Find the volume of gas, which contains 4 * 10 ^ 25 molecules at a temperature of 147 ° C and a pressure of 138 kPa.

| September 5, 2021 | education

We translate all the values ​​from given to the SI system:
t = 147 ° C = 420 K = T.
p = 138 kPa = 138,000 Pa.
Mendeleev-Clapeyron equation
pV = (m / M) * R * T, where p is the gas pressure, V is the gas volume, m is the gas mass, M is the molar mass of the gas, R is the universal gas constant 8.31 J / (mol * K), T is the gas temperature.
Let’s write an expression to determine the amount of a substance:
ν = m / M = N / Na, where m is the mass of the substance, M is the molar mass of the substance, N is the number of particles, Na is Avogadro’s constant Na = 6.023 * 10 ^ 23 1 / mol.
Taking this expression into account, we write down the Mendeleev-Clapeyron equation:
pV = (m / M) * R * T = (N / Nа) * R * T
Let us express the volume from this equation:
V = N * R * T / (p * Na)
Substitute the numbers and find the volume:
V = N * R * T / (p * Na) = 4 * 10 ^ 25 * 8.31 * 420 / (138000 * 6.023 * 10 ^ 23) = 1.68 m³.
Answer: the volume of gas is 1.68 m³.



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