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Question

Given that the rms speed of a helium atom at a certain temperature is $1350 \mathrm{~m} / \mathrm{s}$, find by proportion the rms speed of an oxygen $\left(\mathrm{O}_2\right)$ molecule at this temperature. The molar mass of $\mathrm{O}_2$ is $32.0 \mathrm{~g} / \mathrm{mol}$, and the molar mass of $\mathrm{He}$ is $4.00 \mathrm{~g} / \mathrm{mol}$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2To solve this problem we have to note that at the same temperature both species will have the same kinetic energy so it has to hold

$m_Ov_O^2=m_{He}v_{He}^2$

We can solve this for the oxygen speed

$v_O^2=\frac{m_{He}}{m_O}v_{He}^2=\frac{4}{32}\times 1350^2$

Finally, we have that

$v_O=477\textrm{m/s}$

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