Kinetic Energy of Gases - Video Tutorials & Practice Problems

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Kinetic Energy is the energy an object possesses due to its motion.

Kinetic Energy of Gases

1

concept

Kinetic Energy of Gases

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Now kinetic energy is the energy an object possesses due to its motion. And since we're looking at gases, we're gonna look at how we can use the kinetic energy formulas and relate them to the motion of gases. So here we're gonna say we have 2 different versions. In the first one, we use this when we have the mass and velocity of a gas. Here we say kinetic energy, abbreviated as ke, equals half m times v squared. Here we're going to say that m is the mass of the gas in kilograms. Here it's not in mass in in grams, it's in kilograms. And v equals velocity of the gas in meters per second. Now, kinetic energy, the the value of it will be in joules or if we take a look, this is in kilograms and and velocity is meters over seconds. Right? But it's being squared. So that would mean when we multiply kilograms times meters over second and all that's being squared, that comes out to kilograms times meters squared over seconds squared. So here joules are equivalent to kilograms times meter squared over seconds squared. Now going on the other side, we use this version when we have the moles and temperature of a gas. In this version, we're gonna say kinetic energy now equals 3 over 2, and then we have times moles times r t. Here, n equals the amount of gas in moles, r, remember we use 8.314 when we're talking about velocity, speed, or energy. Here we're talking about kinetic energy, so we're using 8.314. Temperature equals this always in units of Kelvin. And then we're going to say here, when we're multiplying these values out, we get liters times atmospheres as the units. And that's an equal to 101.325 joules. Now here we have these 2 kinetic formulas, realize that neither one is in purple boxes, which means you don't need to memorize them. If you'll be asked to deal with kinetic energy in some way, you tend to see it embedded within the question or on a formula sheet. Just keep in mind, based on if you're dealing with mass and velocity, you use the one on the left. And if you're dealing with moles and temperature, you use the one on the right.

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example

Kinetic Energy of Gases Example 1

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2m

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Here in this example question it says, a 1.56 times 10 to the 13 picogram gaseous particle travels at 6.21 meters per second. Determine its kinetic energy. Alright. Remember, kinetic energy equals half your mass in kilograms times your velocity squared. What we need to do first is convert our picograms into kilograms. So we have 1.56 times 10 to the 13 picograms. Remember, 1 pico is 10 to the negative 12. And then we wanna get rid of grams, so they go on the bottom. Kilograms on top. 1 kilo is 10 to the 3. So that's gonna give me 0.0156 kilograms. We're gonna plug this into our formula. It's gonna be half point 0156 kilograms times 6.21 meters squared meters over seconds, and that's whole thing squared. When you punch this into your calculator, you're gonna get 1.203 kilograms times meter squared over second squared, which is just joules. So this is 1.203 joules. Here it'll specify joules or kilojoules. If we wanna change this to kilojoules, you could just say 1.203 joules. One kilo is 10 to the 3. So this will be 0.00 1203 kilojoules or 1.20 times 10 to the minus 3 joules. And then this one here would be 1.20 joules. Having oh, kilojoules. Having 1 in kilojoules and 1 in joules. Both here are acceptable answers, because again I didn't specify what units to have kinetic energy in, so either one is acceptable.

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Problem

Problem

A baseball with a mass of 503 g possesses a kinetic energy of 0.815 kJ. Calculate its velocity in m/s.

A

18.5 m/s

B

28.2 m/s

C

38.6 m/s

D

56.9 m/s

E

69.1 m/s

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Problem

Problem

A 10.0 L flask contains a mixture of neon and argon gases at a pressure of 2.38 atm. Calculate the total kinetic energy of the gaseous mixture.