A vessel has 6 g of oxygen at pressure p and | vedclass

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(C) Given,initial pressure,$p_i = p$. Final pressure,$p_f = \frac{p}{2}$. Initial temperature,$T = 400 \ K$. Final temperature,$T' = 300 \ K$. Initial

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(C) Given,initial pressure,$p_i = p$. Final pressure,$p_f = \frac{p}{2}$. Initial temperature,$T = 400 \ K$. Final temperature,$T' = 300 \ K$. Initial mass of gas,$m = 6 \ g$. From the ideal gas equation,$pV = nRT = \frac{m}{M}RT$. Initial condition: $pV = \frac{m}{M}RT$ $(i)$. Final condition: $p'V = \frac{m'}{M}RT'$ (ii). Dividing Eq. (ii) by Eq. $(i)$: $\frac{p'V}{pV} = \frac{m'RT' / M}{mRT / M} \implies \frac{p'}{p} = \frac{m'T'}{mT}$. Substituting the values: $\frac{p/2}{p} = \frac{m' 	imes 300}{6 	imes 400} \implies \frac{1}{2} = \frac{m' 	imes 3}{6 	imes 4} = \frac{m'}{8}$. $m' = \frac{8}{2} = 4 \ g$. Mass of oxygen leaked,$\Delta m = m - m' = 6 \ g - 4 \ g = 2 \ g$.

$A$ vessel has $6 \ g$ of oxygen at pressure $p$ and temperature $400 \ K$. $A$ small hole is made in it so that oxygen leaks out. How much oxygen has leaked out if the final pressure is $\frac{p}{2}$ and final temperature is $300 \ K$ (in $g$)?

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