So, they are giving us a volume, right over here. They are also giving us a temperature, right over here. They're also giving us, I'm trying to use all of my colors here, they're giving us a pressure. And they want us to figure out the number of moles. I'm gonna use a green color here. So they want to know, so we often use the lowercase letter, n, to represent the number of moles.
And so, do we know something that connects pressure, temperature, volume, and the number of moles? Well, you might be thinking of the Ideal Gas Law, which tells us that pressure times volume is equal to the number of moles, n, times the ideal gas constant, R, times temperature, T. And so we know everything here except for n, so we can solve for n.
I know what some of you are saying, "Wait, do we know R? And it's going to be dependent on which units we use, and we'll figure out which version of R we use. But that's why I gave you this little table here, that you might see on a formula sheet, if you were taking something like an AP exam. So we actually do know what R is.
So, we just need to solve for n. So, to solve for n, you just divide both sides by RT, and so you are going to get that n is equal to pressure times the volume over R times T, R times T. And so this is going to be equal to what? Well, our pressure is millimeters of mercury. Now, over here, where they give us the ideal gas or the different versions of the ideal gas constants, you don't see any of them that deal with millimeters of mercury.
But they do tell us that each millimeter of mercury is equal to a Torr. If you get very, very, very precise, they are slightly different. But for the purposes of a first-year chemistry class, you can view a millimeter of mercury as being a Torr.
The ideal gas law is used like any other gas law, with attention paid to the units and making sure that temperature is expressed in kelvins. However, the ideal gas law does not require a change in the conditions of a gas sample. The ideal gas law implies that if you know any three of the physical properties of a gas, you can calculate the fourth property. What is its volume? The atm unit is in the numerator of both sides, so it cancels.
On the right side of the equation, the mol and K units appear in the numerator and the denominator, so they cancel as well. The only unit remaining is L, which is the unit of volume we are looking for. We isolate the volume variable by dividing both sides of the equation by 1. At a given temperature, 0. What is its temperature? We are not given the number of moles of Hg directly, but we are given a mass. We can use the molar mass of Hg to convert to the number of moles.
Pressure is given in units of millimeters of mercury. We can either convert this to atmospheres or use the value of the ideal gas constant that includes the mmHg unit. We will take the second option. Substituting into the ideal gas law,. The mmHg, L, and mol units cancel, leaving the K unit, the unit of temperature. Isolating T all by itself on one side, we get. For a 0. The ideal gas law can also be used in stoichiometry problems.
What volume of H 2 is produced at K and 1. Here we have a stoichiometry problem where we need to find the number of moles of H 2 produced.
Then we can use the ideal gas law, with the given temperature and pressure, to determine the volume of gas produced. First, the number of moles of H 2 is calculated:. Now that we know the number of moles of gas, we can use the ideal gas law to determine the volume, given the other conditions:.
What pressure of HCl is generated if 3. It should be obvious by now that some physical properties of gases depend strongly on the conditions.
What we need is a set of standard conditions so that properties of gases can be properly compared to each other. Standard temperature and pressure STP is defined as exactly kPa of pressure 0. For simplicity, we will use 1 atm as standard pressure.
Defining STP allows us to compare more directly the properties of gases that differ from each other. One property shared among gases is a molar volume. The molar volume is the volume of 1 mol of a gas.
At STP, the molar volume of a gas can be easily determined by using the ideal gas law:. How to Find Partial Pressures. How to Convert Vapor Pressure to Concentration. How to Find the Number of Moles of Co2. How to Calculate Volume Change. How to Convert mm Hg to in Hg. What Happens When the Pressure and Temperature of a How to Solve for Volume. Science Experiments Involving the Kinetic Molecular How to Calculate the Pressure of Hydrogen Gas.
Wait several minutes after introducing instruments to your sample before taking measurements. When choosing a value of R, choose the one with the appropriate units of the given information sometimes given units must be converted accordingly. Here are some commonly used values of R:. Because of the various value of R you can use to solve a problem. It is crucial to match your units of Pressure, Volume, number of mole, and Temperature with the units of R. How do you know the Ideal Gas Equation is the correct equation to use?
Use the Ideal Gas Equation to solve a problem when the amount of gas is given and the mass of the gas is constant. There are various type of problems that will require the use of the Ideal Gas Equation. Know how to do Stoichiometry. Know your basic equations. Take a look at the problems below for examples of each different type of problem. Attempt them initially, and if help is needed, the solutions are right below them.
Remark: The units must cancel out to get the appropriate unit; knowing this will help you double check your answer. Step 4: You are not done. Be sure to read the problem carefully, and answer what they are asking for. In this case, they are asking for temperature in Celsius, so you will need to convert it from K, the units you have. Step 3: This one is tricky. We need to manipulate the Ideal Gas Equation to incorporate density into the equation.
Find the volume, in mL, when 7. What is the total pressure in the container in atm? After converting it to atm, you have already answered part of the question! Use the ideal gas equation. Introduction Many chemists had dreamed of having an equation that describes relation of a gas molecule to its environment such as pressure or temperature.
In this issue, two well-known assumptions should have been made beforehand: the particles have no forces acting among them, and these particles do not take up any space, meaning their atomic volume is completely ignored.
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