a. What is the total rotational kinetic energy of 1.0 mol of nitrogen gas at 300 K?

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Hey, everyone. Let's go through this problem. A container is filled with 2.5 moles of oxygen gas at a temperature of 350. Kelvins calculate the rotational kinetic energy of the gas inside the container. Option A 3.6 kilojoules, option B 7.3 kilojoules, option C 11 kilojoules and option D kilojoules. Since we're trying to find the uh an amount of energy of the gas, we can use the energy equation which states that for a molecule, the energy of the molecule for one degree of freedom is equal to one half multiplied by the number of molecules multiplied by the Boltzmann constant multiplied by the temperature. T this equation should look familiar to you, but you might have seen it in very slightly different forms because for the one half part of the equation, the numerator here which I've written as a one is specifically referring to the number of degrees of freedom we're dealing with. Now, for the purposes of this problem, we're specifically looking for a rotational kinetic energy, which means that the only degrees of freedom we're worried about are the ones that are there as a result of the molecule's rotation. Now, it's important to realize the problem also tells us that it's oxygen gas we're looking at which is a diatomic molecule, meaning it is two atoms. And if you'll recall a diatomic molecule can only rotate on two axes, it cannot rotate along all three. So that means there are only two degrees of freedom that we're worried about. So I'm going to erase the one here, I've written in the numerator and instead write two because we have two degrees of freedom, two divided by two is one. So the actual rotational kinetic energy here is just N K T. Now, the problem doesn't give us a big N the number of molecules, but we are given the number of moles of the gas. So we can rewrite this term in the other form that we see a lot small N or the number of moles multiplied by the ideal gas constant multiplied by the temperature. So now let's just plug in the value values that we were given because now there shouldn't be anything unknown. The 2.5 moles multiplied by the ideal gas constant, 8.314 Jews per mole. Kelvins multiplied by the temperature 350 Kelvins. And if we put this into a calculator, we find a rotational energy of about 274. jewels. And since all the multiple choice options are written in terms of kilojoules, we can round this by dividing by 1000 and it, and we can round it to 7.3 kilojoules. And if we look at our multiple choice options, we can see that this option exists. It agrees with option B 7.3 kilojoules. So option B is the answer to the problem. And that's it for this video. I hope this video helped you out. If you need more practice. Please check out some of our other videos which will give you more experience with these types of problems. But that's all for now. I hope you all have a good day. Bye bye.

a. What is the total rotational kinetic energy of 1.0 mol of nitrogen gas at 300 K?

Verified Solution

Key Concepts

Rotational Kinetic Energy

Degrees of Freedom

Ideal Gas Law