Question
When a sample of gas is compressed at constant temperature from $$15\,atm$$ to $$60\,atm,$$ its volume changes from $$76\,c{m^3}$$ to $$20.5\,c{m^3}.$$ Which of the following statements are possible explanations of this behaviour?
(i) The gas behaves non-ideally
(ii) The gas dimerises
(iii) The gas is adsorbed into the vessel walls
A.
(i), (ii) and (iii)
B.
(i) and (ii) only
C.
(ii) and (iii) only
D.
(i) only
Answer :
(i) only
Solution :
$$\eqalign{
& {\text{Given,}}\,{P_1} = 15\,atm,\,{P_2} = 60\,atm \cr
& {V_1} = 76\,c{m^3},\,{V_2} = 20.5\,c{m^3}. \cr} $$
If the gas is an ideal gas, then according to Boyle's law, it must follow the equation,
$$\eqalign{
& {P_1}{V_1} = {P_2}{V_2} \cr
& {P_1} \times {V_1} = 15 \times 76 = 1140 \cr
& {P_2} \times {V_2} = 60 \times 20.5 = 1230 \cr
& \therefore \,\,{P_1}{V_1} \ne {P_2}{V_2} \cr} $$
∴ The gas behaves non-ideally.
The given information is not sufficient to comment on other statements.