Find the number of molecules in 0.25 m ^3 of the gas at a pressure 2.0 10^2 kPa and a temperature 300 K . [R = 8.314 J K ⁻¹ mol ⁻¹]

Step-by-step solution

Given: Pressure P = 2.0 10^2 kPa = 2.0 10^5 Pa Volume V = 0.25 m ^3 Temperature T = 300 K Universal gas constant R = 8.314 J K ⁻¹ mol ⁻¹ Using the ideal gas equation, the number of moles n is: PV = nRT n = PV RT = 2.0 10^5 0.25 8.314 300 n = 50000 2494.2 20 mol The total number of molecules N is given by: N = n N_A Substituting Avogadro's number N_A = 6.022 10²³ mol ⁻¹ : N = 20 6.022 10²³ = 1.2044 10²⁵ Answer: 1.2044 10²⁵