At 35°C, argon has a velocity of 300 m/s. What is the velocity of helium at the same temperature?

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Answer 1 · 2018-06-11T20:28:55

$948 m/s$ $"948 m/s"$

Velocity of gas molecules at constant temperature is inversely proportional to square root of Molar mass of gas

$v \propto \frac{1}{\sqrt{M}}$ $"v" ∝ 1/sqrt"M"$

From above

$\frac{v_{He}}{v_{Ar}} = \sqrt{\frac{M_{Ar}}{M_{He}}}$ $"v"_"He"/"v"_"Ar" = sqrt("M"_"Ar"/"M"_"He")$

$v_{He} = v_{Ar} \times \sqrt{\frac{M_{Ar}}{M_{He}}}$ $"v"_"He" = "v"_"Ar" × sqrt("M"_"Ar"/"M"_"He")$

$v_{He} = 300. m/s \times \sqrt{\frac{39.948 g/mol}{4.0026 g/mol}}$ $color(white)("v"_"He") = "300. m/s" × sqrt("39.948 g/mol"/"4.0026 g/mol")$

$v_{He} = 947 ._{8} m/s$ $color(white)("v"_"He") = 947._8 "m/s"$