Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 77

In solving a problem, what types of conditions involving temperature, pressure, volume, or number of moles would allow you to use a. the combined gas law? b. the ideal gas law?

Short Answer

Expert verified
Use the combined gas law when the number of moles remains constant. Use the ideal gas law to find one missing variable when pressure, volume, temperature, and moles are involved.

Step by step solution

01

Definitions of the Gas Laws

Identify the combined gas law and the ideal gas law. The combined gas law is \[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \] and the ideal gas law is \[ PV = nRT \].
02

Conditions for the Combined Gas Law

The combined gas law applies when the relationship between pressure, volume, and temperature is considered while the number of moles of gas remains constant. Use it when comparing changes in state from one set of conditions to another.
03

Conditions for the Ideal Gas Law

The ideal gas law is used when dealing with situations where the number of moles (n) needs to be included along with pressure, volume, and temperature. This law is useful for finding one missing variable when the others are known.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Concepts of the Combined Gas Law
The Combined Gas Law is highly useful in chemistry for understanding how gases operate under different conditions. With the formula \(\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}\), this law helps us see the relationship between pressure (P), volume (V), and temperature (T). The key point here is that the number of moles of gas remains constant.

Use the Combined Gas Law when:
  • Comparing the initial and final states of a gas
  • You're given two sets of temperature, pressure, and volume conditions
  • There are no changes in the number of moles of gas between the initial and final states
This law is perfect for problems that involve changes happening to a gas sample, such as when it’s heated or cooled, but the amount of the gas stays the same.
Understanding the Ideal Gas Law
The Ideal Gas Law is an essential equation in chemistry, represented as \( PV = nRT \). In this formula, P stands for pressure, V for volume, n for the number of moles, R is the gas constant, and T is temperature. Unlike the Combined Gas Law, the Ideal Gas Law takes into account the number of gas particles.

Use the Ideal Gas Law when:
  • You need to find one of the variables (P, V, n, or T) while the others are known
  • Considering the behavior of an 'ideal' gas, which follows the assumptions made in kinetic molecular theory
  • Working with situations where the amount of gas might change
The ideal gas law works best when dealing with hypothetical gases under normal conditions. It gives a good approximation for real gases too, under many conditions.
Pressure-Volume-Temperature Relationship
The relationship between pressure, volume, and temperature is a cornerstone of gas laws. Let's break this down:

According to the idea behind gas laws:
  • If you increase the temperature of a gas while keeping the volume constant, its pressure will increase
  • If you increase the volume of a gas while keeping the temperature constant, the pressure will decrease
  • Likewise, if you increase the temperature while keeping the pressure constant, the volume will increase
These relationships arise because gas particles move faster when heated, leading to more collisions and pressure, or they need more space, leading to volume changes. This interconnected behavior is why the gas laws are so valuable for predicting changes.
Importance of Number of Moles
The number of moles (n) is a measure of the quantity of gas particles. It's integral to both the Combined Gas Law (indirectly) and the Ideal Gas Law (directly). Why is it important?

Because:
  • The Ideal Gas Law directly uses the number of moles to relate pressure, volume, and temperature
  • Under certain conditions, the number of moles doesn't change, simplifying use of the Combined Gas Law
  • Whenever the quantity of gas is involved in a problem, knowing the moles helps predict the behavior of the gas under different conditions
Understanding the number of moles connects atomic-level interactions with macroscopic properties like pressure and volume, allowing for precise calculations and predictions.

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

The normal respiratory rate for a human being is \(15,0\) breaths per minute. The average volume of air for each breath is 505 \(cm^{3}\) at \(20.0^{\circ} C\) and \(9.95 \times 10^{4} Pa\) . What is the volume of air at STP that an individual breathes in one day? Give your answer in cubic meters.

Explain the processes involved in the liquefaction of gases. Name some substances that are gases under normal room conditions and that are typically used in the liquid form. Explain why this is so.

A sample of air has a volume of 140.0 mL at 67°C. At what temperature would its volume be 50.0 mL at constant pressure?

a. Why does a gas in a closed container exert pressure? b. What is the relationship between the area a force is applied to and the resulting pressure?

Suppose that 3.11 mol of carbon dioxide is at a pressure of 0.820 atm and a temperature of 39°C. What is the volume of the sample, in liters?
See all solutions

Recommended explanations on Chemistry Textbooks

Ionic and Molecular Compounds

Read Explanation

Nuclear Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Chemistry Branches

Read Explanation

Kinetics

Read Explanation

Inorganic 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