# Simple Question: Units and volume of DNA - Can't get formula correct?

## Homework Statement

Deoxyribonucleic acid (DNA) is thought to be the chemical compound
responsible for the process of heredity. A sample of DNA was found to have
density 1.10 g/cm3 and its molecular weight was estimated to be
3.04 × 108 g. What is the average volume occupied by one DNA molecule?

## The Attempt at a Solution

I am stuck here. I know V = mass/density

Would I go something like:

3.04 x 10^8 g per mol x (1 mol / 6.022x10^23 molecules) x ( 1 cm^3 / 1.10 g)

No thats not right...dammit

Any help would be great. I know its a simple question, but I need to know exactly how to get the answer.

Thanks all!!!

Ignore.

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You know exactly how to get the answer: $v = m / \rho$. What have moles got to do with it?
I thought the correct units for molecular weight is g/mol, and since we are finding the volume of one DNA molecule, I thought I had to do a few conversion factors.

Ignore.
If I do it that way 3.04 x 10^8 / 1.1 I get... 2.76364 x 10^8 cm^3

which is impossible for just one DNA molecule to occupy that space.

gneill
Mentor

## Homework Statement

Deoxyribonucleic acid (DNA) is thought to be the chemical compound
responsible for the process of heredity. A sample of DNA was found to have
density 1.10 g/cm3 and its molecular weight was estimated to be
3.04 × 108 g. What is the average volume occupied by one DNA molecule?

## The Attempt at a Solution

I am stuck here. I know V = mass/density

Would I go something like:

3.04 x 10^8 g per mol x (1 mol / 6.022x10^23 molecules) x ( 1 cm^3 / 1.10 g)

No thats not right...dammit

Any help would be great. I know its a simple question, but I need to know exactly how to get the answer.

Thanks all!!!
Your method looks okay. Why do think it's not right? Are having difficulty with the unit conversions for grams or cubic centimeters?

The molecular weight defines how much mass of something is in a mole, i.e. 6.02(10^23) molecules. You need to normalize the volume to one molecule. Your answer should be correct. Just make sure you put your answer in the units that the answer called for.

I thought the correct units for molecular weight is g/mol, and since we are finding the volume of one DNA molecule, I thought I had to do a few conversion factors.
Forget what I said; I was answering the wrong question.

Your method looks okay. Why do think it's not right? Are having difficulty with the unit conversions for grams or cubic centimeters?
Is there a better way to do this. Can you maybe explain?

When you look at this question, what steps are you thinking to do?

Yes, having little issue with last part (1 cm^3 / 1.10g)

So, when I see something like 1.10g/cm^3, if I want to get rid of the g, i would just go...1cm^3 / 1.10 g

Slightly confused :(

If I do it that way 3.04 x 10^8 / 1.1 I get... 2.76364 x 10^8 cm^3

which is impossible for just one DNA molecule to occupy that space.
DNA molecules are huge (although not that huge; I didn't realize you were still looking at my first stupid answer). Compare its molecular weight with that of a more typical molecule.

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DNA molecules are huge (although not that huge; I didn't realize you were still looking at my first stupid answer). Compare its molecular weight with that of a more typical molecule.
lol, yea its true. They are pretty big.

gneill
Mentor
Is there a better way to do this. Can you maybe explain?
The method that you used is the standard approach, so no need to tinker there.
When you look at this question, what steps are you thinking to do?
Same as you did!
Yes, having little issue with last part (1 cm^3 / 1.10g)

So, when I see something like 1.10g/cm^3, if I want to get rid of the g, i would just go...1cm^3 / 1.10 g

Slightly confused :(
The grams will cancel with another grams earlier in the expression chain. In fact the first item in the chain was the molecular weight given as grams/mol. So the grams in its numerator cancel the grams in the denominator of the density, even though they are separated by other links in the calculation chain.

Great, thanks. Much better understanding now!