Question

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compute the root - mean - square speed of h₂ molecules in a sample of hydrogen gas at a temperature of 200°c

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Explanation:

Step1: Convert temperature to Kelvin

The formula for root - mean - square speed \(v_{rms}=\sqrt{\frac{3RT}{M}}\). First, convert \(T = 200^{\circ}C\) to Kelvin. \(T=(200 + 273.15)\text{K}=473.15\text{K}\). The gas constant \(R = 8.314\text{J/(mol·K)}\), and for \(H_2\), the molar mass \(M=2\times10^{- 3}\text{kg/mol}\) (since the molar mass of \(H\) is \(1\text{g/mol}\) and \(H_2\) has two \(H\) atoms).

Step2: Calculate \(v_{rms}\)

Substitute the values into the formula \(v_{rms}=\sqrt{\frac{3RT}{M}}\).

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Answer:

\(1716\)