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Chapter 10: Problem 76

A sample of \(3.00 \mathrm{~g}\) of \(\mathrm{SO}_{2}(g)\) originally in a \(5.00-\mathrm{L}\) vessel at \(21^{\circ} \mathrm{C}\) is transferred to a \(10.0-\mathrm{L}\) vessel at \(26^{\circ} \mathrm{C}\). A sample of \(2.35 \mathrm{~g} \mathrm{~N}_{2}(g)\) originally in a \(2.50-\mathrm{L}\) vessel at \(20{ }^{\circ} \mathrm{C}\) is transferred to this same 10.0 - \(\mathrm{L}\) vessel. (a) What is the partial pressure of \(\mathrm{SO}_{2}(g)\) in the larger container? (b) What is the partial pressure of \(\mathrm{N}_{2}(g)\) in this vessel? (c) What is the total pressure in the vessel?

Short Answer

Expert verified
The partial pressure of SO₂(g) in the larger container is \(0.139 atm\), the partial pressure of N₂(g) is \(0.248 atm\), and the total pressure in the vessel is \(0.387 atm\).

Step by step solution

01

Find the moles of SO₂ and N₂ gas

To find the moles of each gas, we use the given mass of the gas and the molar mass of the gas. The molar mass of SO₂ is 32.07 g/mol (S) + 2 × 16 g/mol (O) = 64.07 g/mol. The molar mass of N₂ is 2 × 14 g/mol (N) = 28 g/mol. For SO₂: moles = mass / molar mass = 3 g / 64.07 g/mol = 0.0468 mol For N₂: moles = mass / molar mass = 2.35 g / 28 g/mol = 0.0839 mol
02

Calculate initial pressures of both gases

Now that we have the number of moles for each gas, we can use the ideal gas equation to find the pressure of each gas in their initial containers. The ideal gas equation is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (0.08206 Latm/molK), and T is the temperature in Kelvin. First, convert the temperatures from Celsius to Kelvin: T₁ (SO₂) = 21°C + 273.15 = 294.15 K T₂ (N₂) = 20°C + 273.15 = 293.15 K Then, calculate the initial pressures: P₁ (SO₂) = (0.0468 mol × 0.08206 Latm/molK × 294.15 K) / 5.00 L = 0.251 atm P₂ (N₂) = (0.0839 mol × 0.08206 Latm/molK × 293.15 K) / 2.50 L = 0.906 atm
03

Find new temperature and moles of each gas in the 10 L container

Temperature in the new 10 L container is 26°C - convert to Kelvin. T_new = 26°C + 273.15 = 299.15 K Now, we can use the ideal gas equation to find the new volume and partial pressures of the gases in the 10 L container using V₂ = V₁ × (T₂/T₁).
04

Calculate final pressures of both gases

Since both gases are in the same 10 L container and at the same temperature (T_new), we can rearrange the ideal gas equation to solve for the final pressures of each gas. P_new (SO₂) = (0.0468 mol × 0.08206 Latm/molK × 299.15 K) / 10 L = 0.139 atm P_new (N₂) = (0.0839 mol × 0.08206 Latm/molK × 299.15 K) / 8.5 L = 0.248 atm
05

Calculate total pressure inside the container

Now that we have the partial pressures of both gases, we can use Dalton's Law of partial pressures to find the total pressure inside the container: P_total = P_new (SO₂) + P_new (N₂). P_total = 0.139 atm (SO₂) + 0.248 atm (N₂) = 0.387 atm The partial pressure of SO₂(g) in the larger container is \(0.139 atm\), the partial pressure of N₂(g) is \(0.248 atm\), and the total pressure in the vessel is \(0.387 atm\).

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Most popular questions from this chapter

Calcium hydride, \(\mathrm{CaH}_{2}\), reacts with water to form hydrogen gas: $$ \mathrm{CaH}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q)+2 \mathrm{H}_{2}(g) $$ This reaction is sometimes used to inflate life rafts, weather balloons, and the like, when a simple, compact means of generating \(\mathrm{H}_{2}\) is desired. How many grams of \(\mathrm{CaH}_{2}\) are needed to generate \(145 \mathrm{~L}\) of \(\mathrm{H}_{2}\) gas if the pressure of \(\mathrm{H}_{2}\) is 825 torr at \(21{ }^{\circ} \mathrm{C}\) ?

How does a gas compare with a liquid for each of the following properties: (a) density, (b) compressibility, (c) ability to mix with other substances of the same phase to form homogeneous mixtures, \((\mathrm{d})\) ability to conform to the shape of its container?

The temperature of a 5.00-L container of \(\mathrm{N}_{2}\) gas is increased from \(20^{\circ} \mathrm{C}\) to \(250^{\circ} \mathrm{C}\). If the volume is held constant, predict qualitatively how this change affects the following: (a) the average kinetic energy of the molecules; (b) the root-mean-square speed of the molecules; (c) the strength of the impact of an average molecule with the container walls; (d) the total number of collisions of molecules with walls ner second.

Calculate the pressure that \(\mathrm{CCl}_{4}\) will exert at \(40^{\circ} \mathrm{C}\) if \(1.00 \mathrm{~mol}\) occupies \(33.3 \mathrm{~L}\), assuming that (a) \(\mathrm{CCl}_{4}\) obeys the ideal-gas equation; (b) \(\mathrm{CCl}_{4}\) obeys the van der Waals equation. (Values for the van der Waals constants are given in Table 10.3.) (c) Which would you expect to deviate more from ideal behavior under these conditions, \(\mathrm{Cl}_{2}\) or \(\mathrm{CCl}_{4}\) ? Explain.

A 1.42-g sample of helium and an unknown mass of \(\mathrm{O}_{2}\) are mixed in a flask at room temperature. The partial pressure of the helium is 42.5 torr, and that of the oxygen is 158 torr. What is the mass of the oxygen?
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