Eleven molecules have speeds 15, 16, 17, …, 25 m/s. Calculate (a) vₐᵥ₉ and (b) vᵣₘₛ.

Question

Accepted Answer

Hey, everyone. So this problem is dealing with the root square speed of gasses. Let's see what it's asking us. We have a sample of 15 nitrogen molecules that has speeds ranging from 36 m per second, all the way up to 50 m per second in one second, in 1 m per second, increments were asked to determine the average seed and the routine square seed of the nitrogen molecules in the sample. Our multiple choice answers are a 43 milli meter, sorry, 43 m per 2nd and 43.2 m per second. B 44 m per 2nd and 44.2 m per second. D 42 m per 2nd and 42.2 m per second or d 41 m per 2nd and 41.2 m per second. OK. So the first part of this problem is asking for the average speed. And so the average speed is going to be the sum of our speeds of each molecule divided by the number of speeds that we are adding. So this is a kind of straightforward average uh summation here. And so we can write that as the sum from N equals 36 to 50 of each speed divided by 15 because we have 15 molecules. And so we put that into our calculator and we get meters per second divided by 15. And our average speed comes out to meters per second. And so when we look at our multiple choice answers, we can eliminate everything other than answer choice. A but let's solve for part two to make sure that we're on the right track. So our route means square speed or VR MS is equal to the square root of the sum of each of those speeds squared. And again, that's from N equals 36 to all of that divided by 15. And so when we plug that into our calculator, we get 43.2 m per second. And so we can see that yes, we were on the correct track and the correct answer is a, that's all we have for this one. We'll see you in the next video.

Eleven molecules have speeds 15, 16, 17, …, 25 m/s. Calculate (a) vₐᵥ₉ and (b) vᵣₘₛ.

Verified Solution

Key Concepts

Average Speed (vₐᵥ₉)

Root Mean Square Speed (vᵣₘₛ)

Kinetic Theory of Gases