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  • 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?

Q13.3 Figure 13.8 shows plot of PV/T  versus P for 1.00\times 10^{-3}  kg  of oxygen gas at two different temperatures.

(a) What does the dotted plot signify?
(b) Which is true: T_{1}> T_{2}\: \: orT_{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 for1.00\times 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 high temperature
region of the plot) ? (Molecular mass of H_{2}=2.02\mu, of O_{2}=32.0\mu,
R=8.31J mol^{-1}K^{-1}.)

Answers (1)

best_answer

(a) The dotted plot corresponds to the ideal gas behaviour.

(b) We know the behaviour of a real gas tends close to that of ideal gas as its temperature increases and since the plot corresponding to temperature T1 is closer to the horizontal line that the one corresponding to T2 we conclude T1 is greater than T2.

(c)  As per the ideal gas equation

\frac{PV}{T}=nR

The molar mass of oxygen = 32 g

n=\frac{1}{32}

R = 8.314

\\nR=\frac{1}{32}\times 8.314\\ nR=0.256JK^{-1}

(d) If we obtained similar plots for1.00\times 10^{-3}  kg of hydrogen we would not get the same
value of PV/T at the point where the curves meet on the y-axis as 1 g of Hydrogen would contain more moles than 1 g of Oxygen because of having smaller molar mass. 

Molar Mass of Hydrogen M = 2 g

 mass of hydrogen 

m=\frac{PV}{T} \frac{M}{R}={0.256}\times \frac{2}{8.314}=5.48\times10^{-5}Kg

 

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Sayak

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