Question

Figure 13.8 shows plot of PV/T versus P for $1.00\times {10}^{-3}kg$ of oxygen gas at two different temperatures.
(a) What does the dotted plot signify?
(b) Which is true : $T_1>T_{2}or{T}_1<T_2$?
(c) What is the value of PV / T where the curves meet on the y-axis?
(d) If we obtained similar plots for $1.00\times {10}^{-3}kg$ of hydrogen, would we get the same value of PV/T at the point where the curves meet on the y-axis? If not, what mass of hydrogen yields the same value of PV/T (for low pressure high temperature region of the plot) ? (Molecular mass of $H_2=2.02u$, of $O_2=32.0u$, $R=8.31Jmo{l}^{-1}{K}^{-1}$.)

Answer 1

(a) The dotted graph shows a straight line and therefore, it depicts the ideal behaviour of the gas.

(b) As the temperature increase, the real gas approch towards the ideal behaviour. Since the plot of temperature $T_1$ is close to the ideal behaviour, it can be concluded that $T_1>T_2$.

(c) We know that ideal gas equation is written as:

$\frac{PV}{T}=nR$

Since $M_{O_2}=32g$

$nR=\frac{1}{32}\times 8.314$

$nR=0.256J{K}^{-1}$

(d) If similar plots are obtained for $1.00\times {10}^{-3}$ kg of hydrogen, the same value of $PV/T$ cannot be obtained at the point where the curves meet on the y-axis because for the same amount of Hydrogen, it would contain more moles $1g$ of Oxygen because of its molar mass.

Molar Mass of Hydrogen $M=2g$

So, the mass of hydrogen will be:

$m=\frac{PV}{T}\frac{M}{R}$

$=0.256\times \frac{2}{8.314}=5.48\times {10}^{-5}Kg$