**root mean square speed (C**_{rms}):

${\mathbf{C}}_{\mathbf{rms}}\mathbf{=}\sqrt{\frac{\mathbf{3}\mathbf{RT}}{\mathbf{M}}}$

µ_{rms} = rms speed,

R = 8.314 J/(mol·K)

T = temperature, K

M = molar mass, kg/mol

• molar mass of N_{2}:

${\mathbf{M}}_{{\mathbf{N}}_{\mathbf{2}}}\mathbf{=}\mathbf{28}\mathbf{.}\mathbf{02}\mathbf{}\frac{\overline{)\mathbf{g}}}{\mathbf{mol}}\mathbf{}\mathbf{\times}\mathbf{}\frac{\mathbf{1}\mathbf{}\mathbf{kg}}{{\mathbf{10}}^{\mathbf{3}}\mathbf{}\overline{)\mathbf{g}}}$

**M _{N2} = 0.02802 kg/mol**

• molar mass of He:

${\mathbf{M}}_{{\mathbf{N}}_{\mathbf{2}}}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{0026}\mathbf{}\frac{\overline{)\mathbf{g}}}{\mathbf{mol}}\mathbf{}\mathbf{\times}\mathbf{}\frac{\mathbf{1}\mathbf{}\mathbf{kg}}{{\mathbf{10}}^{\mathbf{3}}\mathbf{}\overline{)\mathbf{g}}}$

**M _{N2} = 4.0026x10^{-3} kg/mol**

**C _{rms} N_{2} = C_{rms} He**

At what temperature will He atoms have the same C_{rms} value as N_{2} molecules at 25°C? Solve this problem without calculating the value of C_{rms} for N_{2}. C_{rms} is the root mean square speed.

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