Volume and amount of gas

Four variables are needed to define the physical condition, or state, of a gas temperature, pressure, volume, and amount of gas, usually expressed as number of moles. The equations that express the relationships among these four variables are known as the gas laws. Because volume is easily measured, the first gas laws to be studied expressed the effect of one of the variables on volume, with the remaining two variables held constant. 

If pressure and temperature are constant, state how volume and amount of gas are related and explain phenomena or make predictions based on that relationship. 

You have learned that the temperature of a gas is related to the kinetic energy of the gas molecules. Now you will learn about other properties of gases, including pressure, volume, and amount of gas present, and about the relationships among these properties. 

Use the temperature-pressure relationship (Gay-Lussac s law) to determine the final temperature or pressure when the volume and amount of gas are constant. 

When the Kelvin temperature of a gas is doubled at constant volume and amount of gas, the pressure also doubles. 

If we could observe the molecules of a gas as the temperature rises, we would notice that they move faster and hit the sides of the container more often and with greater force. If we maintain a constant volume and amount of gas, the pressure would increase. In the temperature-pressure relationship known as Gay-Lussac s law, the pressure of a gas is directly related to its Kelvin temperature. This means that an increase in temperature increases the pressure of a gas, and a decrease in tanperatuie decreases the pressure of the gas as long as the volume and amount of gas do not change (see Figure 11.6). 

Aerosol containers can be dangerous if they are heated, because they can explode. Suppose a container of hair spray with a pressure of 4.0 atm at a room temperature of 25 °C is thrown into a fire. If the temperature of the gas inside the aerosol can reaches 402 °C, what will be its pressure, in atmospheres, if the volume and amount of gas do not change The aerosol container may explode if the pressure inside exceeds 8.0 atm. Would you expect it to explode ... 

The properties that do not change, which are volume and amount of gas, are shown below the table. The temperatures given in degrees Celsius must be changed to kelvins. Because we know the initial and final temperatures of the... 

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). 

Exploding or burning the gas with oxygen or air and measuring both the change in volume and amount of waste gases formed by absorption. 

The ideal gas law is an example of an equation of state, an expression showing how the pressure of a substance—in this case, a gas—is related to its temperature, volume, and amount of substance. A hypothetical gas that obeys the ideal gas law under all conditions is called an ideal gas. All real gases are found to obey F.q. 6 with increasing accuracy as the pressure is reduced toward zero (which we write P — 0). Therefore, the ideal gas law is an example of a limiting law, a law that is strictly valid only in some limit—in this case, as P—> 0. Although the ideal gas law is a limiting law, it is in fact reasonably reliable at normal pressures, and so we can use it to describe the behavior of most gases under normal conditions. 

The constant R is called the gas constant and has the same value for all gases because R is independent of the identity of the gas, we say that it is a universal constant. The ideal gas law is an example of an equation of state, an expression showing how the pressure of a substance—in this case, a gas—is related to the temperature, volume, and amount of substance in the sample. 

The Gas Laws activity (eChapter 9.2) allows you to view how the volume of a gas changes when pressure, temperature, and amount of gas are changed. What happens to the volume when the pressure is doubled What law does this illustrate What happens when the amount of gas is doubled What law does this represent ... 

Ideal gas law The equation for an ideal gas that shows the relationship between the product of the pressure and volume to the product of the temperature and amount of gas molecules written as PV = nRT. 

The first of these equations is the familiar ideal gas law, which expresses the relation between the pressure, temperature, volume, and amount of substance... 

Jacques Charles was an eighteenth-century hot-air balloonist who is credited with discovering the relationship between the volume and temperature of a gas. Charles s Law states that the volume of a gas is proportional to its absolute temperature, as long as the pressure and amount of gas are held constant. In algebraic terms, Charles s Law is given as ... 

All gases exhibit an inverse relationship between the volume and the pressure of a gas for a given temperature and amount of gas. Assuming that nothing else changes, if the volume increases, the pressure will decrease a directly proportional amount. 

What happens to the gas in a plastic balloon if you squeeze it, decreasing its volume Because the balloon is closed, the amount of gas is constant. Assume the temperature is held constant. Decreasing the volume pushes the gas particles closer together. Recall from the kinetic-molecular theory that as gas particles are pushed closer together, the number of collisions between particles themselves and between the particles and the walls of their container increases. As the number of collisions per unit time increases, so does the observed pressure. Therefore, as the volume of a gas decreases, its pressure increases. Similarly, if the balloon is no longer squeezed, the volume increases and the pressure decreases. You can see another example of this principle in Figure 14-1. The interdependence of the variables of volume, pressure, temperature, and amount of gas is the basis for the following gas laws. 

Note that the temperature and amount of gas are not stated in this problem thus, the value of 22.414 L atm cannot be used for the constant C. It is necessary only to assume that the temperature does not change as the pump handle is pushed down. If and P2 are the initial and final pressures and Vj and V2 the initial and final volumes, then... 

Describe the relationships among pressure, volume, temperature, and amount of gas (Boyle s Law, Charles s Law, Avogadro s Law, and the Combined Gas Law), and the limitations of each... 

The units of R that are appropriate for ideal gas law calculations are those that involve units of volume, pressure, moles, and temperature. When you use the value R = 0.0821 L atm/mol K, remember to express all quantities in a calculation in these units. Pressures should be expressed in atmospheres, volumes in liters, temperature in kelvins, and amount of gas in moles. In Examples 12-9 and 12-10 we converted pressures from torr to atm. In Example 12-10 the volume was converted from ft to L. 

Boyle s law The volume of a gas varies inversely with the pressure applied to it as long as the temperature and amount of gas remain constant. 

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