Gas Laws

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• published: 30 Jan 2015
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Learn about pressure temperature and volume laws (Boyle’s, Gay-Lussac’s and Charles’ laws) in this video. If you want to know about the ideal gas law (PV=nRT) it get’s it’s own separate video! transcript: __________________________________________ There are four variables that are manipulated in the different gas laws: pressure, temperature, volume and moles. To see how one variable affects another, we have to hold the other two variables constant when we test them. First we’ll look at the relationship between pressure and volume. We’ll hold moles and temperature constant by using a sealed container and consistent temperature. When we decrease the volume the pressure increases. This is an inverse relationship which means the variables will be on the same side of the equation and the constant will be opposite. Here is the equation for pressure and volume. Pressure times volume equals some constant. Now to see where Boyle’s law is coming from we need to look at starting pressure and volumes, and finishing pressure and volumes. Mathematically, we can use substitution to put these two equations together because they both equal the same value, k. and BOOM. That’s Boyle’s law. Let’s try using it. A syringe is filled with air to 60 mL at 1 atmosphere. Then the syringe is sealed and compressed to 20 mL. What is the final pressure? Use boyle’s law: p1v1 = p2v2 and you can rearrange the equation now or after plugging in the numbers, it doesn’t matter, but for neatness, I’m going to rearrange it now. I need the final pressure, or P2, so I’m going to get that isolated by dividing both sides by V2. Then clean it up and plug in the data. And you get 3 atm. Do a concept check to see if that makes sense. volume went down, pressure went up that’s inverse, yup! seems reasonable. The next law looks at pressure and temperature, keeping moles and volume constant, and is sometimes called Gay-Lussac’s law. Look, I don’t speak french, I don’t know how to say this dude’s name. We know that when temperature increases, pressure also increases. This is a direct relationship which means the variables will be on opposite sides of the equation. pressure equals temperature times the constant. Now when we compare the before and after, we use substitution again to get Gay-Lussac’s law. But it’s a little easier to do the substitution if we get the K by itself first. Then use substitution and Boom, the law is born! A flask filled with carbon dioxide is heated from 10 degrees c to 40 degrees c. the starting pressure as 98 kPa, what is the final pressure? We’re using gay-lussac’s law and we need to find the final pressure, so let’s rearrange the equation first. Just multiply both sides by T2 and you get a nice clean equation. Fill in the data and calculate. Ah but be careful, use kelvin instead of celsius so that the mathematical proportions are accurate, and make sure the final temperature is on top, and the initial is on the bottom. And you get 108 kPa, or with sigfigs, 110. Have you ever put a balloon in a freezer? Pull it out after a few hours and you’ll find a shrunken balloon. As it warms up it will come back to full size. As temperature goes down, volume goes down. This is a direct relationship. This is essentially the same as Gay-Lussac’s law except we’re using volume instead of pressure. If you rearrange the equation and then substitute, you get Charle’s law. v1 over t1 = v2 over t2 A balloon is filled with 1.5 L of air at 20 degrees c then placed in a freezer until it reaches a temperature of 5 degrees c. what is the final volume? Let’s rearrange Charles’ law to find V2. Then we plug in our data after we convert celsius to kelvin. And you get 1.4 L, which makes sense because volume and temperature are directly related. Take a look at Boyles’ law, Gay-Lussac’s law and Charles’ law. We can combine these three laws together as long as we hold the number of moles constant! amazing! Oh man, it’s so beautiful. 5.36 liters of nitrogen gas are at -25 degrees C and 733 mm Hg. What would be the volume at 128 degrees c and 1.5 atm? We are trying to find the final volume, so let’s rearrange this equation to get v2 alone. we multiply both sides of the equation with T2 over p2 and when we clean this up we get this pretty equation. Now we plug in the data, being sure to turn celsius into kelvin,have the same type of pressure units, and calculate. I chose to turn atmospheres into mm Hg. The final volume is 5.57 Liters.