# How many small molecules of gas are in a vessel with a capacity of 480 cm³ at a temperature

August 29, 2021 | education

| **How many small molecules of gas are in a vessel with a capacity of 480 cm³ at a temperature of 20 degrees Celsius and a pressure of 25 kPa?**

For an ideal gas, the following formula is valid:

P = n * k * T, where p is the pressure of an ideal gas (p = 25 kPa = 2 * 10 ^ 3 Pa), n is the concentration of molecules (n = N / V, where N is the number of gas molecules, V is the volume of the vessel (V = 480 cm ^ 3 = 480 * 10 ^ -6 m ^ 3)), k – Boltzmann constant (k = 1.38 * 10 ^ -23 J / K), T – absolute temperature (T = 20 С, which corresponds to a temperature T = 293 K).

Hence:

P = (N / V) * k * T;

N = P * V / (k * T) = (25 * 10 ^ 3) * (480 * 10 ^ -6) / (293 * 1.38 * 10 ^ -23) = 2.97 * 10 ^ 21.

Answer. The number of gas molecules is 2.97 * 10 ^ 21.

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