Question

At 258C and 380 mm Hg, the density of sulfur dioxide is 1.31 g/L. The rate of effusion of sulfur dioxide through an orifice is 4.48 mL/s. What is the density of a sample of gas that effuses through an identical orifice at the rate of 6.78 mL/s under the same conditions? What is the molar mass of the gas?

Short answer

Answer: The density of the unknown gas under the given conditions is 0.75 g/L, and its molar mass is 31.2 g/mol.

Step-by-step solution

Write down the given data and relevant equations

We have been given the following data: - Temperature (T) = 258C = 531K (to convert from Celsius to Kelvin, add 273) - Pressure (P) = 380 mm Hg = 0.5 atm (1 atm = 760 mm Hg) - Density of SO2 = 1.31 g/L - Rate of effusion of SO2 = 4.48 mL/s - Rate of effusion of an unknown gas = 6.78 mL/s We will use these equations: - Graham's Law of Effusion: (rate1 / rate2)^2 = (M2 / M1), where M1 and M2 are the molar masses of the two gases, and rate1 and rate2 are their respective rates of effusion. - Ideal gas law equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (0.08206 L atm/mol K), and T is temperature.

Find the molar mass of SO2 using the ideal gas law equation

We can calculate the molar mass of SO2 by dividing the density by the volume and rearranging the ideal gas law equation as follows: M1 = (m/V) = (density * RT) / P M1 = (1.31 g/L * 0.08206 L atm/mol K * 531 K) / 0.5 atm M1 = 71.2 g/mol

Use Graham's Law of Effusion to find the molar mass of the unknown gas

Next, we'll use Graham's Law of Effusion to find the molar mass (M2) of the unknown gas: (rate1 / rate2)^2 = (M2 / M1) (4.48 mL/s / 6.78 mL/s)^2 = (M2 / 71.2 g/mol) 0.4376 = M2 / 71.2 g/mol M2 = 0.4376 * 71.2 g/mol M2 = 31.2 g/mol

Find the density of the unknown gas using the ideal gas law equation

Finally, we'll use the ideal gas law equation again to find the density of the unknown gas: Density = (m/V) = (M2 * P) / (RT) Density = (31.2 g/mol * 0.5 atm) / (0.08206 L atm/mol K * 531 K) Density = 0.75 g/L

Report the final answers

The density of the unknown gas under the given conditions is 0.75 g/L, and its molar mass is 31.2 g/mol.