Question

A scientist measures the speed of sound in a monatomic gas to be 449 m/s at 20∘C. What is the molar mass of this gas?

Answer 1

Answer:

The molar mass of the gas is 36.25 g/mol.

Explanation:

• To solve this problem, we can use the mathematical relation:

ν = $\sqrt{3RT/M}$

Where, ν is the speed of light in a gas (ν = 449 m/s),

R is the universal gas constant (R = 8.314 J/mol.K),

T is the temperature of the gas in Kelvin (T = 20 °C + 273 = 293 K),

M is the molar mass of the gas in (Kg/mol).

ν = $\sqrt{3RT/M}$

(449 m/s) = √ (3(8.314 J/mol.K) (293 K) / M,

by squaring the two sides:

(449 m/s)² = (3 (8.314 J/mol.K) (293 K)) / M,

∴ M = (3 (8.314 J/mol.K) (293 K) / (449 m/s)² = 7308.006 / 201601 = 0.03625 Kg/mol.

∴ The molar mass of the gas is 36.25 g/mol.