Question
Pressure of $$1\,g$$ of an ideal gas $$A$$ at $${27^ \circ }C$$ is found to be $$2\,bar.$$ When $$2\,g$$ of another ideal gas $$B$$ is introduced in the same flask at same temperature the pressure becomes $$3\,bar.$$ What would be the ratio of molecular masses of $$A$$ and $$B?$$
A.
4 : 1
B.
1 : 4
C.
1 : 8
D.
2 : 8
Answer :
1 : 4
Solution :
$$\eqalign{
& {\text{For gas}}\,\,A,{P_A}V = \frac{{{m_A}}}{{{M_A}}}RT\,\,\,\,\,\,\,...\left( 1 \right) \cr
& {\text{For gas}}\,\,B,{P_B}V = \frac{{{m_B}}}{{{M_B}}}RT\,\,\,\,\,\,...\left( 2 \right) \cr} $$
$${\text{Dividing equation}}$$ $${\text{(1) by equation (2) gives}}$$
$$\eqalign{
& \frac{{{P_A}}}{{{P_B}}} = \frac{{{m_A}}}{{{m_B}}}\frac{{{M_B}}}{{{M_A}}} \cr
& {P_A} + {P_B} = 3 \Rightarrow {P_B} = 3 - 2 = 1\,bar \cr
& \frac{{{M_A}}}{{{M_B}}} = \left( {\frac{{{m_A}}}{{{m_B}}}} \right)\left( {\frac{{{P_B}}}{{{P_A}}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{1\,g}}{{2\,g}}} \right)\left( {\frac{{1\,bar}}{{2\,bar}}} \right) \cr
& \Rightarrow \frac{{{M_A}}}{{{M_B}}} = 1:4 \cr} $$