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Chapter 5: Problem 70

Sulfur trioxide, \(\mathrm{SO}_{3}\), is produced in enormous quantities each year for use in the synthesis of sulfuric acid. $$ \begin{aligned} \mathrm{S}(s)+\mathrm{O}_{2}(g) & \longrightarrow \mathrm{SO}_{2}(g) \\ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow & 2 \mathrm{SO}_{3}(g) \end{aligned} $$ What volume of \(\mathrm{O}_{2}(g)\) at \(350 .{ }^{\circ} \mathrm{C}\) and a pressure of \(5.25 \mathrm{~atm}\) is needed to completely convert \(5.00 \mathrm{~g}\) sulfur to sulfur trioxide?

Short Answer

Expert verified
The required volume of O₂(g) at 350°C and a pressure of 5.25 atm to completely convert 5.00 g sulfur to sulfur trioxide is approximately 3.09 L.

Step by step solution

01

Determine the number of moles of sulfur.

Given that we have 5.00 g of sulfur, we can use the molar mass of sulfur to convert the mass to the number of moles. The molar mass of sulfur (S) is approximately 32.06 g/mol. Number of moles of sulfur = (mass of sulfur) / (molar mass of sulfur) = \(5.00 \mathrm{\ g}\) / \(32.06 \mathrm{\ g/mol}\) = 0.1559 mol
02

Find the stoichiometric ratio of O₂ to S.

From the balanced chemical equations, we can find the stoichiometric ratio of O₂ to S for the complete conversion to SO₃: S(s) + O₂(g) → SO₂(g) 2 SO₂(g) + O₂(g) → 2 SO₃(g) From the first equation, 1 mol of S requires 1 mol of O₂ to form SO₂. From the second equation, 2 mol of SO₂ requires 1 mol of O₂ to form 2 mol of SO₃. Since 1 mol of S forms 1 mol of SO₂, the overall stoichiometry between O₂ and S in the conversion to SO₃ is: 1 mol S + 2 mol O₂ → 2 mol SO₃ Thus, 1 mol of S requires 2 mol of O₂ to fully convert into SO₃.
03

Calculate the moles of O₂ required.

Using the stoichiometric ratios, we can find the moles of O₂ required to convert 0.1559 mol of S to SO₃: Moles of O₂ = (Moles of S) × (Stoichiometric ratio of O₂ : S) = 0.1559 mol × (2 mol O₂ / 1 mol S) = 0.3118 mol So, 0.3118 mol of O₂ is required for the complete conversion of 5.00 g sulfur to sulfur trioxide.
04

Use the ideal gas law to find the volume of O₂.

Now, we'll use the ideal gas law (PV = nRT) to find the volume of O₂ at the given pressure and temperature: P = 5.25 atm n = 0.3118 mol R = 0.0821 L * atm / (K * mol) (gas constant) T = 350°C + 273.15 = 623.15 K Rearranging the ideal gas law to solve for the volume V: V = (n * R * T) / P V = \((0.3118 \mathrm{\ mol}) (0.0821 \mathrm{\ L\cdot atm / (mol\cdot K)})(623.15 \mathrm{\ K}) \ / \ (5.25 \mathrm{\ atm})\) V ≈ 3.09 L So, the required volume of O₂(g) at 350°C and a pressure of 5.25 atm to completely convert 5.00 g sulfur to sulfur trioxide is approximately 3.09 L.

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Most popular questions from this chapter

Do all the molecules in a 1 -mole sample of \(\mathrm{CH}_{4}(g)\) have the same kinetic energy at \(273 \mathrm{~K} ?\) Do all molecules in a 1 -mole sample of \(\mathrm{N}_{2}(g)\) have the same velocity at \(546 \mathrm{~K} ?\) Explain.

Silane, \(\mathrm{SiH}_{4}\), is the silicon analogue of methane, \(\mathrm{CH}_{4}\). It is prepared industrially according to the following equations: $$ \begin{aligned} \mathrm{Si}(s)+3 \mathrm{HCl}(g) & \longrightarrow \operatorname{HSiCl}_{3}(l)+\mathrm{H}_{2}(g) \\ 4 \mathrm{HSiCl}_{3}(l) & \longrightarrow \mathrm{SiH}_{4}(g)+3 \mathrm{SiCl}_{4}(l) \end{aligned} $$ a. If \(156 \mathrm{~mL} \mathrm{HSiCl}_{3}(d=1.34 \mathrm{~g} / \mathrm{mL})\) is isolated when \(15.0 \mathrm{~L}\) \(\mathrm{HCl}\) at \(10.0 \mathrm{~atm}\) and \(35^{\circ} \mathrm{C}\) is used, what is the percent yield of \(\mathrm{HSiCl}_{3}\) ? b. When \(156 \mathrm{~mL} \mathrm{HSiCl}_{3}\) is heated, what volume of \(\mathrm{SiH}_{4}\) at \(10.0\) atm and \(35^{\circ} \mathrm{C}\) will be obtained if the percent yield of the reaction is \(93.1 \%\) ?

An ideal gas at \(7^{\circ} \mathrm{C}\) is in a spherical flexible container having a radius of \(1.00 \mathrm{~cm}\). The gas is heated at constant pressure to \(88^{\circ} \mathrm{C}\). Determine the radius of the spherical container after the gas is heated. [Volume of a sphere \(\left.=(4 / 3) \pi r^{3} .\right]\)

Consider two separate gas containers at the following conditions: $$ \begin{array}{|ll|} \text { Container A } & \text { Container B } \\ \text { Contents: } \mathrm{SO}_{2}(g) & \text { Contents: unknown gas } \\ \text { Pressure }=P_{\mathrm{A}} & \text { Pressure }=P_{\mathrm{B}} \\ \text { Moles of gas }=1.0 \mathrm{~mol} & \text { Moles of gas }=2.0 \mathrm{~mol} \\ \text { Volume }=1.0 \mathrm{~L} & \text { Volume }=2.0 \mathrm{~L} \\ \text { Temperature }=7^{\circ} \mathrm{C} & \text { Temperature }=287^{\circ} \mathrm{C} \\ \hline \end{array} $$ How is the pressure in container \(\mathrm{B}\) related to the pressure in container \(\mathrm{A}\) ?

Which of the following statements is(are) true? a. If the number of moles of a gas is doubled, the volume will double, assuming the pressure and temperature of the gas remain constant. b. If the temperature of a gas increases from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\), the volume of the gas would double, assuming that the pressure and the number of moles of gas remain constant. c. The device that measures atmospheric pressure is called a barometer. d. If the volume of a gas decreases by one half, then the pressure would double, assuming that the number of moles and the temperature of the gas remain constant.
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