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The r.m.s. velocity of hydrogen at 27^{o}C, R = 8.314 J mol^{-1 }K^{-1} is :

The average velocity of gas particles is found using the root mean square velocity formula

μ

_{rms}= (3RT/M)

^{½}

where

μ

_{rms}= root mean square velocity in m/sec

R= ideal gas constant = 8.3145 (kg·m

^{2}/sec

^{2})/K·mol

T = absolute temperature in Kelvin

M = mass of a mole of the gas in

**kilograms**.

The temperature must be converted to Kelvin and the molar mass must be found in kg to complete this problem.

**Step 1**Find the absolute temperature using the Celsius to Kelvin conversion formula:

T = °C + 273

T = 27 + 273

T = 300 K

**Step 2**Find molar mass in kg:

From the periodic table molar mass of hydrogen = 1 g/mol.

Hydrogen gas (H

_{2}) is comprised of two hydrogen atoms bonded together. Therefore:

Molar mass of H

_{2}= 2 x 1

molar mass of H

_{2}= 2 g/mol

Convert this to kg/mol:

molar mass ofH

_{2}= 2 g/mol x 1 kg/1000 g

molar mass of H

_{2}= 0.2 x 10

^{-3}kg/mol

**Step 3**- Find μ

_{rms}

μ

_{rms}= (3RT/M)

^{½}

μ

_{rms}= [3(8.3145 (kg·m

^{2}/sec

^{2})/K·mol)(300 K)/0.2 x 10

^{-3}kg/mol]

^{½}

μ

_{rms}= (2.128 x 10

^{5}m

^{2}/sec

^{2})

^{½}

μ

_{rms}=193.4 m/sec

**Answer:**

The average velocity or root mean square velocity of a molecule in a sample of oxygen at 27 °C is 193.4 m/sec.

Regards

**
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