Question

Question 5.5 Pressure of 1 g of an ideal gas A at 27 °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 a relationship between their molecular masses.

Class XI States of Matter Page 153

Answer 1

gas A and gas B are in same flask it means volume remains same for both gases. and same temperature .
so, volume and temperature is same for both gases . Let volume is V and temperature is T.

now, use gaseous formula, PV = nRT
$for\: gas \:A ,\\ P_AV=n_ART........(1)\\\\for\:gas\:B,\\P_BV=n_BRT........(2)$
now, number of mole of gas A = mass of gas A/molar mass of gas A
$n_A=\frac{1}{M_A}$

similarly for gas B
mole of gas B = mass of gas B/molar mass of gas B
$n_B=\frac{2}{M_B}$
now, total pressure= pressure of gas A + pressure of gas B
$P_{total}=P_A+P_B=2bar+P_B=3\\P_B=1bar$
because V , R and T are constant
hence,
P is directly proportional to n
now, from equations (1) and (2)
$so,\frac{P_A}{P_B}=\frac{n_A}{n_B}\\\\=\frac{1\times\:M_B}{2\times\:M_A}\\\\\frac{M_B}{M_A}=\frac{2P_A}{P_B}\\\\=\frac{2\times2}{1}=4$
$hence,M_B=4M_A$