# A deep-sea diver uses a gas cylinder with a volume of 10.0 L and a content of 51.2 g of O_2, and 32.6 g of He. What is the partial pressure of each gas and the total pressure if the temperature of the gas is 19°C?

Jun 12, 2016

${P}_{\text{Total"=P_"helium"+P_"dioxygen}}$ $\cong$ $24 \cdot a t m$

#### Explanation:

Dalton's law of partial pressures states that in a gaseous mixture, the partial pressure exerted by a component gas is the SAME as if that gas had occupied the container ALONE.

Thus we can calculate the partial pressures of each component by means of separate Ideal Gas Equations $P = \frac{n R T}{V}$:

${P}_{H e}$ $=$ $\frac{32.6 \cdot g}{4.00 \cdot g \cdot m o {l}^{-} 1} \times 0.0821 \cdot L \cdot a t m \cdot {K}^{-} 1 \cdot m o {l}^{-} 1 \times 292 \cdot K \times \frac{1}{10.0 \cdot L}$

$=$ $19.5 \cdot a t m$

${P}_{\text{dioxygen}}$ $=$ $\frac{51.2 \cdot g}{32.00 \cdot g \cdot m o {l}^{-} 1} \times 0.0821 \cdot L \cdot a t m \cdot {K}^{-} 1 \cdot m o {l}^{-} 1 \times 292 \cdot K \times \frac{1}{10.0 \cdot L}$

$=$ $3.84 \cdot a t m$

${P}_{\text{Total}}$ $=$ ${P}_{H e} + {P}_{\text{dioxygen}}$ $=$

$\left(19.5 + 3.84\right) \cdot a t m$

Interestingly, the reason why divers use helium in these circumstances, is that the alternative, dinitrogen, is highly intoxicating at high pressures, and at depth may cause nitrogen narcosis.