Two rigid vessels A and B , each having a volume of 200 cm ^3 , contain an ideal gas ( C_V = 12.5 J K ⁻¹ mol ⁻¹ ). These vessels are connected to a manometer tube containing mercury, as shown in the figure. The temperature is 300 K and the pressure in both vessels is 75 cm of mercury. Determine the number of moles of the gas in each vessel. Use the gas constant R = 8.3 J K ⁻¹ mol ⁻¹ .

Step-by-step solution

Given: Volume of each vessel, V = 200 cm ^3 = 200 10⁻⁶ m ^3 Temperature, T = 300 K Pressure, P = 75 cm of Hg = 0.75 m of Hg Gas constant, R = 8.3 J K ⁻¹ mol ⁻¹ First, we convert the pressure into SI units (Pascals): P = g h Using density of mercury = 13600 kg m ⁻³ and g = 9.8 m s ⁻² : P = 13600 9.8 0.75 = 99960 Pa Using the ideal gas equation, PV = nRT , we can find the number of moles n in each vessel: n = PV RT Substituting the values: n = 99960 200 10⁻⁶ 8.3 300 n = 19.992 2490 0.008 mol The number of moles of th