Test Index

Kinetic Theory

© examsnet.com
Question : 3 of 14
Marks: +1, -0
Figure shows plot of PV/T versus P for 1.00×1031.00 \times 10^{-3} kg of oxygen gas at two different temperatures.
(a) What does the dotted plot signify?
(b) Which is true: T1>T2 or T1<T2T_1 > T_2 \text{ 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 × 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, of O2=32.0u,R=8.31Jmol1K1.)\mathrm{H}_2 = 2.02\,\mathrm{u}, \text{ of } \mathrm{O}_2 = 32.0\,\mathrm{u}, R = 8.31\,\mathrm{J}\,\mathrm{mol}^{-1}\,\mathrm{K}^{-1}.)
Solution:  
(a) Since the dotted plot is parallel to P-axis, it tells that value of PVT(=nR)\frac{PV}{T} (= nR) remains constant even when P is changed.
(b) Curve at temperature T1T_1 is more close to the dotted plot than the curve at the temperature T2T_2. Since the behaviour of a real gas approaches the perfect gas behaviour, as the temperature is increased therefore T1>T2.T_1 > T_2.
(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(=8.31Jmol1K1).R (= 8.31\,\mathrm{J}\,\mathrm{mol}^{-1}\,\mathrm{K}^{-1}). For oxygen, molecular mass is 32.0 g i.e. 32.0×103kg32.0 \times 10^{-3}\,\mathrm{kg}. Since mass of oxygen gas under considerations is 1.0×1031.0 \times 10^{-3} kg, the value of PV/T, where the curves meet the PV/T-axis is given by
PVT=8.3132.0×103×1.0×103\frac{PV}{T} = \frac{8.31}{32.0 \times 10^{-3}} \times 1.0 \times 10^{-3}
=0.26JK1= 0.26\,\mathrm{J}\,\mathrm{K}^{-1}
(d) If we obtained similar plots for 1.0×1031.0 \times 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 2.02×1032.02 \times 10^{-3}kg, the mass of hydrogen that will yield same value of PV/T i.e.,0.26JK10.26\,\mathrm{J}\,\mathrm{K}^{-1} will be
2.02×1038.31×0.26\frac{2.02 \times 10^{-3}}{8.31} \times 0.26
=6.32×105kg= 6.32 \times 10^{-5}\,\mathrm{kg}
© examsnet.com
Go to Question: