An oxygen cylinder of volume 60 litre has 36.40 moles of oxygen. After some oxygen is withdrawn from

Question

An oxygen cylinder of volume 60 litre has 36.40 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature $27^{\circ} \mathrm{C}$. The mass of the oxygen withdrawn from the cylinder is nearly equal to [Given, $R=\frac{100}{12} \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$, and molecular mass of $\mathrm{O}_2=32, 1 \mathrm{~atm}$ pressure $=1.01 	imes 10^5 \mathrm{~N} / \mathrm{m}^2$ ]

Professor PC Thomas Classes · Answer

(a) : Initially volume of cylinder $V_1 = 60 \mathrm{~L} = 60 	imes 10^{-3} \mathrm{~m}^3$, moles $n_1 = 36.40$. Initial mass $m_1 = n_1 M = 36.40 	imes 32 = 1164.8 \mathrm{~g}$. Final gauge pressure $P_g = 11 \mathrm{~atm}$, so absolute pressure $P_2 = 11 + 1 = 12 \mathrm{~atm} = 12 	imes 1.01 	imes 10^5 \mathrm{~Pa}$. Temperature $T = 300 \mathrm{~K}$. Final moles $n_2 = \frac{P_2 V_2}{R T} = \frac{(12 	imes 1.01 	imes 10^5) 	imes (60 	imes 10^{-3})}{8.3 	imes 300} = 29.20$. Final mass $m_2 = 29.20 	imes 32 = 934.4 \mathrm{~g}$. Mass withdrawn $= m_1 - m_2 = 1164.8 - 934.4 = 230.4 \mathrm{~g} \approx 0.230 \mathrm{~kg}$.