Question

Consider three sealed steel tanks, labeled \(\mathrm{X}, \mathrm{Y},\) and \(Z\). Each tank has the same volume and the same temperature. In each tank, one mole of \(\mathrm{CH}_{4}\) is represented by a circle, one mole of oxygen by a square, and one mole of \(\mathrm{SO}_{2}\) by a triangle. Assume that no reaction takes place between these molecules. (a) In which tank is the total pressure highest? (b) In which tank is the partial pressure of \(\mathrm{SO}_{2}\) highest? (c) In which tank is the mass of all three gases the same? (d) Which tank has the heaviest contents?

Short answer

To determine the tank with the highest total pressure, calculate the total pressure for each tank using the ideal gas law and compare the values.

Step-by-step solution

(a) Determining the tank with highest total pressure

Compare the total number of moles (n) of all gases present in each tank, keeping in mind that the volume and temperature are the same for all tanks. To do this: 1. For each tank, calculate the total pressure based on the ideal gas law formula: Total Pressure (P) = (n_total * R * T) / V, where n_total is the sum of moles of all gases in the given tank. 2. Compare the total pressure values of the tanks X, Y, and Z to determine the highest total pressure.

(b) Determining the tank with the highest partial pressure of SO2

Compare the number of moles (n) of SO2 present in each tank, keeping in mind that the volume and temperature are the same for all tanks. To do this: 1. Calculate the partial pressure for SO2 based on the ideal gas law: Partial pressure of SO2 (Ps_SO2) = (n_SO2 * R * T) / V, where n_SO2 is the number of moles of SO2 in the given tank. 2. Compare Ps_SO2 values for the tanks X, Y, and Z to determine the tank with the highest partial pressure of SO2.

(c) Determining the tank with the same mass for all three gases

Compare the mass of gases in each tank. To do this: 1. Calculate the mass for each gas using the number of moles (n) multiplied by the molar mass (M): Mass (M_CH4) = n_CH4 * M_CH4 Mass (M_O2) = n_O2 * M_O2 Mass (M_SO2) = n_SO2 * M_SO2 2. For each tank, compare the mass of all three gases to find a tank with equal mass for CH4, O2, and SO2.

(d) Determining the tank with the heaviest contents

Compare the total mass of all gases present in each tank. To do this: 1. Calculate the total mass for each tank by summing masses of CH4, O2, and SO2: Total Mass (M_total) = M_CH4 + M_O2 + M_SO2 2. Compare M_total values for the tanks X, Y, and Z to determine the tank with the heaviest contents.