Chem question >_<

[stan18]

yes, its took weeks before school (for me) and i'm thinking about chemistry.

 

 

 

my friend just approached me with a question that we can't seem to figure out - is the speed of a light gaseous molecule faster than that of a heavier one when: the temperature, pressure, and volume are held constant?

 

 

 

the problem he showed me involved balloons with different substances, all with 1L of gas, thus the pressure is constant, and at 30 degrees C. i was taught by my chem teacher that, with gases, the only thing that mattered was the number of moles. no qualitative properties of the gas mattered (unless it increased moles), so i figured that the mass of substances wouldn't make a difference. but when we approached people who finished chem AP (two who got 5 on the ap test), their answers did not agree.

 

 

 

so, could someone help me out? its 11:17 pm and i still haven't found an answer :x

[ice_ring]

I don't really know, but what I think is :

 

 

 

Heavier gases = more energy needed to move the atoms, and since there is the same amount of energy (the temperature) the lighter gas would need less energy to be moved so they would move at different speeds.

 

 

 

I wouldn't trust my answer too much though, because I just started Chemistry a week ago. :-w

[Devilsdragon]

Speed of the molecules.. wtf are you talking about

 

I took chem and we learned nothing of that

 

 

 

but cheating in chem= instawin

[ice_ring]

Speed of the molecules.. * are you talking about

 

I took chem and we learned nothing of that

 

 

 

but cheating in chem= instawin

 

 

 

You went through chemistry and didn't learn that molecules are always moving...wow...that is some extreme cheating :shame:

[stan18]

Speed of the molecules.. * are you talking about

 

I took chem and we learned nothing of that

 

 

 

but cheating in chem= instawin

 

 

 

woah, you really didn't learn that? :shock: thats really weird

[Turnip]

I finished AP Chem this year, and we learned about this stuff. When it comes to 2 gases of different mass, the one with a lower molar mass will be faster than that with a higher one.

 

 

 

This presents the equation--

 

 

 

r1/r2=square root of(M2/M1)

 

with..

 

r1 = root-mean-square speed of the first gas

 

r2 = root-mean-square speed of the second gas

 

M1 = molar mass of the first gas

 

M2 = molar mass of the second gas

 

 

 

To show some proof using the equation, let's be given this.

 

There are two gases, one is hydrogen (H2 since hydrogen is a diatomic atom) and the other is an unknown of unknown mass. The speed of the H2 is 4 while the other unknown gas is 2.

 

 

 

So let's plug everything into the equation--

 

 

 

2/4=square root of(2.02/x)

 

we square both sides to get rid of the route so we're given

 

 

 

4/16=2.02/x

 

cross multiply and we get

 

 

 

4x = 32.32

 

divide both sides by 4

 

 

 

8.08 grams

 

 

 

So, the gas with the slower speed of 2m/s or whatever has a mass of 8.08 grams, which is higher than the hydrogen (molar mass of 2.02g) which has a speed of 4m/s.

 

 

 

Hope that helps, Im a little rusty since I am already forgetting everything i learned haha, might want to double check on that.

[Adolpha]

this is a poorly constructed problem. to really solve it, you need to know the number of moles in each balloon.

 

 

 

however, assuming that the number of moles are equal, then, yes, the lighter molecule is moving faster than the heavier one.

 

 

 

we know this because we can think of gaseous pressure as the force generated by molecules striking the walls of their containers (in this case, the balloons). this force, which can be also loosely called kinetic energy, is determined by the mass of the molecules and their velocity (which in this case is the same as the speed). the mathematical formula for kinetic energy is KE=(1/2)(m)(v^2).

 

 

 

now, you may also have learned that pressure, temperature, volume, and the number of moles are related in the equation PV=nRT (R=a constant). since the problem states that P, V, T, and n (assumingly) are all held constant, the only variables we are left with are m (particle mass) and v (velocity/speed).

 

 

 

since pressure is equal (while n, V, and T are held constant), we also know that the molecules kinetic energy must also be equal. so, by simple mathematics, we can conclude that the molecule with the lower mass(m) must be moving at a greater velocity(v).

 

 

 

in turnip's post, he pretty much used graham's law (i think that's what it was called) to illustrate the same principles.

 

 

 

well, i hope that made sense. good luck.

 

 

 

btw, i took ap chem last yr and got a 5 on my ap test. but i havnt touched chem in 2 months so take what i say with a grain of salt...haha

[stan18]

OMG thanks guys, i'm going into ap chem this year. looks fun :)

 

 

 

grahams law... i didn't even think of that. probably 'cause i learned that in bio instead of chem :x

 

 

 

thanks again :D

[killmenub]

I havent even done Chem and i know that molecules are constantly moving, and the higher in temperature they are the faster they move, the more energy they have, and the more they bump into eachother :P

[runesmithie]

I havent even done Chem and i know that molecules are constantly moving, and the higher in temperature they are the faster they move, the more energy they have, and the more they bump into eachother :P

 

 

 

But the temperatures in his problem are the same ;)