$8\mathrm{.}13$ A mixture of benzene vapour and nitrogen gas at $105$kPa and $330K$ contains benzene vapour to the extent that it exerts a partial pressure of $15$kPa. The vapour pressure of benzene is given by the Antoine equation

$ln{P}^S=13\mathrm{.}8858-\frac{2788\mathrm{.}51}{T-52\mathrm{.}36}$

Determine the following:

$($a$)$ The mole fraction of benzene in the mixture

$($b$)$ The weight fraction of benzene in the mixture

$($c$)$ The molal humidity

$($d$)$ The absolute humidity

$($e$)$ The molal saturation humidity

$($f$)$ The absolute saturation humidity

$($g$)$ The mass of benzene in $100m^3$ of the mixture

$($h$)$ The percent humidity

$($i$)$ The percent relative humidity

$8\mathrm{.}14$ A mixture of benzene vapour and air contains $10\%$ benzene by volume at $300K$ and $101\mathrm{.}3$kPa. The vapour pressure of benzene at $300K$ is $13\mathrm{.}8$kPa. Calculate the following:

$($a$)$ The partial pressure of benzene in the mixture

$($b$)$ The weight fraction of benzene in the mixture

$($c$)$ The molal humidity

$($d$)$ The absolute humidity

$($e$)$ The percent saturation

$($f$)$ The percent relative saturation

$($g$)$ The mass of air in $100m^3$ of the mixture

$8\mathrm{.}15$ The percent saturation of a mixture of acetone vapour and nitrogen at $105$kPa and $300K$ is found to be $80\%.$ The vapour pressure $(kPa)$ of acetone is given by the Antoine equation with constants, $A=14\mathrm{.}39155,B=2795\mathrm{.}817$ and $C=43\mathrm{.}198.$ Calculate the following:

$($a$)$ The molal humidity

$($b$)$ The absolute humidity

$($c$)$ The partial pressure of acetone

$($d$)$ The relative saturation

$($e$)$ The dew point

$8\mathrm{.}16$ Moist air contains $0\mathrm{.}025kg$ water vapour per cubic metre of the mixture at $313K$ and $101\mathrm{.}3$kPa. Calculate the following:

$($a$)$ The partial pressure of water vapour

$($b$)$ The relative saturation

$($c$)$ The absolute humidity of the air

$($d$)$ The percent saturation

$($e$)$ The temperature to which the mixture be heated so that its percent saturation becomes $10\%$no