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.

a plasma is a warm ionized gasoline consisting of approximately equal numbers of definitely charged ions and negatively charged electrons. the characteristics of plasmas are notably unique from the ones of ordinary neutral gases in order that plasmas are considered a awesome "fourth kingdom of remember."