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## AP®︎/College Chemistry

### Course: AP®︎/College Chemistry>Unit 3

Lesson 4: Ideal gas law

# Worked example: Using the ideal gas law to calculate number of moles

The ideal gas law relates four macroscopic properties of ideal gases (pressure, volume, number of moles, and temperature). If we know the values of three of these properties, we can use the ideal gas law to solve for the fourth. In this video, we'll use the ideal gas law to solve for the number of moles (and ultimately molecules) in a sample of gas. Created by Sal Khan.

## Want to join the conversation?

• At , how come the unit millimeters can be used to measure pressure? • Where on KA can I learn about Torr and mmHg and pressure and other units? • how did he get the number 6.022x10^23? • At , Sal says that 754 mm Hg is a unit of pressure. Why? I feel like I missed a video. • Yeah mm Hg (millimeters of mercury) is a unit of pressure. It's also called a Torr after Italian scientist Evangelista Torricelli who invented the barometer. The definition itself it based on the mercury barometer which measures atmospheric pressure.

The way a barometer works is if you have a thin tube closed at one end with all the air evacuated from it so that it is a vacuum inside. Placing that tube with the open air into a body liquid will result in some of the liquid flowing into the tube and reaching a certain height above the rest of the liquid's surface. Essentially what happens is that the liquid is forced into the tube by the pressure of the atmosphere pushing on the liquid's surface. The more force applied to the liquid's surface, the higher the level inside the tube rises. So what the barometer is really doing is measuring atmospheric pressure based on the height of that liquid.

Now the type of liquid you choose also determines how high the liquid level rises to; specifically it depends on its density. The actual numerical height is determined by Jurin's law. Without getting too much into the math, the greater the density of the liquid the smaller the height of the liquid in the tube. So if you're designing a barometer the most convenient liquid would probably be water. However the density of water is so low that it would result in such a high liquid height that it would make the barometer impractical to use. Torricelli chose mercury instead because its density was much greater than that of water which required a much smaller barometer whose height would amount to less than 10 centimeters at atmospheric pressure.

So the height of mercury, read in millimeters, in a mercury barometer tells us the amount of pressure applied by the atmosphere. But since it's just measuring pressure we can use mm of Hg as a pressure unit for other things, not just barometers. In case you're curious one of the places where it's used is to measure blood pressure. The two numbers in blood pressures are in units of mm Hg.

Hope that helps.
• At Sal divided by the temperature when the formula says it should be multiplied. Was there a reason for this in the video I missed? • The ideal gas law says that PV = nRT. We would multiply by T if we wanted to find something like pressure of volume. However, this problem asks us to solve for the number of moles of gas, or n. To do this, you can solve for n in the equation as Sal did, and get n = PV / RT. Here, you can see that to get n, we multiply pressure and volume, and then divide by temperature and R.
• would this same process work if you had to solve for pressure or volume? with minor adjustments of course • Yes, if you were dealing with an ideal gas the ideal gas law would still apply which could be used to calculate (in addition to number of moles) temperature, pressure, and volume of the gas.

Since the ideal gas law is: PV = nRT, it has four variables (P, V, n, and T), we would need to know three of the four to calculate the fourth variable. But with the appropriate given information it allows us to know any of the four variables.

Hope that helps.
(1 vote)
• How do we calculate the volume of a gas produced from a reaction?
(1 vote) • In this video, Sal found the number of moles of air there were. However, air is made up of many different kinds of molecules, with different numbers and types of atoms and different masses. How does this work out?
(1 vote) • Sal is using the ideal gas law which assumes the gases to be ideal. An ideal gas is composed of spherical particles which have no mass or forces of attraction to each other or the walls of the container. It's not really what the real gases are since we have a mixture of molecules in air, but using an ideal gas approximation simplifies the math and produces answers with acceptable accuracy. So here we view all moles of gas, regardless of what compound they actually are, as the same.

Hope that helps.
• but what is the relation between P1V1/T1 = P2V2/T2 &
PV=nRT?
(1 vote) • I was wondering how to tell the number of significant figures. Isn't the original temperature given in 2 significant figures? Do we change it to three because of the conversion?
(1 vote) • In general with sig figs your answer should have no more digits than the number with the smallest number of sig figs. But the particulars depend on which mathematical operation you're performing.

If we're multiplying/dividing then we consider the digits of the entire number for sig fig purposes. If we're adding/subtracting then we only consider the digits to the right of the decimal point for sig fig purposes. Side note There's also rules for using exponents/logarithms but I won't cover them here because they're not relevant for the video's problem.

So before Sal performed the final calculation, he converted the temperature from °C to K. This involves adding 273.15 to the temperature in °C to do so. So mathematically this would look like: 273.15 + 21 = 294.15, but for sig fig purposes we need to look at the decimal digits. The 273.15 has two decimal digits, but the 21 has zero decimal digits so the answer should have as many decimal digits as the number with the fewest decimal digits; or zero. So the answer accounting for sig figs should be just 294 K, which is now three sig figs. Now this is only an intermediate calculation so technically we shouldn't round off before the last calculation.

When Sal performed the final calculation it was all multiplication/division. For that calculation we need to identify how many sig figs there are for all the numbers and remember that are answer should have as many as the number with the fewest sig figs. So between the numbers: 754 Torr (3 sig figs), 1.85 L (3 sig figs), 62.36 L Torr mol^-1 K^-1 (4 sig figs), and 294 K (3 sig figs); three sig figs is the smallest number of sig figs so the final answer should only have three sigs.

Hope that helps.