The Gas Laws of Boyle, Charles, and Avogadro

In this section we will consider several mathematical laws that relate the properties of gases. These laws derive from experiments involving careful measurements of the relevant gas properties. From these experimental results, the mathematical relationships among 

Copyright 2010 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. 

A J-tube similar to the one used by Boyle. When mercury is added to the tube, pressure on the trapped gas is increased, resulting in a decreased volume. 

We will take a historical approach to these laws to give you some perspective on the scientific method in action. 

The first quantitative experiments on gases were performed by an Irish chemist, Robert Boyle (1627-1691). Using a J-shaped tube closed at one end (Fig. 5.4), which he reportedly set up in the multistory entryway of his house, Boyle studied the relationship between the pressure of the trapped gas and its volume. Representative values from Boyle s experiments are given in Table 5.1. These data show that the product of the pressure and volume for the trapped air sample is constant within the accuracies of Boyle s measurements (note the third column in Table 5.1). This behavior can be represented by the equation 

Unless otherwise noted, all arton this page is O Cengage Learning 2014. 

It is convenient to represent the data in Table 5.1 by using two different plots. The first type of plot, P versus V, forms a curve called a hyperbola [Fig. 5.5(a)]. Looking at this plot, note that as the pressure drops by about half (from 58.8 to 29.1), the volume doubles (from 24.0 to 48.0). hi other words, there is an inverse relationship between pressure and volume. The second type of plot can be obtained by rearranging Boyle s law to give 

---

Pressure Units of Pressure The Gas Laws of Boyle, Charles, and Avogadro Boyle s Law Charles s Law Avogadro s Law The Ideal Gas Law Gas Stoichiometry Molar Mass of a Gas Dalton s Law of Partial Pressures... 

Pressure is defined as force/area measured in atm, bar, pascal, and torn The empirical gas laws of Boyle, Charles, and Avogadro combine to give the ideal gas law PV = nRT. 

The combined gas law combines the laws of Boyle, Charles, and Avogadro and relates pressure, volume, temperature, and number of moles without assuming that any of the parameters is constant... 

The relationships discovered by Boyle, Charles and Avogadro are limiting laws. Boyle s law, for example, does not describe the properties of any gas precisely, but is exact in the limit of zero pressure. Another way of looking at these laws is that they precisely describe the properties of a hypotheti-... 

Avogadro s principle and the laws of Boyle, Charles, and Gay-Lussac can be combined into a single mathematical statement that describes the relationship among pressure, volume, temperature, and number of moles of a gas. This formula works best for gases that obey the assumptions of the kinetic-molecular theory. Known as ideal gases, their particles occupy a negligible volume and are far enough apart that they exert minimal attractive or repulsive forces on one another. 

The inter-relationships between P, V, n and T, summarized in the gas laws of Charles, Boyle and Avogadro, are inbuilt into the ideal gas equation, and the equation makes the separate use of these laws in calculations redundant. For example, the ideal gas equation shows that if the pressure and the number of moles of gas does not change, then V is proportional to T. In other words, it predicts Charles law. 

The behavior of all gases that obey the laws of Boyle and Charles, and Avogadro s hypothesis, can be expressed by the ideal gas equation ... 

Was this your answer Gas laws work best for gases at low pressures and high temperatures. At atmospheric pressure, the distances between air molecules are much greater than the sizes of the air molecules. Also, air is well above its boiling points (N2 boils at-i96°C and02 at -i83°C). This, of course, permitted the gas law discoveries of Boyle, Charles, Avogadro, and others. 

It is found experimentally that, to within the reliability of the gas laws (better than 1% under ordinary conditions) the volume of a sample of any gas is determined by only three quantities the pressure of the gas, the temperature of the gas, and the number of molecules in the sample of the gas. The law describing the dependence of the volume of the gas on the pressure is called Boyle s law that describing the dependence of the volume on the temperature is called the law of Charles and Gay-Lussac and that describing the dependence of the volume on the number of molecules in the sample of gas is called Avogadro s law. 

Ideal Gas Concept Measurement of Gases Boyle s Law Charles s Law Combined Gas Law A Clinical Perspective Autoclaves and the Gas Laws Avogadro s Law Molar Volume of a Gas Gas Densities The Ideal Gas Law An Environmental Perspective The Greenhouse Effect and Global Warming... 

This is the combined gas law that combines Charles s law (V — constant Twhere Cn, P = constant), Boyle s law pV = constant where c, T = constant) and Gay-Lussac s law (p T = constant where m, V = constant). Avogadro s law expresses that the ratio of a given gas volume to the amount of gas molecules within that volume is constant (where T,p = constant) ... 

THE GAS LAWS (SECTION 10.3) Studies have revealed several simple gas laws For a constant quantity of gas at constant temperature, the volume of the gas is inversely proportional to the pressure (Boyle s law). For a fixed quantity of gas at constant pressure, the volume is directly proportional to its absolute temperature (Charles s law). Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules (Avogadro s hypothesis). For a gas at constant temperature and pressure, the volume of the gas is directly proportional to the number of moles of gas (Avogadro s law). Each of these gas laws is a special case of the ideal-gas equation. 

The earliest equations of state for gases were determined by Boyle, Charles, Amontons, Avogadro, Gay-Lussac, and others. We know these equations as the various gas laws. In the case of Boyle s gas law, the equation of state involves multiplying the pressure by the volume to get a number whose value depended on the temperature of the gas ... 

The Simple Gas Laws—The most common simple gas laws are Boyle s law relating gas pressure and volume (equation 6.5, Fig. 6-6) Charles s law relating gas volume and temperature (equation 6.8, Fig. 6-7) and Avogadro s law, relating volume and amount of gas. Some important ideas that originate from the simple gas laws are the Kelvin (absolute) scale of temperature (equation 6.6), the standard conditions of temperature and pressure (STP), and the molar volume of a gas at STP— 22.7 L/mol (expression 6.10). 

---