Using Gas Laws to Solve Problems

You will need to use the ideal gas law to solve the problem PV = nRT. Because moles can be calculated by dividing the mass of the sample by its molecular weight, the ideal gas law becomes... 

D) Let 1 represent the initial state and 2 represent the final state. The nnmber of moles of gas remains constant in this problem. Use the combined form of the ideal gas law to solve for the pressnre change. 

L. The number of moles of gas (10 mol) remains constant. The other three factors (pressure, temperature, and volume) all change between initial and final states, so you need to use the combined gas law. The initial values (290 atm, 283 K, 0.80 L) all come from the excimple problem. The final temperature and pressure are known (273 K, 1 atm) because the question states that the gas ends up at STP. So the only unknown is the final volume. Recirrange the combined gas law to solve for this value ... 

Boyle s law can be used to solve for changes in volume when pressure changes. The gas must be in a closed system and the temperature must remain constant. You can use Charles law to solve for changes in volume with temperature changes. This law works only in a closed system in which pressure remains constant. Gay-Lussac s law can solve problems in which the amount and volume of gas remain constant while the temperature and pressure change. 

You have already learned that the ideal gas law can be used to solve for different variables in several different types of situations. As you may recall, the term stoichiometry" refers to the relationship between the number of moles of the reactants and the number of moles of the products in a chemical reaction. In this section, you will learn how to use Gay-Lussac s law of combining volumes and the ideal gas law to solve stoichiometric problems that involve gases. 

You are given the volume, temperature, and pressure of a gas sample. When using the ideal gas law to solve for n, choose the value of R that contains the pressure and temperature units given in the problem. Known Unknown... 

The correct answer is (D). There are a few things to look out for in this problem. First the temperature is given in degrees Celsius (so it must be converted). The second is the stoichiometry. The balanced equation states that two moles of carbon are needed for each mole of oxygen. In the problem, the amount of carbon given is an excess since the 1.20 mol of O2 will only require 2.40 mol of C. It is very important, then, to not use the 3.50 mol value in the calculation. The number of moles of CO that are produced will be twice that of the oxygen that is used. Because 1.2 moles of oxygen are consumed, 2.4 mol of CO will be produced. With this out of the way, we can use the ideal gas law to solve for P ... 

Note that both n and T remain constant—only P and V change. Thus we could simply use Boyle s law P V = 2 2) to solve for P2. However, we will use the ideal gas law to solve this problem to introduce the idea that one equation—the ideal gas equation—can be used to solve almost any gas problem. 

This problem could also be solved by realizing that 200 L of O2(g) would be consumed in burning 100 L of methane and then using the ideal gas law to calculate the moles of oxygen gas. Try it. 

Skill 3.1a-Solve problems using the ideal gas law and use the ideal gas law to predict pressure-volume, pressure-temperature, and volume-temperature relationships... 

The gas laws require us for the first time to use algebraic equations in solving problems. (We could have used equations earlier, for example, as early as density calculations in Section 2.4, but the factor label method proved to be easier in most cases.)... 

In Chapters 3 and 4, we encountered many reactions that involved gases as reactants (e.g., combustion with O2) or as products (e.g., a metal displacing H2 from acid). From the balanced equation, we used stoichiometrically equivalent molar ratios to calculate the amounts (moles) of reactants and products and converted these quantities into masses, numbers of molecules, or solution volumes (see Figure 3.10). Figure 5.11 shows how you can expand your problem-solving repertoire by using the ideal gas law to convert between gas variables (F, T, and V) and amounts (moles) of gaseous reactants and products. In effect, you combine a gas law problem with a stoichiometry problem it is more realistic to measure the volume, pressure, and temperature of a gas than its mass. 

Note that in solving Example 13.10, we actually obtained Boyle s law (PjVj = P2V2) the ideal gas equation. You might well ask, "Why go to all this trouble " The idea is to learn to use the ideal gas equation to solve all types of gas law problems. This way you will never have to ask yourself, "Is this a Boyle s law problem or a Charles s law problem "... 

Using the combined gas law The combined gas law enables you to solve problems involving change in more than one variable. 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. 

Strategy This problem gives the volume, temperature, and pressure of PAN. Is the gas undergoing a change in any of its properties What equation should we use to solve for moles of PAN Once we have determined moles of PAN, we can convert to molarity and use the first-order rate law to solve for rate. 

We are trying to find the mass of a sample of gas. If we knew how many moles of CO2 were in the sample, we could easily use the molar mass to find the mass of the sample. And since the problem involves a gas, we can attempt to use the ideal gas law to find the number of moles. We are given values for V, P, and T, so we will be able to solve for n. Some of the units given are unusual, so we will need to be careful to handle them properly. 

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