Question

compute the root - mean - square speed of h₂ molecules in a sample of hydrogen gas at a temperature of 101°c
use the references to access important values if needed for this question.

Explanation:

Step1: Convert temperature to Kelvin

The formula for root - mean - square speed is \(v_{rms}=\sqrt{\frac{3RT}{M}}\). First, convert the temperature \(T = 101^{\circ}C\) to Kelvin. Using the formula \(T(K)=T(^{\circ}C)+273.15\), we have \(T=(101 + 273.15)K=374.15K\).

Step2: Identify molar mass

For \(H_2\), the molar mass \(M = 2\times10^{- 3}kg/mol\) (since the molar mass of \(H\) is \(1g/mol\) and \(H_2\) has two \(H\) atoms). The gas constant \(R = 8.314J/(mol\cdot K)\).

Step3: Calculate root - mean - square speed

Substitute \(R = 8.314J/(mol\cdot K)\), \(T = 374.15K\), and \(M=2\times 10^{-3}kg/mol\) into the formula \(v_{rms}=\sqrt{\frac{3RT}{M}}\).

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Answer:

\(2161m/s\)