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.

Answer 2

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

What is molar mass?

The molar mass of a compound is the mass of the compound by the amount of the substance in the sample.

Given,

The speed of the sound is 449 m/s

Temperature is 20∘C

Converted to kelvin 293 k

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

By the equation of speed of sound

$\bold{v= \sqrt{\dfrac{3RT}{M} } }$

$\bold{(449 m/s)= \sqrt{\dfrac{3(8.314 J/mol.K) (293 K)}{M} } }$

By squaring both sides

$\bold{(449 m/s)^2= \sqrt{\dfrac{3((8.314 J/mol.K) (293 K))^2}{M} } }$

$\bold{3\dfrac{((8.314 J/mol.K) (293 K))^2}{(449 m/s)^2} = \dfrac{7308.006}{201601} = 0.03625 Kg/mol }$

Thus, the mass is 36.25 g/mol.

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