(a) The dotted plot in the graph signifies the ideal behaviour of the gas,
`PV/T` i.e the ratio is equal .`muR(mu` is the number of moles and R is the universal gas constant) is a constant quality. It is not dependent on the pressure of the gas.
(b) The dotted plot in the given graph represents an ideal gas. The curve of the gas at temperature `T_1 `is closer to the dotted plot than the curve of the gas at temperature `T_2`. A real gas approaches the behaviour of an ideal gas when its temperature increases. Therefore, `T_1 gt T_2` is true for the given plot.
(c) The value of the ratio PV/T, where the two curves meet, is `muR`. This is because the ideal gas equation is given as:
`PV =mu RT`
`(PV)/(T)=mu R`
Where
P is the pressure
T is the temprature
V is the volume
`mu `is the number of moles
R is the universal consatn
Molecular mass of oxgen =32.0 g
Mass of oxygen `=1xx10^(-3) kg =1g`
` R = 8.314 J "mole" ^-1 K^-1`
` therefor (PV)/(T)=(1)/(32)xx8.314`
` =0.26 J K^-1` Therefore, the value of the ratio PV/T, where the curves meet on the y-axis, is
(d) If we obtain similar plots for `1.00 × 10^(–3)` kg of hydrogen, then we will not get the same value of PV/T at the point where the curves meet the y-axis. This is because the molecular mass of hydrogen (2.02 u) is different from that of oxygen (32.0 u).
We have: `(PV)/(T)=0.26 J K^-1`
` R=8.314 J "mole" ^-1K^-1`
Molecular mass (M) of `H_2` =2.02 u
`(PV)/(T)=mu R `at constant temperature
Where `mu =(m)/(M)`
m=Mass of` H_2`
`therefore m=(PV)/(T)xx(M)/R`
`=(0.26xx2.02)/(8.31)`
`= 6.3 × 10^–2 g = 6.3 × 10^–5 ` kg of `H_2 `will yield the same value of PV/T.
