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Chapter 5: Problem 77

Consider three sealed tanks all at the same temperature, pressure, and volume Tank A contains \(\mathrm{SO}_{2}\) gas. Tank B contains \(\mathrm{O}_{2}\) gas. Tank C contains \(\mathrm{CH}_{4}\) gas.

Short Answer

Expert verified
Question: Compare the properties of SO2, O2, and CH4 gases in three tanks A, B, and C, all at the same temperature, pressure, and volume. Calculate the total number of moles of gas in each tank, the average mass of the gas particles in each tank, and the density of each gas in the tanks. Answer: All three tanks have the same number of moles (n) since their temperature, pressure, and volume are the same. However, the average mass of gas particles and the density of the gases differ due to their different molar masses. The molar masses are 64 g/mol for SO2, 32 g/mol for O2, and 16 g/mol for CH4. The average mass of particles and density can be calculated for each gas using these molar masses and the volume of the tanks.

Step by step solution

01

Calculating the number of moles in each tank

Since all the tanks share the same temperature, pressure, and volume, we can use the ideal gas law formula to find the number of moles in the tanks: PV = nRT Here, P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (8.314 J/(mol·K)), T is temperature (in Kelvin). The ideal gas equation can be rewritten as: n = PV/RT Since P, V, and T are the same for all tanks, the number of moles (n) in each tank will also be the same.
02

Calculate the average mass of gas particles in each tank

The molar mass of each gas is as follows: SO2: 1 S atom + 2 O atoms = 32 + 2*16 = 64 g/mol O2: 2 O atoms = 2*16 = 32 g/mol CH4: 1 C atom + 4 H atoms = 12 + 4*1 = 16 g/mol The average mass of particles in each tank can be calculated by dividing the molar mass by Avogadro's number (6.022 x 10^23 particles/mol).
03

Calculate the density of each gas in the tanks

The density of a gas can be found using the formula: Density = (Mass of gas) / Volume We can rewrite the formula in terms of the number of moles, n, using the definition of molar mass: Density = (n x Molar mass) / V Here, V is the volume of the tank shared among all tanks. Calculate the density for each gas using their respective molar masses from Step 2 and the number of moles from Step 1 (which are equal in each tank).
04

Comparing the properties of the gases in the tanks

Compare the average mass of the gas particles and the density of the gases in each tank. You'll notice that although the number of moles is the same in all three tanks, the average mass of the particles, and hence the density, will differ due to each type of gas having different molar masses.

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Most popular questions from this chapter

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