Calculate the number of molecules of methane in 0.50 m^3 of the gas at a pressure of 2.0 × 10^2 kPa and a temperature of exactly 300 K.

Question

Calculate the number of molecules of methane in 0.50 m³ of the gas at a pressure of 2.0 × 10² kPa and a temperature of exactly 300 K.

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Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

Given :

V = 0.5 m³,

P = 2.0 × 10 kPa = 2.0 × 10⁵ Pa

T = 300 K,

R = 8.314 J K^-1 mol^-1

To find :

Number of molecules of methane gas

Formula :

PV = nRT

Calculation :

According to ideal gas equation,

n = \(\frac{PV}{RT}\)

= \(\frac{2.0\times 10^5 \times 0.5}{8.314 \times 300}\)

= 40 mol

Number of molecules = n × NA

= 40 × 6.022 × 10²³

= 2.4088 × 10²³ ≈ 2.409 × 10²⁵

∴ The number of molecules of methane gas present is 2.409 × 10²⁵ molecules.

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