Question

Gas Note: Figure not drawn to scale. 2005Bb6. ideal gas A piston fitting closely in the cylinder is lightweight and frictionless, and objects of different mass m can be placed on top of it, as shown in the figure above. In order to determine n, you perform an experiment that consists of adding 1 kg masses one at a time on top of the piston, compressing the gas, and allowing the gas to return to room temperature Tbefore measuring the new volume V.) The data collected are given in the table below. You are given a cylinder of cross-sectional area A containing n moles of an m (kg) V (m3) 6.0 x 10-s 4.5 × 10-5 3.6 x 10-3 3.0 x 10-5 2.6 x 10-5 1/V (m-3) 1.7×104 2.2 x 104 2.8 × 104 3.3x 10‘ 3.8 x 104 P (Pa) a. Write a relationship between total pressure P and volume V in terms of the giver quantities and fundamental constants that will llow you to determine n.) PVR b. Calculate the value of P for each value of m and record your values in the data table c. Plot the data on the graph below, labeling the axes with appropriate numbers to You also determine that A-3.0 x 104 m2 and T 300 K. above. indicate the scale. l/V d. Using your graph in part (c), calculate the experimental value of n. 64332 01234

Answer 1

Area (A) = 3.0 times 10^-4 m^2: T = 300 k (a) PV = nRT implies n = PV/RT R = 8.314 J/mol - k When mass of piston = 0 kg, then pressure is Atmosphere pressure. P_a = 1 atm = 101325 Pa 1 kg implies extra pressure P = F/A = mg/A = 1 kg times 9.8 m/s^2/3.0 times 10^-4 = 32,666.6 Pa 2 kg implies 65, 333.2 Pa 3 kg implies 97, 999.8 Pa 4 kg implies 130, 666.4 Pa P_t = P_at + P_ext n = PV/RT implies 0.00243 for 1 kg from Boyle's law Therefore P proportional 1/v