Answer to Question #264379 in Molecular Physics | Thermodynamics for nicole

Question

A 25.0L tank contains 2.0kg of neon gas with a pressure of 98.0 atm at 28 degrees celcius. How many kilograms of oxygen can fill the tank under the same pressure and temperature?

Answer 1

Solution.

$V=25.0\sdot 10^{-3}m^3;$

$m=2.0 kg;$

$M(Ne)=20.2\sdot 10^{-3}kg/mol;$

$M(O_2)=32\sdot10^{-3} kg/mol;$

$p=98.0 atm=9929850 Pa;$

$T=301K;$

$pV=\dfrac{m(Ne)}{M(Ne)}RT\implies V=\dfrac{m(Ne)}{M(Ne)p}RT;$

$V=\dfrac{2.0}{20.2\sdot10^{-3}\sdot9929850}\sdot8.31\sdot301=0.025 m^{-3};$

$p=const; T=const;$

$pV=\dfrac{m(O_2)}{M(O_2)}RT\implies m(O_2)=\dfrac{pVM(O_2)}{RT};$

$m(O_2)=\dfrac{9929850\sdot25.0\sdot10^{-3}\sdot32\sdot10^{-3}}{8.31\sdot301}=3.2kg;$

Answer: $m(O_2)=3.2kg.$