The r.m.s. velocity of hydrogen at 27oC, R = 8.314 J mol-1 K-1 is :

Dear Student,

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

μrms = (3RT/M)½

where
μrms = root mean square velocity in m/sec
R= ideal gas constant = 8.3145 (kg·m2/sec2)/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 (H2) is comprised of two hydrogen atoms bonded together. Therefore:
Molar mass of H2= 2 x 1
molar mass of H2= 2 g/mol

Convert this to kg/mol:

molar mass ofH2 = 2 g/mol x 1 kg/1000 g
molar mass of H2 = 0.2 x 10-3 kg/mol

Step 3 - Find μrms

μrms = (3RT/M)½
μrms = [3(8.3145 (kg·m2/sec2)/K·mol)(300 K)/0.2 x 10-3 kg/mol]½
μrms = (2.128 x 105 m2/sec2)½
μrms =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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