Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 124

Calculate the pressure exerted by 0.5000 mole of \(\mathrm{N}_{2}\) in a 10.000 -L container at \(25.0^{\circ} \mathrm{C}\) a. using the ideal gas law. b. using the van der Waals equation. c. Compare the results. d. Compare the results with those in Exercise 123.

Short Answer

Expert verified
a. Using the Ideal Gas Law, the pressure exerted by the nitrogen gas is \(1.2217\: atm\). b. Using the van der Waals equation, the pressure is calculated as \(1.2244\: atm\). c. The difference between the two values is small (0.0027 atm), suggesting the Ideal Gas Law offers a good approximation in this case. d. Compared to Exercise 123, the pressure difference in this problem is less significant, indicating that the Ideal Gas Law is less accurate under the conditions of Exercise 123.

Step by step solution

01

Calculate the temperature in Kelvin

To calculate the pressure, we first need to convert the given temperature from Celsius to Kelvin. To do this, simply add 273.15 to the Celsius value. \( T_K = 25.0 + 273.15 = 298.15 \: K \)
02

a. Calculate the pressure using the Ideal Gas Law

The Ideal Gas Law is given by the equation: \(PV = nRT\) Where P = pressure, V = volume, n = number of moles, R = gas constant, and T = temperature in Kelvin. We are given n, V, and T and want to find P. The gas constant R for pressure in atm and volume in liters is 0.0821 L atm/mol K. Therefore, \( P = \frac{nRT}{V} \) Plug in the values, n = 0.5000 mol, R = 0.0821 L atm/mol K, T = 298.15 K, and V = 10.000 L: \( P = \frac{(0.5000)(0.0821)(298.15)}{10} = 1.2217\: atm\)
03

b. Calculate the pressure using the van der Waals equation

The van der Waals equation takes into account the molecular size and intermolecular forces. It is given by: \( \left(P + \frac{an^2}{V^2}\right)(V-nb) = nRT\) For N₂, van der Waals coefficients are \(a = 1.390\:L^2\: atm/mol^2\) and \(b = 0.0391\: L/mol^2\). We need to solve for P. To do this, let's isolate P in the equation: \( P = \frac{nRT}{V-nb} - \frac{an^2}{V^2}\) Now plug in the values, n = 0.5000 mol, R = 0.0821 L atm/mol K, T = 298.15 K, V = 10.000 L, a = 1.390 L² atm/mol², and b = 0.0391 L/mol: \( P = \frac{(0.5000)(0.0821)(298.15)}{10 - (0.5000)(0.0391)} - \frac{1.390(0.5000)^2}{10^2}\) \( P = 1.2244 \: atm \)
04

c. Compare the results

The pressures calculated using the Ideal Gas Law and the van der Waals equation are: Ideal Gas Law: \(P = 1.2217 \: atm\) van der Waals equation: \(P = 1.2244 \: atm\) The difference between these two values is small, only about 0.0027 atm. This suggests that the ideal gas law gives a good approximation of the gas pressure in this case.
05

d. Compare with Exercise 123

In exercise 123, we found that the pressure difference between the ideal gas law and the van der Waals equation was much more significant. This indicates that the ideal gas law is less accurate under those conditions than it is under the conditions of this problem.

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

A \(1.0-\mathrm{L}\) sample of air is collected at \(25^{\circ} \mathrm{C}\) at sea level \((1.00 \mathrm{atm}) .\) Estimate the volume this sample of air would have at an altitude of 15 \(\mathrm{km}\) ( see Fig.5.30) .At \(15 \mathrm{km},\) the pressure is about 0.1 \(\mathrm{atm} .\)

Consider a children’s cartoon illustrating a child holding the strings of several helium balloons and being lifted into the sky. a. Estimate the minimum number of 10.-L balloons it would take to lift a 50.-lb child. Assume air has an average molar mass of 29 g/mol, and assume the masses of the balloons and strings are negligible. b. Explain why the balloons can lift the child.

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.

You have an equimolar mixture of the gases \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2},\) along with some \(\mathrm{He}\), in a container fitted with a piston. The density of this mixture at STP is 1.924 \(\mathrm{g} / \mathrm{L}\) . Assume ideal behavior and constant temperature and pressure. a. What is the mole fraction of He in the original mixture? b. The \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) react to completion to form \(\mathrm{SO}_{3} .\) What is the density of the gas mixture after the reaction is complete?

Consider three identical flasks filled with different gases. Flask \(\mathrm{A} : \mathrm{CO}\) at 760 torr and \(0^{\circ} \mathrm{C}\) Flask \(\mathrm{B} : \mathrm{N}_{2}\) at 250 torr and \(0^{\circ} \mathrm{C}\) Flask \(\mathrm{C} : \mathrm{H}_{2}\) at 100 torr and \(0^{\circ} \mathrm{C}\) a. In which flask will the molecules have the greatest average kinetic energy? b. In which flask will the molecules have the greatest average velocity?
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Chemical Reactions

Read Explanation

Kinetics

Read Explanation

Inorganic Chemistry

Read Explanation

Organic Chemistry

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