A vessel has 6 text{ g} of hydrogen at pressu | vedclass

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(D) Using the ideal gas equation $PV = nRT$, where $n = \frac{m}{M}$ ($m$ is mass, $M$ is molar mass of $H_2 = 2 	ext{ g/mol}$).Initial state: $P_1 =

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(D) Using the ideal gas equation $PV = nRT$, where $n = \frac{m}{M}$ ($m$ is mass, $M$ is molar mass of $H_2 = 2 	ext{ g/mol}$).Initial state: $P_1 = P$, $V_1 = V$, $T_1 = 500 	ext{ K}$, $m_1 = 6 	ext{ g}$.$PV = \frac{6}{2} R(500) = 3R(500) = 1500R$.Final state: $P_2 = \frac{P}{2}$, $V_2 = V$, $T_2 = 300 	ext{ K}$, $m_2 = ?$.$\frac{P}{2} V = \frac{m_2}{2} R(300) = 150 m_2 R$.Divide the two equations: $\frac{PV}{(P/2)V} = \frac{1500R}{150 m_2 R} \implies 2 = \frac{10}{m_2}$.$m_2 = 5 	ext{ g}$.Amount of hydrogen leaked = $m_1 - m_2 = 6 	ext{ g} - 5 	ext{ g} = 1 	ext{ g}$.

$A$ vessel has $6 \text{ g}$ of hydrogen at pressure $P$ and temperature $500 \text{ K}$. $A$ small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is $\frac{P}{2}$ and the temperature falls to $300 \text{ K}$ (in $\text{ g}$)?

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