Skip to main content
Ch 18: A Macroscopic Description of Matter
Chapter 18, Problem 18

Five grams of nitrogen gas at an initial pressure of 3.0 atm and at 20°C undergo an isobaric expansion until the volume has tripled. a. What is the gas volume after the expansion?

Verified step by step guidance
1
Identify the initial conditions and the constants: The initial temperature (T1) is 20°C, which needs to be converted to Kelvin. Use the formula T(K) = T(°C) + 273.15.
Use the ideal gas law in the form PV = nRT to find the initial volume (V1). Rearrange the formula to solve for V1: V1 = \frac{nRT1}{P1}. Here, n is the number of moles of nitrogen, R is the ideal gas constant (0.0821 L atm K^{-1} mol^{-1}), P1 is the initial pressure, and T1 is the initial temperature in Kelvin.
Calculate the number of moles of nitrogen (n) using its mass and molar mass. The molar mass of nitrogen (N2) is approximately 28 g/mol. Use n = \frac{mass}{molar mass}.
Since the process is isobaric (constant pressure), the final volume (V2) can be directly calculated by tripling the initial volume: V2 = 3V1.
Summarize the process and the formula used to find the final volume after the expansion, ensuring the understanding that the pressure remains constant and only the volume changes.

Verified Solution

Video duration:
6m
This video solution was recommended by our tutors as helpful for the problem above.
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. In this scenario, understanding how pressure and volume interact is crucial, especially since the process is isobaric (constant pressure), allowing us to focus on the relationship between volume and temperature.
Recommended video:
Guided course
07:21
Ideal Gases and the Ideal Gas Law

Isobaric Process

An isobaric process is one in which the pressure remains constant while the volume and temperature of the gas change. For this question, since the pressure is constant at 3.0 atm, we can use the initial and final volumes and temperatures to determine the new volume after the gas expands.
Recommended video:
Guided course
06:44
Heat Equations for Isobaric & Isovolumetric Processes

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. This principle is essential for calculating the final volume of nitrogen gas after the isobaric expansion, as the temperature will increase when the volume triples, allowing us to find the new volume using the initial conditions.
Recommended video:
Related Practice
Textbook Question
A gas with an initial temperature of 900°C undergoes the process shown in FIGURE EX18.35. c. How many moles of gas are there?

727
views
Textbook Question
10 g of dry ice (solid CO₂) is placed in a 10,000 cm^3 container, then all the air is quickly pumped out and the container sealed. The container is warmed to 0°C, a temperature at which CO₂ is a gas. a. What is the gas pressure? Give your answer in atm. The gas then undergoes an isothermal compression until the pressure is 3.0 atm, immediately followed by an isobaric compression until the volume is 1000 cm^3.
467
views
Textbook Question
A container of gas at 2.0 atm pressure and 127°C is compressed at constant temperature until the volume is halved. It is then further compressed at constant pressure until the volume is halved again. b. Show this process on a pV diagram.
675
views
Textbook Question
Five grams of nitrogen gas at an initial pressure of 3.0 atm and at 20°C undergo an isobaric expansion until the volume has tripled. b. What is the gas temperature after the expansion (in °C)? The gas pressure is then decreased at constant volume until the original temperature is reached.
375
views
Textbook Question
In Problems 67, 68, 69, and 70 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). p₂=300 cm^3/ 100 cm^3 ×1×2 atm
330
views
Textbook Question
In Problems 67, 68, 69, and 70 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). (T₂+273) K=200 kPa / 500 kPa ×1×(400+273) K
300
views