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 the dotted plot signify?
(b) Which is true: T1 > T2 or T1 < T2?
(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 high temperature region of the plot)? (Molecular mass of H2 = 2.02 u, of O2 = 32.0 u, R = 8.31 J mo1–1 K–1.)
(a) Seeing that the dotted line doesn’t vary with pressure and by using the Ideal Gas Law (PV = nRT ) we can say that it implies the ideal behaviour of Gas.
Wkt…
PV = nRT
⇒ nR = PV/T = constant
The dotted plot implies PV/T = constant.
(b) T2 is heavily deviates from ideal behaviour than T1.
⇒ T1 > T2 is true.
T1 > T2 is true.
(c) Using PV = nRT
⇒ PV/T = nR
Given: Mass of the gas = 1 × 10-3 kg = 1 g
Molecular mass of Oxygen = 32g/mole
So, number of moles = given weight/molecular weight
⇒ number of moles = 1/32
So, nR = 1/32 × 8.314 J / mol /K = 0.26 J/K
Hence, value of PV/T = 0.26 J/K.
(d) 1g of Hydrogen doesn't represent the same number of mole. molecular mass of H2 = 2g/mol
Hence, number of moles of Hydrogen required is 1/32
So, mass of H2 required = no of moles of H2 × molecular mass of H2
⇒ mass of H2 required = 1/32mole × 2 g/mol = 1/16 g = 0.0625 g
⇒ Hence the mass of H2 required = 0.0625 g