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Question -

Figure 13.8 shows plot of PV/T versus P for 1.00×10-3 kg of oxygen gas at two different temperatures.

(a) What does thedotted plot signify?

(b) Which is true: T1 > T2 or T1 < T2?

(c) What is the value of PV/Twhere the curves meet on the y-axis?

(d) If we obtained similar plotsfor 1.00×10-3 kg of hydrogen,would we get the same value of PV/T at the point where the curves meet on they-axis? If not, what mass of hydrogen yields the same value of PV/T (for lowpressure high temperature region of the plot)? (Molecular mass of H2 = 2.02 u, of O2 = 32.0 u, R = 8.31J mo1–1 K–1.)



Answer -

(a) dotted plot is parallel to X-axis, signifying that nR [PV/T= nR] is independent of P. Thus it is representing ideal gas behaviour

(b) the graph at temperature T1 is closer to ideal behaviour (because closer todotted line) hence, T1 >T2 (higher thetemperature, ideal behaviour is the higher)

(c) use PV = nRT

PV/ T = nR

Mass of the gas = 1 x 10-3 kg= 1 g

Molecular mass of O2 = 32g/ mol

Hence,

Number of mole = given weight / molecular weight

= 1/ 32

So, nR = 1/ 32 x 8.314 = 0.26 J/ K

Hence,

Value of PV / T = 0.26 J/ K

(d) 1 g of H2 doesn’trepresent the same number of mole

Eg. molecular mass of H2 = 2 g/mol

Hence, number of moles of H2 require is 1/32 (as per the question)

Therefore,

Mass of H2 required= no. of mole of H2 xmolecular mass of H2

= 1/ 32 x 2

= 1 / 16 g

= 0.0625 g

= 6.3 x 10-5 kg

Hence, 6.3 x 10-5 kgof H2 wouldyield the same value

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