**Root Mean Square Speed **allows for the determination of the velocity of 1 type of gas molecule.

Root Mean Square Speed

1

concept

## Root Mean Square Speed

1m

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So here we're going to say that the root, mean, square speed formula is used to determine the velocity off one type of gas molecules. So if I want to find the root, mean square speed of core in gas or oxygen gas, this is the formula I would use. So root mean square speed is abbreviated as the R M s equals. Now the term root is used in naming this so route would mean square root, so it equals the square root of three rt over em. Here, M stands for the molar mass of the gas not in grams per mole, but kilograms per mole. And here are remember, ours value can change if we're talking about speed, velocity or energy. Since we're talking about speed here it becomes 8.314 jewels over moles, times K. And then finally, temperature will be, as always, in units of Kelvin. So here this represents our root mean square speed formula. When looking at one particular type of gas molecule

2

example

## Root Mean Square Speed Example 1

2m

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here we have to calculate the root mean square speed of NH three molecules at degrees Celsius. Alright, So NH three is ammonia and remember, root mean square speed. So V r mass equals the square root of three rt over the molar mass of the gas. Here. We're going to say we have temperature of 50 degrees Celsius, so we're gonna add to 73.15 to that. That gives us 3 23.15. Kelvin, remember, because we're dealing with speed, the are we use is 8.314 Yeah. Also remember that when we talk about jewels, jewels are kilograms times meter squared over seconds squared. So here, if we're dealing with, are are constant, which is in jewels over moles. Times k weaken. Substitute this in for Jules. So that becomes kilograms times meter squared over second squared times moles times K. So that is all of our units that we have here Old times k temperature 3 23 15 k divided by the molar mass of the gas in kilograms, not grams per mole. So NH three itself with its one nitrogen and it's three. Hydrogen has a mass of 17.34 g per mole. But if we want to do it in kilograms per mole, remember we have 10 to the 3 g and then 1 kg grams cancel out. So this is 0.17034 kg per mole. So then that is 0.17034 kg per mole here. Then we look and see what units cancel out. So kilograms cancel out with kilograms moles cancel out with moles. Kelvin's cancel out with Kelvin's So we have left is meters squared over seconds squared And if we're taking the square root, that's going to just leave us with meters per second here, 50 has one sigfig but here, having won six figures not great in terms of calculating are root, mean square speed. So here we're going to disregard Sig Figs at least from what's given to us within the question, we're just gonna go with 6 87 point 9 m per second. So here I'm using four significant figures because one significant figure is not accurate enough. If we went by one sigfig, this would round upto 700 m per second, which is Ah, bit different from our actual answer. All right, so just remember the units needed in order to isolate your root, mean square speed.

3

Problem

Determine which gas would have a root mean square speed of 515.59 m/s at 405 K.

A

Cl

_{2}B

CO

_{2}C

F

_{2}D

NH

_{3}E

CH

_{4}4

Problem

The root mean square speed of gas molecules is 283.0 m/s at a given temperature T when the recorded molar mass is 42.0 g/mol. What would be the root mean square speed for a gas with a molar mass of 152.0 g/mol?

A

103.7 m/s

B

128.2 m/s

C

148.8 m/s

D

177.2 m/s

E

205.1 m/s

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