligned}\)
If \(N_A\) and \(N_B\) be the number of molecules of oxygens in vessels \(A\) and \(B\) respectively, then according to ideal gas equation,
\(\begin{aligned} n_B \times \frac{p_A V_A}{T_A} & =n_A \times \frac{p_B V_B}{T_B} \\ \Rightarrow \quad \frac{N_B}{M} \cdot \frac{p_A V_A}{T_A} & =\frac{N_A}{M} \times \frac{p_B V_B}{T_B} \\ \Rightarrow \quad \frac{N_B}{N_A} & =\frac{p_B V_B T_A}{p_A V_A T_B} \\ \frac{N_B}{N_A} & =\frac{3 p_A \cdot 2 V_A \cdot T_A}{p_A \cdot V_A \cdot \frac{T_A}{2}} \\ \frac{N_B}{N_A} & =\frac{12}{1} \Rightarrow \frac{N_A}{N_B}=\frac{1}{12} \Rightarrow N_A: N_B=1: 12\end{aligned}\)