Question

Ideal gas has a volume of 10 litres at ${20}^{o}C$ and a pressure of 750 $mm$ $Hg$. Find the expressions which is needed to determine the volume of the same amount of gas at $STP$?

• A. $10\times \frac{750}{760}\times \frac{0}{20}L$
• B. $10\times \frac{750}{760}\times \frac{293}{273}L$
• C. $10\times \frac{760}{750}\times \frac{0}{20}L$
• D. $10\times \frac{760}{750}\times \frac{273}{293}L$
• E. $10\times \frac{750}{760}\times \frac{273}{293}L$

Answer 1

The correct option is E $10\times \frac{750}{760}\times \frac{273}{293}L$

Initial volume $V_1=10L$
Final volume $V_2=?$
Initial pressure $P_1=750mmHg$
Final pressure $P_2=760mmHg$
Initial temperature $T_1={20}^{o}C=293K$
Final temperature $T_2=273K$

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}\frac{750\times 10}{293}=\frac{760\times V2}{273}{V}_2=10\times \frac{750}{760}\times \frac{273}{293}$
Hence, the option (E) is the correct answer.