Question

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

1. What does the dotted plot signify? 

2. Which is true: T₁ > T₂ or T₁ < T₂? 

3. What is the value of PV/T where the curves meet on the yaxis? 

4. 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 high-temperature region of the plot)? (Molecular mass of H₂ = 2.02 u, of 0₂ = 32.0 u, = 8.31 J mol^-1 K^-1.)

Answer 1

1. The dotted plot signifies the behavior of equal amount of an ideal gas. Since the ideal gas satisfies the equation PV = nRT, nR = \(\frac{PV}{T}\) is a constant forgiven amount (n) of an ideal gas.

Thus \(\frac{PV}{T}\) is independent of pressure.

2. The \(\frac{PV}{T}\) curve at temperature T₁ is closer to the dotted line (ideal gas) than the \(\frac{PV}{T}\) curve at T₂. Since a real gas at higher temperature behaves more like an ideal gas than a real gas at lower temperature, T₁ >T₂.

3. Since all three curves meet on the y-axis the value of \(\frac{PV}{T}\) = nR, where n is the no of moles of ideal gas. 

∴ n = no. of moles of oxygen gas

∴\(\frac{PV}{T}\) = nR = 0.031 × 8.314

= 0.26 J K^-1

4. Since the molecular mass of hydrogen is less than that of oxygen, the number of moles is 1 g of hydrogen is more than that of oxygen. There fore, the value of \(\frac{PV}{T}\) at the point where the curves meet the Y-axis will not be same for oxygen and hydrogen gases.

n = 0.031 mol of H₂ will yield same \(\frac{PV}{T}\)

as that of 1 g of O₂ gas.

∴ Mass of H₂ gas

= 0. 311 × 2.02 = 0. 0626g.