The Combined Gas Law Equation

Unless othen/vise noted, all content on this page is Cengage Learning. 

We have seen that both temperature and pressure affect the volumes (and therefore the densities) of gases. It is often convenient to choose some standard temperature and pressure as a reference point for discussing gases. Standard temperature and pressure (STP) are, by international agreement, exactly 0°C (273.15 K) and one atmosphere of pressure (760. torr). 

Boyle s Law relates the pressures and volumes of a sample of gas at constant temperature, P Vi = P2V2. Charles s Law relates the volumes and temperatures at constant pressure, Vi/Ti = V2IT2. Combination of Boyle s Law and Charles s Law into a single expression gives the Combined Gas Law equation. 

When any five of the variables in the equation are known, the sixth variable can be calculated. 

A sample of neon occupies 105 liters at 27°C under a pressure of 985 torn What volume would it occupy at standard temperature and pressure (STP)  

---

Provide Boyles and Charles gas laws starting with the combined gas law equation. 

Combining Boyle s Law, Charles s Law, and Gay-Lussac s Law forms a combined gas law equation. The combined gas law equation can be used when temperature, pressure, and volume are changing. Essentially, this equation can replace the three individual law equations, and if one of the properties is constant, it can be crossed out and ignored. 

This combined law lets you work out problems involving more variables that change, and it also provides a way for you to remember the other three laws without memorizing each equation. If you can write out the combined gas law equation, equations for the other laws can be derived from it by remembering which variable is held constant in each case. 

Fj/Tj = F2/T2. Combination of Boyle s Law and Charles s Law into a single expression gives the combined gas law equation. 

A sample of gas is changing in all three quantities P, V, and T. This suggests that we use the combined gas law equation. We tabulate what is known and what is asked for, solve the combined gas law equation for the unknown quantity, V2, and substitute known values. 

The combined gas law equation is derived by combming Boyle s and Charles s Laws, so the comments in earlier Problem-Solving Tips also apply to this equation. Remember to express all temperatures in kelvins. Volumes can be expressed in any units as long as both are in the same units. Similarly, any pressure units can be used, so long as both are in the same units. Example 12-4 uses torr for both pressures Example 12-5 uses kPa for both pressures. 

The ideal gas equation deals with one set of volume, temperature, and pressure conditions the combined gas law equation deals with two sets of conditions. Derive the combined gas law equation from the ideal gas equation. Redraw Figure 12-12 so that it not only depicts the decrease in space between molecules as the system is cooled from 600. K to 300. K but also emphasizes the change in kinetic energy. 

The equation above is often called the combined gas law equation. It can be used to do calculations such as Example 13.4 and Exercise 13.2, which follow the sample study sheet below. 

Sample Study Sheet 13.2 Using the Combined Gas Law Equation... 

Step 2 Write out the combined gas law equation, but eliminate the variables for any constant properties. (You can assume that the properties not mentioned in the problem remain constant.)... 

Step 2 We write the combined gas law equation, eliminating variables for properties that are constant. Because moles of gas are not mentioned, we assume that they are constant n = nj). 

Let s look at another gas-related issue that Lilia s sister Rebecca needs to consider in designing the pressure valve for the reaction vessel at her chemical plant. She knows that, for safety reasons, the overall pressure must be kept below 1000 kPa, and she knows that the most likely cause of increased pressure is increased temperature. To get an idea of how high the temperature can go safely, she could use the combined gas law equation to calculate the temperature at which the pressure of the gas will reach 1000 kPa if the initial temperature was 825 °C (1098 K) and the initial pressure was... 

The combined gas law equation will need to be rearranged to solve for Vf. First cross-multiply the temperatures to put the equation on a single line ... 

Use the combined gas law (Equation 6.8) to calculate the unknown quantity for each gas sample described in the following table. 

The Absolute Temperature Scale 12-6 Standard Temperature and Pressure 12-7 The Combined Gas Law Equation 12-8 Avogadro s Law and... 

We strategize by building a solution map that shows how the combined gas law equation takes us from the given quantities to the find quantity. 

From this expression, any value can be calculated if the other five are known. Note that each of the gas laws can be obtained from the combined gas law when the proper variable is constant. For example, Boyle s law is obtained when the temperature is constant. Because Tj =T2, and T2 will cancel out on both sides of the combined gas law equation, giving Boyle s law. 

---