question_answer 1)

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. Find the relationship between their molecular masses.

Answer:

\[PV=\frac{w}{M}RT\] Case I: When gas A is filled in the tube: \[2\times V\frac{1}{{{M}_{A}}}\times RT\,\,\,\,\,\,\,\,\,.....(i)\] Case II: When gas A and B both are filled in the tube: \[3\times V=\left( \frac{1}{{{M}_{A}}}+\frac{2}{{{M}_{B}}} \right)\times RT\,\,\,\,\,\,\,\,\,\,\,.....(ii)\] Dividing Eqn. (ii) by (i) we get: \[{{M}_{B}}=4{{M}_{A}}\]