Determine the number of molecules present in 1 cm ^3 of an ideal gas at 0^ C and a pressure of 10⁻⁵ mm of mercury.

Step-by-step solution

Given, Volume V = 1 cm ^3 = 10⁻⁶ m ^3 Temperature T = 0^ C = 273 K Pressure P = 10⁻⁵ mm of Hg = 10⁻⁵ 760 1.013 10^5 N/m ^2 1.33 10⁻³ N/m ^2 Using the ideal gas equation, PV = nRT = N N_A RT where N is the number of molecules and N_A is Avogadro's number. N = PV N_A RT Substituting the values, N = 1.33 10⁻³ 10⁻⁶ 6.022 10²³ 8.314 273 N = 8.009 10¹⁴ 2269.7 N 3.53 10¹¹