What is Loschmidt’s number? How is it related to Avogadro’s number?
1 answer:
1. Loschmidt’s number also called as Loschmidt’s constant, n₀ is the number of particles of an ideal gas in a given volume (m³). The unit is m⁻³. At standard pressure (1 atm) and temperature (0 °C) the value of <span>Loschmidt’s number is 2.686 x 10</span>²⁵ m⁻³.
2. Loschmidt’s number,n₀ can be expressed as,
n₀ =
where P is the pressure of the gas, K is the Boltzmann constant and T is the <span>thermodynamic temperature.
Since, k = R/NA (where R is the universal gas constant and NA is the Avogadro constant)
</span>n₀ =
n₀ =
Hence, n₀ α NA
2. Loschmidt’s number,n₀ can be expressed as,
n₀ =
where P is the pressure of the gas, K is the Boltzmann constant and T is the <span>thermodynamic temperature.
Since, k = R/NA (where R is the universal gas constant and NA is the Avogadro constant)
</span>n₀ =
n₀ =
Hence, n₀ α NA
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Answer:
The molar mass of the gas is 36.25 g/mol.
Explanation:
- To solve this problem, we can use the mathematical relation:
ν =
Where, ν is the speed of light in a gas <em>(ν = 449 m/s)</em>,
R is the universal gas constant <em>(R = 8.314 J/mol.K)</em>,
T is the temperature of the gas in Kelvin <em>(T = 20 °C + 273 = 293 K)</em>,
M is the molar mass of the gas in <em>(Kg/mol)</em>.
ν =
(449 m/s) = √ (3(8.314 J/mol.K) (293 K) / M,
<em>by squaring the two sides:</em>
(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.
<em>∴ The molar mass of the gas is 36.25 g/mol.</em>