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Chapter 11: Problem 36

According to Avogadro, a. what is the relationship between gas volume and number of moles at constant temperature and pressure? b. what is the mathematical expression denoting this relationship?

Short Answer

Expert verified
a. Volume is directly proportional to the number of moles at constant temperature and pressure. b. The relationship is given by \[ V = k \times n \]

Step by step solution

01

Understanding Avogadro's Law

Avogadro's Law states that at a constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas.
02

Expressing the Relationship

To express the relationship mathematically, we use the equation: \( V \propto n \), where \( V \) is the volume of the gas and \( n \) is the number of moles.
03

Using the Proportionality Constant

To remove the proportionality, we introduce a constant \( k \). Thus, the equation becomes: \[ V = k \times n \]

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Key Concepts

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

Gas Volume
Gas volume is an important concept in chemistry. It refers to the amount of space that a gas occupies. The volume of gas can change based on certain conditions, such as pressure, temperature, and the number of moles. When it comes to Avogadro's Law, understanding gas volume helps you see how gasses behave under different scenarios.
Imagine you have a balloon with gas inside it. If you add more gas molecules to the balloon, it will expand, meaning the gas volume increases. Similarly, if you remove gas, the balloon shrinks, so the gas volume decreases. This simple idea leads us to the next core concept.
Number of Moles
The number of moles refers to the quantity of gas molecules in a given sample. One mole contains Avogadro's number of molecules, which is approximately 6.022 x 10^23 molecules. The number of moles is usually represented by the letter 'n'.
In Avogadro's Law, the volume of gas is directly affected by the number of moles. More moles mean more molecules, which take up more space. This is why increasing the number of moles increases the gas volume, whereas decreasing the number of moles reduces it.
Understanding the number of moles helps you predict how changes in the quantity of gas affect its volume at constant pressure and temperature.
Constant Temperature and Pressure
For Avogadro's Law to hold, temperature and pressure must remain constant. This means that as you change the number of moles of gas, neither the temperature nor the pressure changes.
Temperature is a measure of the average kinetic energy of molecules. Pressure is the force that the gas molecules exert on the walls of their container.
Keeping these two conditions steady allows us to see the pure effect of changing the number of moles on gas volume without any complications. In real-life experiments, ensuring constant temperature and pressure can be tricky but it's essential for accurate results.
Direct Proportionality
Direct proportionality means that two quantities increase or decrease together at the same rate. In the context of Avogadro's Law, gas volume and the number of moles are directly proportional.
This is represented in the equation: \[ V = k \times n \]
Here, \( V \) is the gas volume, \( n \) is the number of moles, and \( k \) is a constant. When the number of moles doubles, the gas volume also doubles. If the number of moles is halved, the gas volume is halved too.
Direct proportionality makes it easy to predict how changing one variable affects the other, as long as temperature and pressure remain constant.

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