1. Tardigrade
  2. Question
  3. Chemistry
  4. The compressibility factor for N2 at 223 K and 81.06 MPa is 1.95, and at 373 K and 20.265 MPa, it is 1.10. A certain mass of N2 occupies a volume of 1.0 dm3 at 223 K and 81.06 MPa. What is the volume occupied by the same quantity of N2 at 373 K and 20.265 MPa?

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Q. The compressibility factor for $N_2$ at $223\, K$ and $81.06 \,MPa$ is $1.95$, and at $373\, K$ and $20.265$ MPa, it is $1.10$. A certain mass of $N_2$ occupies a volume of $1.0 \,dm^{3}$ at $223 K$ and $81.06$ MPa. What is the volume occupied by the same quantity of $N_2$ at $373 \,K$ and $20.265$ MPa?

States of Matter

Solution:

For $T=223 K$, $P=81.06$ Mpa, $Z=1.95$, and $V=1.0 dm^{3}$ $=10^{3} cm^{3}$, we have
$n=\frac{PV}{ZRT}$ $=\frac{81.06\times10^{3}}{1.95\times8.314\times223}=22.42$ mole
Now, at $T = 373 K$, $P = 20.265$ MPa, $Z = 1.10$, the volume occupied will be
$V=\frac{ZnRT}{P}$ $=\frac{1.10\times22.42\times8.314\times373}{20.265}$ $=3774.0 cm^{3}$
$\therefore $ $\quad$ $V=3.774$ $dm^{3}$