Kinetic Energy of Gases - Online Tutor, Practice Problems & Exam Prep

Kinetic energy, denoted as KE, is the energy an object possesses due to its motion. It can be calculated using two different formulas depending on the available information. When the mass (in kilograms) and velocity (in meters per second) of a gas are known, KE is determined by the equation:

$\mathrm{KE}=\frac{1}{2}m{v}^2$

with the resulting energy in joules (kg·m²/s²). Alternatively, when dealing with the amount of gas in moles and its temperature in Kelvin, the kinetic energy can be calculated using:

$\mathrm{KE}=\frac{3}{2}nRT$

where 'n' is the number of moles, 'R' is the ideal gas constant (8.314 J/mol·K), and 'T' is the temperature in Kelvin. The units of this calculation are in liters·atmospheres, which can be converted to joules using the conversion factor 1 L·atm = 101.325 J. It's important to select the appropriate formula based on whether mass and velocity or moles and temperature are the known variables.

Kinetic Energy of Gases

Now, kinetic energy is the energy an object possesses due to its motion, and since we're looking at gases, we're going to look at how we can use the kinetic energy formulas and relate them to the motion of gases. So here we're going to say we have two different versions. In the first one we use this one we have the mass and velocity of a gas. Here we say kinetic energy, abbreviated as KE, equals half m * v².

Here we're going to say that M is the mass of the gas in kilograms. Here it's not in mass and in grams, it's in kilograms, and V equals velocity of the gas in meters per second. Now kinetic energy, the value of it will be in joules, or if we take a look, this is in kilograms 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 second 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 going to say kinetic energy now equals 32 and then we have times moles times RT. 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 two 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 use the one on the left and if you're dealing with moles and temperature you use the one on the right.

Kinetic Energy of Gases Example 1

Here in this example question it says a 1.56×1013 picogram gaseous particle travels at 6.21 meters per second. Determine its kinetic energy. All right, 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 1.56×1013 picograms. Remember 1 pico is 10-12 and then we want to get rid of grams so they go on the bottom kilograms. On top, 1K is 103, so that's going to give me 0.0156 kilograms.

We're going to plug this into our formula. So it's going to be half 0.0156kg × 6.21 meters squared a meters over seconds, and that's holding squared. When you punch this into your calculator, you're going to get 1.203 kilograms times meter squared over second squared, which is just joules. This is 1.203 Joules.

Here it'll specify joules or kilojoules. If we want to change this to kilojoules, you could just say 1.203 joules. 1K is 103, so this will be 0.001203 kilojoules or 1.20×10-3 joules. And then this one here would be 1.20 joules having oh kilojoules having one in kilojoules and one in joules. Both here are acceptable answers because again, I didn't specify what units to have kinetic energy in, so either one is is acceptable.

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

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.

• A. 2815 J
• B. 3620 J
• C. 3850 J
• D. 4750 J
• E. 5250 J

Here’s what students ask on this topic:

Why does gas have the most kinetic energy?

Gases have the most kinetic energy among the states of matter (solid, liquid, and gas) due to the nature of their particles. In a gas, the particles are much farther apart compared to solids and liquids, and they move freely and rapidly in all directions. This high-speed movement of particles is a manifestation of kinetic energy.

Since there are no significant forces holding the gas particles close together, they collide with each other and the walls of their container in a random and continuous manner. These collisions are perfectly elastic, meaning the gas particles do not lose energy when they collide; instead, they transfer kinetic energy to each other and their surroundings.

The temperature of a gas is directly related to the average kinetic energy of its particles. As the temperature increases, the particles move faster, thus increasing the kinetic energy of the gas. This is why, at the same temperature, gas particles have more kinetic energy than the particles in solids or liquids, where the movement is more restricted.