A mixture of N _ 2 and Ar gases in a cylinder contains 7g of N _ 2...

Mass of ${N}_{2}=7g$

Moles of ${N}_{2} = \dfrac{7}{28} = \dfrac{1}{4}$

Mass of $Ar = 8g$

Moles of $Ar = \dfrac{8}{40} = \dfrac{1}{5}$

${\left(Partialpressure\right)}_{{N}_{2}} = {P}_{T} \times {\left(molefraction\right)}_{{N}_{2}}$

$= 27 \times \dfrac{1 / 4}{1 / 4 + 1 / 5}$

$= 27 \times \dfrac{1 / 4}{9 / 20}$

$= 27 \times \dfrac{20}{4 \times 9}$

$= 3 \times 5$

$= 15\text{bar}$