Answer to Question #149496 in General Chemistry for Kookie

Question

at room temperature, an average hydrogen molecule travels at a speed of 1700 meters/second (about 3000 miles/hr) what is the speed of an average oxygen molecule under the same conditions?

Answer 1

Average speed

$v = \sqrt{\frac{8RT}{πM}}$

R = gas constant

T = temperature

M = molar mass

Since R and T are constants:

$\frac{v}{v’} = \sqrt{\frac{M’}{M}}$

v = velocity of H₂ = 1700 m/s

v’ = velocity of O₂

M(H₂) = 2 g/mol

M(O₂) = 32 g/mol

$v’ = v \sqrt{\frac{M(H_2)}{M(O_2)}} \\ = 1700 \sqrt{\frac{2}{32}} \\ = 1700 \times 0.25 \\ = 425 \; m/s$

Answer: 425 m/s