Question $4(30$ Marks$)($a$)($b$)($c$)$ Show that, for a mixture of Ideal Gases, the mole fraction of each component of the mixture is equal to the partial pressure of that component divided by the total pressure of the mixture. $(6$ Marks$)$ Natural gas $($approximated as CH$4)$ is burned with air at an air:fuel ratio of $50$:$1($on a mass basis$).$ Find $($i$)($ii$)$ the relative air:fuel ratio $($$)$ of the mixture; $(6$ Marks$)$ the molar concentration of CO$2$ in the exhaust products, assuming ideal combustion $(4$ Marks$)$ A passenger car consumes $5\mathrm{.}6$ litres of diesel per $100$ km travelled. Modelling diesel as C$12$H$22,$ with a density of $840$ kg$.$m$-3,$ calculate the vehicle$$s CO$2$ emissions in grams of CO$2$ per km travelled.