Question

A container has 3.2g of a certain gas at NTP. What would be the mass of the same gas contained in the same vessel at ${200}^{o}C$ and 16 atm pressure?

Answer 1

At NTP, $V=22.4L,P=1atm,R=0.0821,T=273K$

$PV=nRT$

$\Rightarrow n=\frac{3.2}{\text{Molar mass(M)}}$

$\Rightarrow PV=\left(\frac{3.2}{M}\right)0.0821\times 273$

or, $M=\frac{3.2\times 0.0821\times 273}{1\times 22.4}=3.2019$

Now, $M$=Molar weight= $\frac{3.2}{V\times 22.4}=3.2019$

$\therefore V=22.38$

Now, at $16atm$ pressure & ${200}^{o}C$, $T=200+273=473K$

$\Rightarrow PV=nRT$

$\Rightarrow PV=\frac{W}{M}RT$

$\Rightarrow 16\times 22.38=\frac{W}{3.2019}\times 0.0821\times 473$

$\Rightarrow W=\frac{16\times 22.38\times 3.2019}{0.0821\times 473}=29.524g$