Question

Question: The lowest possible temperature in outer space is 2.7 K. What is the rms speed of hydrogen molecules at this temperature? (The molar mass is$\mathbf{2}\mathbf{.}\mathbf{02}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathit{k}\mathit{g}\mathbf{/}\mathit{m}\mathit{o}\mathit{l}$).

Short answer

Answer:

The RMS speed of the hydrogen molecules is $1.8\times {10}^{2}m/s$.

Step-by-step solution

Given data

The temperature is T = 2.7 K

The molar mass of hydrogen molecules is,$M=2.02\times {10}^{-3}kg/mol$

Concept introduction

We can find the rms speed using its formula in terms of R, temperature, and molar mass.

The expression for the RMS speed is given by,

$v=\sqrt{\frac{3RT}{M}}$

Calculate the rms speed of hydrogen molecules at the given temperature 

The RMS speed of hydrogen molecules is

$v=\sqrt{\frac{3RT}{M}}$

Molar mass of hydrogen is$M=2.02\times {10}^{-3}kg/mol$

$$\begin{gathered} v=\sqrt{\frac{3\left(8.314\right)\left(2.7\right)}{2.02\times {10}^{-3}}} \\ v=182.58 \\ \approx 1.8\times {10}^{2}m/s \end{gathered}$$

Therefore the RMS speed of the hydrogen molecules is$1.8\times {10}^{2}m/s$ .