# The total pressure is 600 mmHg after 0.50 moles of nitrogen gas, N_2, and 1.0 mole of nitrogen dioxide, NO_2, gas are mixed in a closed container. There is no reaction between the gases. What is the partial pressure of the nitrogen dioxide?

Jun 27, 2017

${P}_{N {O}_{2}} = 400 \cdot m m \cdot H g$

#### Explanation:

Old $\text{Dalton's Law of partial pressures}$ tells us that in a gaseous mixture, the partial pressure exerted by a component gas is the same as the pressure it would exert if it ALONE occupied the container.

The total pressure is the sum of the individual partial pressures.

Thus ${P}_{\text{Total}} = {P}_{N {O}_{2}} + {P}_{{N}_{2}} = 600 \cdot m m \cdot H g$

But ${P}_{N {O}_{2}} = \frac{1.0 \cdot m o l \times R T}{V}$

And ${P}_{{N}_{2}} = \frac{0.50 \cdot m o l \times R T}{V} = \frac{1}{2} \times {P}_{N {O}_{2}}$

And so ${P}_{\text{Total}} = 600 \cdot m m \cdot H g = \frac{3}{2} \times {P}_{N {O}_{2}}$

And finally, ${P}_{N {O}_{2}} = 400 \cdot m m \cdot H g$, and ${P}_{{N}_{2}} = 200 \cdot m m \cdot H g$; the which satisfies Dalton's Law....