# A mixture of Nitrogen, Oxygen, and Helium gas is collected in a container at 1 atmosphere, if the partial pressure of oxygen is 320 mm and helium's pressure is 112, what is the partial pressure of the nitrogen?

May 10, 2018

$\text{The sum of the partial pressures is equal to the total pressure....}$

#### Explanation:

And so ${P}_{\text{Total"=SigmaP_"n}}$

And we know $1 \cdot a t m \equiv 760 \cdot m m \cdot H g$....here a unit of length is used as a unit of pressure.

$1 \cdot a t m = \left\{\frac{\left(320 + 112 + {P}_{{N}_{2}}\right) \cdot m m \cdot H g}{760 \cdot m m \cdot H g \cdot a t {m}^{-} 1}\right\}$

${P}_{{N}_{2}} = \left(760 - 320 - 112\right) \cdot m m \cdot H g = 328 \cdot m m \cdot H g$

${P}_{{N}_{2}} = \frac{328 \cdot m m \cdot H g}{760 \cdot m m \cdot H g} \cong \frac{1}{2} \cdot a t m$

May 10, 2018

328 mmHg

#### Explanation:

Assumptions made: Partial pressures given for oxygen and helium are in mmHg and required answer is in mm Hg.

First, convert the total pressure of system 1 atm to mm Hg:

${P}_{\text{total}} = 1 a t m \cdot \frac{760 m m H g}{1 a t m} = 760 m m H g$

According to Dalton's Law of partial pressure:

${P}_{\text{total"=P_"oxygen"+P_"helium"+P_"nitrogen}}$

$760 = 320 + 112 + {P}_{\text{nitrogen}}$

${P}_{\text{nitrogen}} = 760 - 320 - 112 = 328 m m H g$

If you need the value in atmosphere:
${P}_{\text{nitrogen}} = 328 m m H g \cdot \frac{1 a t m}{760 m m H g} = 0.432 a t m$