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A student forgot to add the reaction mixture to the round bottomed flask at \(27^{\circ} \mathrm{C}\) but instead he/she placed the flask on the flame. After a lapse of time, he realized his mistake, and using a pyrometer he found the temperature of the flask was \(477^{\circ} \mathrm{C}\). What fraction of air would have been expelled out ?
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Let us assume that volume of vessel \(=\mathrm{V} \mathrm{cm}{ }^3\)
or, volume of air in the flask at \(27^{\circ} \mathrm{C}=\mathrm{V} \mathrm{cm}{ }^3\)
Since, \(\frac{V_1}{T_1}=\frac{V_2}{T_2}\) or \(\frac{V}{300}=\frac{V_2}{750}\)
or, \(\mathrm{V}_2=2.5 \mathrm{~V}\)
\(\therefore \quad\) Volume expelled \(=2.5 \mathrm{~V}-\mathrm{V}=1.5 \mathrm{~V}\)
\(\therefore\) Fraction of air expelled \(=\frac{1.5 \mathrm{~V}}{2.5 \mathrm{~V}}=\frac{3}{5}\)
or, volume of air in the flask at \(27^{\circ} \mathrm{C}=\mathrm{V} \mathrm{cm}{ }^3\)
Since, \(\frac{V_1}{T_1}=\frac{V_2}{T_2}\) or \(\frac{V}{300}=\frac{V_2}{750}\)
or, \(\mathrm{V}_2=2.5 \mathrm{~V}\)
\(\therefore \quad\) Volume expelled \(=2.5 \mathrm{~V}-\mathrm{V}=1.5 \mathrm{~V}\)
\(\therefore\) Fraction of air expelled \(=\frac{1.5 \mathrm{~V}}{2.5 \mathrm{~V}}=\frac{3}{5}\)
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