Question

At $25^{\circ} C$ and $760\, mm$ of $Hg$ pressure, a gas occupies $600\, mL$ volume. What will be its pressure at a height where temperature is $10^{\circ} C$ and volume of the gas is $640 \, mL$ ?

• A. $677\, mm\, Hg$
• B. $600\, mm\, Hg$
• C. $700\, mm \, Hg$
• D. $752 \, mm \, Hg$

Answer 1

Answer: (A)

$p_{1}=760 \,mm \,Hg , $
$V_{1}=600\, mL$
$T_{1}=25+273=298 \,K$
$V_{2}=640 \,mL$
and $T_{2}=10+273=283 \,K$
According to combined gas law,
$\frac{p_{1} V_{1}}{T_{1}} =\frac{p_{2} V_{2}}{T_{2}} $
$\Rightarrow p_{2}=\frac{p_{1} V_{1} T_{2}}{T_{1} V_{2}}$
$\Rightarrow p_{2}=\frac{(760 \,mm\,Hg ) \times(600\, mL ) \times(283 \,K )}{(640 \,mL ) \times(298 \,K )}$
$=676.6 \,mm\,Hg$
$\approx 677 \,mm\, Hg$