Question

Figure shows plot of pV/T versus p for 1.00 x 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 < T₂?

(i) What is the value of pV/T where curves meet on the y-axis?

(d) If we obtained similar plots for 1.00 x 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 pressure high temperature region of the plot)? (Molecular mass of H₂ = 2.02 u. of O₂ = 32.0 u, R = 8.31 J mol^-1).

Answer 1

(a) The dotted plot shows the pV/T is a constant quantity (= uR)

This signifies the ideal gas behaviour.

(b) Here T₁ > T₂

(c) At the point where the curve meets the y-axis, we have pV/T = uR

where u is the number of moles of oxygen gas. Here, Mass of oxygen,

Also, molecular mass, M = 32 x 10^-3 kg

No. of moles, u = m/M = {1.00 x 10^-3}/{32 x 10^-3} = 1/32

pV/T = uR = 1/32 x 8.31

= 0.26 J K^-1

(d) Since the value of pV/T depends upon the number of moles, we will not get the same value for pV/T in case of hydrogen. To obtain the same value of u (i.e., 1/32) and hence pV/T, we must have

= {Mass of hydrogen}/{Molecular mass of hydrogen} = 1/32

Hence, mass of hydrogen = 1/32 x molecular mass

= 1/32 x 2 x 10^-3 kg = 6.25 x 10^-5 kg