# What is partial pressure of oxygen at sea level?

Sep 4, 2017

${P}_{{O}_{2}} = 0.21 \times 1 \cdot a t m$

#### Explanation:

This illustrates old Dalton's Law of Partial Pressures. In a gaseous mixture, the partial pressure exerted by a component gas is the same as if it alone occupied the container.....

${P}_{\text{Total"=SigmaP_"component gases}}$

$= {P}_{1} + {P}_{2.} \ldots . + {P}_{n}$, assuming ideality.....

${P}_{\text{Total}} = \frac{{n}_{1} R T}{V} + \ldots \ldots \ldots \ldots \frac{{n}_{n} R T}{V}$

${P}_{\text{Total}} = \frac{R T}{V} \left\{{n}_{1} + {n}_{2} + \ldots . {n}_{n}\right\}$

And thus ${P}_{1} / {P}_{\text{Total}} = \frac{\frac{R T}{V} {n}_{1}}{\frac{R T}{V} \left\{{n}_{1} + {n}_{2} + \ldots . {n}_{n}\right\}}$

${P}_{1} / {P}_{\text{Total}} = \frac{{n}_{1}}{\left\{{n}_{1} + {n}_{2} + \ldots . {n}_{n}\right\}} = {\chi}_{{n}_{1}}$

Where ${\chi}_{{n}_{1}} = \text{mole fraction of the component }$

And here the container is conveniently the atmosphere, which to a first approx. is 78% dinitrogen, and 21% dioxygen......

And so what is ${P}_{{O}_{2}}$?