Kinetic Theory

Question : 3

Total: 14

Figure shows plot of PV/T versus P for 1.00×10–3 kg of oxygen gas at two different temperatures.

(a) What does the dotted plot signify?
(b) Which is true: T1>T2‌or‌T1<T2?
(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 × 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 hightemperature region of the plot)?
(Molecular mass of H2=2.02u,of‌O2=32.0u,R=8.31Jmol–1K–1.)

Solution:

(a) Since the dotted plot is parallel to P-axis, it tells that value of

(=nR) remains constant even when P is changed.
(b) Curve at temperature T1 is more close to the dotted plot than the curve at the temperature T2. Since the behaviour of a real gas approaches the perfect gas behaviour, as the temperature is increased therefore T1>T2.
(c) If the amount of gas under consideration is 1 mole, then the value of PV/T, where the curves meet PV/T-axis will be R(=8.31Jmole–1K–1). For oxygen, molecular mass is 32.0 g i.e. 32.0×10–3kg. Since mass of oxygen gas under considerations is 1.0×10–3 kg, the value of PV/T, where the curves meet the PV/T-axis is given by

8.31

32.0×10−3

×1.0×10−3
=0.26JK−1
(d) If we obtained similar plots for 1.0×10–3 kg of hydrogen, the value of PV/T, where the curves meet the y-axis will not be the same.
Since molecular mass of hydrogen is 2.02×10–3kg, the mass of hydrogen that will yield same value of PV/T i.e.,0.26JK–1 will be

2.02×10−3

8.31

×0.26
=6.32×10−5 kg

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