identifying gas

[chiddler]

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A gas with empirical formula CH is found to take about 40% more time to diffuse the same distance as neon. What is the molecular formula of the gas?

A. CH4
B. C2H2
C. C3H3
D. C4H4

What i'm incorrectly doing:
Vneon / Vcarbon = sqrt( mmcarbon / mmneon)
1/ 0.4 = sqrt( mmcarbon / 20)

i think the numbers for velocity that i'm using are incorrect....on further thought, it's definitely wrong. How do I translate the "40% more time" to velocity ratio?

 

[MedPR]

A gas with empirical formula CH is found to take about 40% more time to diffuse the same distance as neon. What is the molecular formula of the gas?

A. CH4
B. C2H2
C. C3H3
D. C4H4

What i'm incorrectly doing:
Vneon / Vcarbon = sqrt( mmcarbon / mmneon)
1/ 0.4 = sqrt( mmcarbon / 20)

i think the numbers for velocity that i'm using are incorrect....on further thought, it's definitely wrong. How do I translate the "40% more time" to velocity ratio?

Let's try again.

1.4Vneon = 1Vunknown.

Vunknown/Vneon = sqrt(20/Munkown)

1.4/1 = sqrt(20/Munkown)

M=10.

Why do you multiply by 20? 1.4sqrtM=sqrt20..

 

[chiddler]

huh. so simple!

oh wait it is wrong.

 

[chiddler]

NONO you did it right! algebra error. You multiply 20*2, not divide!

edit: You made this mistake because you wrote the formula incorrectly. not algebra error. lol.

 

[MedPR]

What?

 

[chiddler]

1.4 Vne = Vunk

Vne / Vunk = sqrt(MMunk/MMne)

you switched the right side of the equation up so you put sqrt (MMne/MMunk).

1.4 = sqrt(x/20)

x=40

like i said. so simple 😛 stupid errors

 

[SaintJude]

No, I'm still getting 10.

"Vne / Vunk " doesn't ≠ 1.4 It equals "1/1.4 "

And I checked for a rewrite of graham's law on wiki to make sure i wasn't confused and I still got to 10
If Neon is sbustanced 1, then

M2 = (20 * 1)/ 1.96
~ 10

I guess it' doesn't really matter. Most important is that "40% extra" means 1.4(original)

 

[MedPR]

1.4 Vne = Vunk

Vne / Vunk = sqrt(MMunk/MMne)

you switched the right side of the equation up so you put sqrt (MMne/MMunk).

1.4 = sqrt(x/20)

x=40

like i said. so simple 😛 stupid errors

With the way you have it written, it would be:

1/1.4 = sqrt(x/20)

So 1/2=x/20

x=10.

 

[SaintJude]

Actually, chiddler what's the answer?

The empirical formula weight is 10.
So the molecular formula is a multiple of that...

 

[MedPR]

Actually, chiddler what's the answer?

The empirical formula weight is 10.
So the molecular formula is a multiple of that...

But if it's a CH combound, the minimum empirical weight is 13.

 

[chiddler]

crap . you're right.

answer is c

Book explanation: Choice A can easily be eliminated because not CH. The speed of diffusion and effusion are both inversely proportional to the square root of the mass. Thus the mass should be inversely proportional to the square root of the diffusion rate. 1.4^2 is about 2, so the mass should be about twice that of neon. Checking the periodic table gives C as the answer.

 

[MedPR]

crap . you're right.

answer is c

Book explanation: Choice A can easily be eliminated because not CH. The speed of diffusion and effusion are both inversely proportional to the square root of the mass. Thus the mass should be inversely proportional to the square root of the diffusion rate. 1.4^2 is about 2, so the mass should be about twice that of neon. Checking the periodic table gives C as the answer.

Are you sure you typed the question right?

A gas with empirical formula CH is found to take about 40% more time to diffuse the same distance as neon. What is the molecular formula of the gas?

Should it say that CH takes 40% less time?

 

[chiddler]

Are you sure you typed the question right?



Should it say that CH takes 40% less time?

Very sure. See for yourself, it's question 198 in gchem EK 1001 book if you have it.

 

[ljc]

You all are confusing me. Here's how I did it:

Rate of diffusion = square root(compound 1 weight/compound 2 weight)
1.4 = square root [(compound 1 weight)/20]
2.0 = (compound 1 weight)/20
40 = compound 1 weight

Now look for the one that weighs closest to 40. Choice C is 39, so we'll go with that.

C3H3 weighs approximately 2x the amount of neon, so it will take root(2)=1.4 times longer to diffuse.

 

[chiddler]

Medpr, you reversed the Vne and Vunk values. I had it written Vne = 1.4, Vunk = 1. This gives the correct answer where you had Vne = 1, Vunk = 1.4

Velocity of neon is faster because it is lighter.

 

[MedPR]

1.4 Vne = Vunk

Vne / Vunk = sqrt(MMunk/MMne)

you switched the right side of the equation up so you put sqrt (MMne/MMunk).

1.4 = sqrt(x/20)

x=40

like i said. so simple 😛 stupid errors

Medpr, you reversed the Vne and Vunk values. I had it written Vne = 1.4, Vunk = 1. This gives the correct answer where you had Vne = 1, Vunk = 1.4

Velocity of neon is faster because it is lighter.

Uh, check your math again. Yes, neon is faster, 40% faster, but that's not what you have written.


1.4 Vne = Vunk

Vne / Vunk = sqrt(MMunk/MMne)

you switched the right side of the equation up so you put sqrt (MMne/MMunk).

1.4 = sqrt(x/20)

You have 1.4Vne = Vunknown and Vne/Vunknown = sqrt(Munknown/Mne)

If 1.4Vne = 1 Vunknown, then your equation should be 1Vne/1.4Vne, not
1.4Vne/1Vne.

 

[MedPR]

You all are confusing me. Here's how I did it:

Rate of diffusion = square root(compound 1 weight/compound 2 weight)
1.4 = square root [(compound 1 weight)/20]
2.0 = (compound 1 weight)/20
40 = compound 1 weight

Now look for the one that weighs closest to 40. Choice C is 39, so we'll go with that.

C3H3 weighs approximately 2x the amount of neon, so it will take root(2)=1.4 times longer to diffuse.

In your example, compound 2 is Neon. The rate of neon is 1.4 times the rate of the unknown. So 1.4rate2 = rate1

So, your equation: rate2/rate1 = sqrt(weight1/weight2)

should be rate2/1.4rate2 = sqrt(weight1/weight2).

simplifies to:

1/1.4 = sqrt(x/20)

x=10.

How are you guys getting 1.4 as the numerator and 20 as the denominator on the other side? What am I missing?

 

[MedPR]

This is what it seems like you two are doing.

Given 1.4x = y, Zx=20 and x/y=sqrt(Zy/Zx)

You are doing:

1.4x/y = sqrt(Zy/Zx)

1.4 = sqrt(Zy/20)

Zy=40

I don't understand how you are canceling out the y without replacing the x term with a y term?

 

[chiddler]

Here:

Vunknown = 100% speed = 1 Vunkown
Vneon = 140% speed of Vunk = 1.4 Vunknown

Yes?

So Vneon / Vunknown = 1.4Vunknown / 1 Vunknown = 1.4 as the V's cancel out.

is this wrong?

in the next part, molecular mass of neon is in the denominator so you multiply it with this 1.4 (then square it after).

 

[ljc]

In your example, compound 2 is Neon. The rate of neon is 1.4 times the rate of the unknown. So 1.4rate2 = rate1

So, your equation: rate2/rate1 = sqrt(weight1/weight2)

should be rate2/1.4rate2 = sqrt(weight1/weight2).

simplifies to:

1/1.4 = sqrt(x/20)

x=10.

How are you guys getting 1.4 as the numerator and 20 as the denominator on the other side? What am I missing?

I'm super tired so I can't really follow what you're saying. But hopefully this will help:
The easiest way, in my mind, is to ignore the equation subscripts all together. Understand that the difference in speeds will be equal to the square root of the heavier mass over the lighter mass. For example, you have two gasses, one weighing 90g and the other weighing 10g. Ignore their identities for now, just look at the weights. Plug that into the equation, yielding root(90/10) = 3. So now you know ONE of the gases moves at 3x the rate of the other. Just think about it - which should move faster, the 90g or the 10g? Obviously, the 10g. So now you know the 90g diffuses at a rate one third that of the 10g.

Hopefully that helped. I think using an intuitive approach is better because it prevents you from mixing up silly subscripts, which seems to always happen with these sorts of equations (in Doppler effect, for instance)

Edit: and for the sake of flash card'ing, this is the equation I use in simple form:
Relative rate of diffusion or effusion = root(Heavy/Light)


Edit 2: Found your mistake.
In your example, compound 2 is Neon. The rate of neon is 1.4 times the rate of the unknown. So 1.4rate2 = rate1
You say compound 2 is neon, then you say that compound 1 is travelling 1.4x the speed of neon. Your equation should be the other way around: rate2=1.4rate1, where 2 is neon and 1 is the unknown

 

[MedPR]

Here:

Vunknown = 100% speed = 1 Vunkown
Vneon = 140% speed of Vunk = 1.4 Vunknown

Yes?

So Vneon / Vunknown = 1.4Vunknown / 1 Vunknown = 1.4 as the V's cancel out.

is this wrong?

in the next part, molecular mass of neon is in the denominator so you multiply it with this 1.4 (then square it after).

Yes, I agree with this and I now realize where my error was. You actually made the same error, but made another error afterwards and they canceled each other out.

Originally you had this

1.4 Vne = Vunk

Vne / Vunk = sqrt(MMunk/MMne)

When you work that out properly, you get Munkown=10.

However, you are correct now that you have 1.4Vunk=1Vne.

I always have a problem with this type of algebra and I don't know why. I just figured it out by plugging in numbers.

For example, Vne is 1.4 times faster than Vunkown. Initially you (well, I) want to write 1.4Vne=1Vunkown, but that's wrong.

If Vunkown is 10, then Vne is 14. And therefore 1.4Vunkown=1Vne.

So, just to be sure I understand:

Vne is 1.4x faster than Vunk.
1.4Vunk=Vne

Vne/Vunkown=sqrt(Munkown/Mne)
1.4Vunk/Vunk=sqrt(M/20)
1.4^2=M/20
2=M/20
M=40

The mistake that I (and SaintJude) made was making 1.4Vne=Vunk, instead of correctly making 1Vne=1.4Vunk.

 

[MedPR]

I'm super tired so I can't really follow what you're saying. But hopefully this will help:
The easiest way, in my mind, is to ignore the equation subscripts all together. Understand that the difference in speeds will be equal to the square root of the heavier mass over the lighter mass. For example, you have two gasses, one weighing 90g and the other weighing 10g. Ignore their identities for now, just look at the weights. Plug that into the equation, yielding root(90/10) = 3. So now you know ONE of the gases moves at 3x the rate of the other. Just think about it - which should move faster, the 90g or the 10g? Obviously, the 10g. So now you know the 90g diffuses at a rate one third that of the 10g.

Hopefully that helped. I think using an intuitive approach is better because it prevents you from mixing up silly subscripts, which seems to always happen with these sorts of equations (in Doppler effect, for instance)

Edit: and for the sake of flash card'ing, this is the equation I use in simple form:
Relative rate of diffusion or effusion = root(Heavy/Light)


Edit 2: Found your mistake.
In your example, compound 2 is Neon. The rate of neon is 1.4 times the rate of the unknown. So 1.4rate2 = rate1
You say compound 2 is neon, then you say that compound 1 is travelling 1.4x the speed of neon. Your equation should be the other way around: rate2=1.4rate1, where 2 is neon and 1 is the unknown

Yea, I just realized that was the mistake being made. I certainly understand the concept, it's just the algebra that keeps getting me.

 

[chiddler]

you actually made the same error, but made another error afterwards and they canceled each other out.

 

[TexasApp2013]

.

 

[SaintJude]

Finally, looking at this problem again I realize why it's confusing so many people. It's the grammar!

More often, textbooks (and likely AAMC) will phrase the velocity statement something more like this: "A gas with empirical formula CH is found to take x % longer than neon to travel the same distance."
Maybe it makes no difference to others, but for me this sentence structure translates more easily into math.

 

[SanDiegoHopeful]

Actually this is how you can do this.

we know d = v * t

since the have the same distance

v(neon) * t(neon) = v(unk) * t(unk)

unk takes 1.4 * time of neon. Hence

v(neon) * t(neon) = V(unk) * 1.4 * t(neon). t(neon) cancels out and do the math you get

v(neon) / v(unk) = 1.4

Therefore 1.4 = sqrt( x / 20 ) --> 2 = x / 20 --> x = 40.