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Chapter 11: Problem 69

Consider the reaction \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g)\) (a) What volume in liters of oxygen gas at STP is required to produce 2 moles of sulfur trioxide gas? (b) What volume in liters of oxygen gas at \(25.0^{\circ} \mathrm{C}\) and 1 atm pressure is required to produce 2 moles of sulfur trioxide gas?

Short Answer

Expert verified
(a) The required volume of oxygen gas at STP to produce 2 moles of sulfur trioxide is \(22.4 \,\mathrm{L}\). (b) The required volume of oxygen gas at \(25.0^{\circ}\mathrm{C}\) and 1 atm pressure to produce 2 moles of sulfur trioxide is \(24.5 \,\mathrm{L}\).

Step by step solution

01

Write down the balanced chemical equation

The given balanced chemical equation is: \(2\mathrm{SO}_{2}(g) + \mathrm{O}_{2}(g) \rightarrow 2\mathrm{SO}_{3}(g)\)
02

Use the stoichiometry to find the moles of oxygen required

According to the balanced equation, 1 mole of oxygen \(\mathrm{O}_{2}\) reacts with 2 moles of sulfur dioxide \(\mathrm{SO}_{2}\) to produce 2 moles of sulfur trioxide \(\mathrm{SO}_{3}\). So, to produce 2 moles of \(\mathrm{SO}_{3}\), we would need 1 mole of \(\mathrm{O}_{2}\).
03

Step 3a: Find the required volume of oxygen at STP

At STP, the conditions are 273.15 K temperature and 1 atm pressure. Using the ideal gas law formula with n = 1 mole, R = 0.0821 L⋅atm/mol⋅K, T = 273.15 K, and P = 1 atm: \(V = \frac{nRT}{P} = \frac{(1)(0.0821)(273.15)}{1} = 22.4 \,\mathrm{L}\) So, the required volume of oxygen gas at STP to produce 2 moles of sulfur trioxide is 22.4 L.
04

Step 3b: Find the required volume of oxygen at 25.0°C and 1 atm pressure

Now, we need to find the volume of oxygen gas at 25.0°C (298.15 K) and 1 atm pressure. Using the ideal gas law formula with n = 1 mole, R = 0.0821 L⋅atm/mol⋅K, T = 298.15 K, and P = 1 atm: \(V = \frac{nRT}{P} = \frac{(1)(0.0821)(298.15)}{1} = 24.5 \,\mathrm{L}\) So, the required volume of oxygen gas at 25.0°C and 1 atm pressure to produce 2 moles of sulfur trioxide is 24.5 L.

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Most popular questions from this chapter

In the Haber process, nitrogen reacts with hydrogen to produce ammonia: \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g)\) (a) Suppose \(2.0 \mathrm{~L}\) of \(\mathrm{N}_{2}\) gas at STP is combined with \(6.0 \mathrm{~L}\) of \(\mathrm{H}_{2}\) gas, with the two gases being at the same temperature and pressure. Is this reaction being run in a balanced fashion or in a limiting fashion? Explain how you can tell without doing any calculations. (b) If \(50.0 \mathrm{~L}\) of \(\mathrm{N}_{2}\) gas at \(200.0 \mathrm{lb} / \mathrm{in}^{2}\) and \(22.0^{\circ} \mathrm{C}\) is combined with \(100.0 \mathrm{~L}\) of \(\mathrm{H}_{2}\) gas at \(240.0 \mathrm{lb} / \mathrm{in}^{2}\) and \(22.0^{\circ} \mathrm{C}\), what mass in grams of ammonia is produced? \(\left[14.70 \mathrm{lb} / \mathrm{in}^{2}=760.0 \mathrm{~mm} \mathrm{Hg}\right]\)

A gas tank contains \(\mathrm{CO}_{2}\) at a pressure of \(6.80 \mathrm{~atm}\). What would the \(\mathrm{CO}_{2}\) pressure be if the container were (a) twice as large and (b) one-fourth as large?

A sample of hydrogen gas, \(\mathrm{H}_{2}\), is in an outdoor 1000.0-gallon tank. It is winter, and the temperature is \(-4.50^{\circ} \mathrm{C}\). A pressure gauge indicates that the pressure inside the tank is \(32.6\) atm. How many pounds of hydrogen are left in the tank? (Hint: Examine the solution to Problem 11.9.)

Explain why gases always occupy the entire container they are in, but solids and liquids do not.

You are on the balcony of the upper floor of a high-rise building in Chicago. Way down below on the street, your friend is engaged in conversation with someone and is drinking a particularly flavorful mixed drink. You decide to take a sip from his glass without his knowing, so you collect together every drinking straw in the apartment and start taping them together to create a very long drinking straw. If the atmospheric pressure is currently \(760 \mathrm{~mm} \mathrm{Hg}\), what is the longest straw you can use to get a sip of your friend's drink? (Assume the density of the drink is the same as pure water, \(1.0 \mathrm{~g} / \mathrm{mL}\).)
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