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Hi.

The root mean square velocity of oxygen molecules is 480m/s while the pressure is 20kPa.

What is the concentration (particles/volume) of oxygen?

PV=nRT

[tex] E_{kin}=\frac{m \overline{v}^2}{2}=\frac{3}{2}kT [/tex]

[tex] m \overline{v}^2=3kT \Rightarrow T= \frac{m \overline{v}^2}{3k} [/tex]

[tex] PV=nR \frac{m \overline{v}^2}{3k} \Rightarrow n=\frac{3kPV}{Rm \overline{v}^2} [/tex] where [tex] m=2 \times 16 \times 1.66 \times 10^{-27} kg [/tex]

I set V=1m^3 and get n=8.137mol and therefore [tex] \frac{n \times n_{a}}{V}=4.899 m^{-3} [/tex] where [tex] n_{a}=6.02 \times 10^{23} [/tex]

Is this correct? I'm sure there's a simpler way to do this.

**1. Homework Statement**The root mean square velocity of oxygen molecules is 480m/s while the pressure is 20kPa.

What is the concentration (particles/volume) of oxygen?

**2. Homework Equations**PV=nRT

[tex] E_{kin}=\frac{m \overline{v}^2}{2}=\frac{3}{2}kT [/tex]

**3. The Attempt at a Solution**[tex] m \overline{v}^2=3kT \Rightarrow T= \frac{m \overline{v}^2}{3k} [/tex]

[tex] PV=nR \frac{m \overline{v}^2}{3k} \Rightarrow n=\frac{3kPV}{Rm \overline{v}^2} [/tex] where [tex] m=2 \times 16 \times 1.66 \times 10^{-27} kg [/tex]

I set V=1m^3 and get n=8.137mol and therefore [tex] \frac{n \times n_{a}}{V}=4.899 m^{-3} [/tex] where [tex] n_{a}=6.02 \times 10^{23} [/tex]

Is this correct? I'm sure there's a simpler way to do this.

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