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?
1 answer:
Answer:
The molar mass of the gas is 36.25 g/mol.
Explanation:
- To determine this, we utilize the mathematical relationship:
ν =
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 =
(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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