During its manufacturing, an electric bulb of volume 250 cc is sealed at a pressure of 10⁻³ mm of mercury and a temperature of 27^ C . Determine the number of air molecules contained in the bulb. (Take the Avogadro constant = 6 10²³ mol ⁻¹ , density of mercury = 13600 kg m ⁻³ , and g = 10 m s ⁻² )

Step-by-step solution

Given: Volume of the bulb, V = 250 cc = 250 10⁻⁶ m ^3 Pressure, P = 10⁻³ mm of Hg = 10⁻⁶ m of Hg Density of mercury, = 13600 kg m ⁻³ Acceleration due to gravity, g = 10 m s ⁻² Temperature, T = 27^ C = 300 K The pressure in Pascals is: P = h g = 10⁻⁶ 13600 10 = 0.136 Pa Using the ideal gas equation: PV = nRT = N N_A RT Rearranging for the number of molecules N : N = PVN_A RT Substituting the values (using R = 8.314 J mol ⁻¹ K ⁻¹ ): N = 0.136 250 10⁻⁶ 6 10²³ 8.314 300 N = 0.136 250 2 10¹⁷ 8.314 N = 68 10¹⁷ 8.314 8.17