Ascientist 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?

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

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

By squaring both sides

Thus, the mass is 36.25 g/mol.

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

Explanation:

ν =

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 =

(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.

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