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Chapter 5: Problem 44

Consider the following chemical equation. $$ 2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g) $$ If \(25.0 \mathrm{~mL} \mathrm{NO}_{2}\) gas is completely converted to \(\mathrm{N}_{2} \mathrm{O}_{4}\) gas under the same conditions, what volume will the \(\mathrm{N}_{2} \mathrm{O}_{4}\) occupy?

Short Answer

Expert verified
The volume of N鈧侽鈧� gas produced when 25.0 mL of NO鈧� gas is completely converted under the same conditions is \(12.5 \mathrm{~mL}\).

Step by step solution

01

Write down the balanced chemical equation

The balanced chemical equation is given by: \[ 2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g) \]
02

Identify the stoichiometry of the reaction

According to the balanced chemical equation, 2 moles of NO鈧� combine to form 1 mole of N鈧侽鈧�. We can express this stoichiometry as a ratio: \[ \frac{\text{moles of NO}_2}{\text{moles of N}_2 \text{O}_4} = \frac{2}{1} \]
03

Use the stoichiometry to find the volume of N鈧侽鈧�

Since the temperature and pressure conditions remain the same, we can apply the stoichiometry of the reaction directly to the volumes: \[ \frac{\text{volume of NO}_2}{\text{volume of N}_2 \text{O}_4} = \frac{2}{1} \] We are given the volume of NO鈧� gas as \( 25.0 \mathrm{~mL} \). We can now solve for the volume of N鈧侽鈧� gas: \[ \text{volume of N}_2 \text{O}_4 = \frac{1}{2} \times \text{volume of NO}_2 \]
04

Calculate the volume of N鈧侽鈧�

Substitute the given volume of NO鈧� gas and calculate the volume of N鈧侽鈧� gas: \[ \text{volume of N}_2 \text{O}_4 = \frac{1}{2} \times 25.0 \mathrm{~mL} = 12.5 \mathrm{~mL} \] Hence, the volume of N鈧侽鈧� gas produced when 25.0 mL of NO鈧� gas is completely converted is 12.5 mL

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Most popular questions from this chapter

At room temperature, water is a liquid with a molar volume of \(18 \mathrm{~mL}\). At \(105^{\circ} \mathrm{C}\) and 1 atm pressure, water is a gas and has a molar volume of over \(30 \mathrm{~L}\). Explain the large difference in molar volumes.

A \(2.00-\mathrm{L}\) sample of \(\mathrm{O}_{2}(g)\) was collected over water at a total pressure of 785 torr and \(25^{\circ} \mathrm{C}\). When the \(\mathrm{O}_{2}(g)\) was dried (water vapor removed), the gas had a volume of \(1.94 \mathrm{~L}\) at \(25^{\circ} \mathrm{C}\) and 785 torr. Calculate the vapor pressure of water at \(25^{\circ} \mathrm{C}\).

You have a sealed, flexible balloon filled with argon gas. The atmospheric pressure is \(1.00 \mathrm{~atm}\) and the temperature is \(25^{\circ} \mathrm{C}\). Assume that air has a mole fraction of nitrogen of \(0.790\), the rest being oxygen. a. Explain why the balloon would float when heated. Make sure to discuss which factors change and which remain constant, and why this matters. Be complete. b. Above what temperature would you heat the balloon so that it would float?

Given that a sample of air is made up of nitrogen, oxygen, and argon in the mole fractions \(78 \% \mathrm{~N}_{2}, 21 \% \mathrm{O}_{2}\), and \(1.0 \% \mathrm{Ar}\), what is the density of air at standard temperature and pressure?

A container is filled with an ideal gas to a pressure of \(40.0\) atm at \(0^{\circ} \mathrm{C}\). a. What will be the pressure in the container if it is heated to \(45^{\circ} \mathrm{C}\) ? b. At what temperature would the pressure be \(1.50 \times 10^{2}\) atm? c. At what temperature would the pressure be \(25.0 \mathrm{~atm} ?\)
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