Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 27

In Example \(5.11\) of the text, the molar volume of \(\mathrm{N}_{2}(g)\) at STP is given as \(22.42 \mathrm{~L} / \mathrm{mol} \mathrm{N}_{2}\). How is this number calculated? How does the molar volume of \(\mathrm{He}(g)\) at STP compare to the molar volume of \(\mathrm{N}_{2}(\mathrm{~g})\) at STP (assuming ideal gas behavior)? Is the molar volume of \(\mathrm{N}_{2}(g)\) at \(1.000 \mathrm{~atm}\) and \(25.0^{\circ} \mathrm{C}\) equal to, less than, or greater than \(22.42 \mathrm{~L} / \mathrm{mol}\) ? Explain. Is the molar volume of \(\mathrm{N}_{2}(g)\) collected over water at a total pressure of \(1.000\) atm and \(0.0^{\circ} \mathrm{C}\) equal to, less than, or greater than \(22.42\) \(\mathrm{L} / \mathrm{mol}\) ? Explain.

Short Answer

Expert verified
The molar volume of N₂(g) at STP (0°C and 1 atm) is calculated using the Ideal Gas Law, which gives a value of 22.42 L/mol. The molar volumes of N₂(g) and He(g) at STP are the same as they are both ideal gases. At 1.000 atm and 25.0°C, the molar volume of N₂(g) is greater than 22.42 L/mol due to the increased temperature. When collected over water at 1.000 atm and 0.0°C, the molar volume of N₂(g) is less than 22.42 L/mol because of the presence of water vapor, which decreases the partial pressure of N₂(g).

Step by step solution

01

1. Understand the Ideal Gas Law

Ideal Gas Law is given by PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the Gas Constant, and T is the temperature in Kelvin. Standard Temperature and Pressure (STP) is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atm (101.3 kPa).
02

2. Calculate the molar volume of N₂(g) at STP

To find the molar volume of N₂(g) at STP, we will use the Ideal Gas Law, considering 1 mole of N₂. We have T = 273.15 K, P = 1 atm, and R = 0.0821 L atm/mol K. \(PV = nRT\) \(V = \frac{nRT}{P}\) Plugging in the values: \(V = \frac{(1 \mathrm{~mol})(0.0821 \mathrm{~L~atm/mol~K})(273.15 \mathrm{~K})}{1 \mathrm{~atm}}\)
03

3. Compare molar volumes of N₂(g) and He(g) at STP

For ideal gases, the molar volume is independent of the type of gas and depends only on the temperature and pressure. Therefore, the molar volume of N₂(g) and He(g) at STP (0°C and 1 atm) will be the same.
04

4. Determine molar volume of N₂(g) at 1.000 atm and 25.0°C

We will use the Ideal Gas Law again to determine the molar volume of N₂(g) at the given conditions. The temperature is 25.0°C (or 298.15 K) and pressure is 1.000 atm. Using the Ideal Gas Law: \(V = \frac{nRT}{P}\) Plugging in the values: \(V = \frac{(1 \mathrm{~mol})(0.0821 \mathrm{~L~atm/mol~K})(298.15 \mathrm{~K})}{1 \mathrm{~atm}}\) The molar volume at these conditions will be compared to the initial molar volume at STP (22.42 L/mol) to determine if it is equal, less, or greater.
05

5. Determine molar volume of N₂(g) collected over water at a total pressure of 1.000 atm and 0.0°C

For this case, we need to consider the partial pressure of N₂(g) by using the total pressure and the vapor pressure of water at 0.0°C. Total pressure = Partial pressure of N₂(g) + Vapor pressure of water Use the vapor pressure of water at 0.0°C (which is approximately 4.6 torr or 0.00604 atm) and the total pressure to find the partial pressure of N₂(g). Next, use the Ideal Gas Law with the partial pressure and temperature (0.0°C or 273.15 K) to find the molar volume of N₂(g) collected over water. Finally, compare the molar volume calculated in this step to the initial molar volume at STP (22.42 L/mol) to determine if it is equal, less, or greater.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Urea \(\left(\mathrm{H}_{2} \mathrm{NCONH}_{2}\right)\) is used extensively as a nitrogen source in fertilizers. It is produced commercially from the reaction of ammonia and carbon dioxide: $$ 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) \underset{\text { Pressure }}{\text { Heat }}{\mathrm{H}}_{2} \mathrm{NCONH}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(g) $$ Ammonia gas at \(223^{\circ} \mathrm{C}\) and \(90 .\) atm flows into a reactor at a rate of \(500 . \mathrm{L} / \mathrm{min}\). Carbon dioxide at \(223^{\circ} \mathrm{C}\) and 45 atm flows into the reactor at a rate of \(600 . \mathrm{L} / \mathrm{min} .\) What mass of urea is produced per minute by this reaction assuming \(100 \%\) yield?

In 1897 the Swedish explorer Andreé tried to reach the North Pole in a balloon. The balloon was filled with hydrogen gas. The hydrogen gas was prepared from iron splints and diluted sulfuric acid. The reaction is $$ \mathrm{Fe}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{FeSO}_{4}(a q)+\mathrm{H}_{2}(g) $$ The volume of the balloon was \(4800 \mathrm{~m}^{3}\) and the loss of hydrogen gas during filling was estimated at \(20 . \%\). What mass of iron splints and \(98 \%\) (by mass) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) were needed to ensure the complete filling of the balloon? Assume a temperature of \(0^{\circ} \mathrm{C}\), a pressure of \(1.0\) atm during filling, and \(100 \%\) yield.

In the "Méthode Champenoise," grape juice is fermented in a wine bottle to produce sparkling wine. The reaction is $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)+2 \mathrm{CO}_{2}(g) $$ Fermentation of \(750 . \mathrm{mL}\) grape juice (density \(=1.0 \mathrm{~g} / \mathrm{cm}^{3}\) ) is allowed to take place in a bottle with a total volume of \(825 \mathrm{~mL}\) until \(12 \%\) by volume is ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\). Assuming that the \(\mathrm{CO}_{2}\) is insoluble in \(\mathrm{H}_{2} \mathrm{O}\) (actually, a wrong assumption), what would be the pressure of \(\mathrm{CO}_{2}\) inside the wine bottle at \(25^{\circ} \mathrm{C}\) ? (The density of ethanol is \(0.79 \mathrm{~g} / \mathrm{cm}^{3} .\).)

Consider two gases, A and B, each in a 1.0-L container with both gases at the same temperature and pressure. The mass of gas \(\mathrm{A}\) in the container is \(0.34 \mathrm{~g}\) and the mass of gas \(\mathrm{B}\) in the container is \(0.48 \mathrm{~g}\). a. Which gas sample has the most molecules present? Explain. b. Which gas sample has the largest average kinetic energy? Explain. c. Which gas sample has the fastest average velocity? Explain. d. How can the pressure in the two containers be equal to each other since the larger gas B molecules collide with the container walls more forcefully?

Consider the following samples of gases at the same temperature. Arrange each of these samples in order from lowest to highest: a. pressure b. average kinetic energy c. density d. root mean square velocity Note: Some samples of gases may have equal values for these attributes. Assume the larger containers have a volume twice the volume of the smaller containers, and assume the mass of an argon atom is twice the mass of a neon atom.
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

Physical Chemistry

Read Explanation

Inorganic Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Kinetics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free