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mars1129
8 days ago
11

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?

Chemistry
1 answer:
Tems11 [2.4K]8 days ago
7 0

Answer:

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

Explanation:

  • To determine this, we utilize the mathematical relationship:

ν = \sqrt{3RT/M}

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

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

T stands for 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 both sides:

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

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

Thus, the molar mass of the gas is 36.25 g/mol.


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