For a gas at room temperature of 27^{circ}C,t | vedclass

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Question

(A) Given: Temperature $T = 27^{\circ}C = 27 + 273 = 300 \, K$. Root mean square speed $
u_{rms} = 1930 \, m/s$. Gas constant $R = 8.3 \, J/mol \cdot

Vedclass · Accepted Answer

$H_2$

Vedclass · Answer

(A) Given: Temperature $T = 27^{\circ}C = 27 + 273 = 300 \, K$. Root mean square speed $
u_{rms} = 1930 \, m/s$. Gas constant $R = 8.3 \, J/mol \cdot K$. The formula for $
u_{rms}$ is $
u_{rms} = \sqrt{\frac{3RT}{M}}$. Squaring both sides,we get $
u_{rms}^2 = \frac{3RT}{M}$. Rearranging for molar mass $M$,we get $M = \frac{3RT}{
u_{rms}^2}$. Substituting the values: $M = \frac{3 	imes 8.3 	imes 300}{(1930)^2}$. $M = \frac{7470}{3724900} \approx 0.002 \, kg/mol = 2 \, g/mol$. The molar mass of $H_2$ is $2 \, g/mol$. Therefore,the gas is $H_2$.

For a gas at room temperature of $27^{\circ}C$,the value of $\nu_{rms}$ is $1930 \, m/s$. The gas is.......... $(R = 8.3 \, J/mol \cdot K)$.

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