Chemistry math problem - finding volume

[Ladybug]

Hello all!

I'm not really sure what category to put this in, so I just put it here if that's ok.

I had a test today and didn't know the answer to one question. It's my first chemistry test (just started chemistry with lab a few weeks ago in school). I'm pretty sure I got it wrong because I just guessed, I was so confused! Anyway, here's the problem:

A fisherman wants to determine the volume of his lead sinker. If lead's density is 11.4 grams per cc and the sinker has a mass of 0.123 kg, what is the volume of the sinker?

So we have cc or cm cubed or mL, and kg. First of all I didn't know the relationship between grams and liters so that confused me also. Dividing the mass in grams by the volume in liters will get the density, right? I converted and changed 11.4 mL to .0114 L and .123 kg to 123 g. I was still really confused and finally just put .0114 as the answer just because I had nothing better at the time.

It's probably simple, I just couldn't see it. Thanks in advance!

 

[Deleted member 4993]

Hello all!

I'm not really sure what category to put this in, so I just put it here if that's ok.

I had a test today and didn't know the answer to one question. It's my first chemistry test (just started chemistry with lab a few weeks ago in school). I'm pretty sure I got it wrong because I just guessed, I was so confused! Anyway, here's the problem:

A fisherman wants to determine the volume of his lead sinker. If lead's density is 11.4 grams per cc and the sinker has a mass of 0.123 kg, what is the volume of the sinker?

So we have cc or cm cubed or mL, and kg.

First of all I didn't know the relationship between grams and liters so that confused me also. Dividing the mass in grams by the volume in liters will get the density, right? I converted and changed 11.4 mL to .0114 L and .123 kg to 123 g. I was still really confused and finally just put .0114 as the answer just because I had nothing better at the time.

It's probably simple, I just couldn't see it. Thanks in advance!

$\displaystyle Density \, = \, \frac{mass}{Volume}$

$\displaystyle Volume \, = \, \frac{mass}{Density} \, = \, \frac{gm}{\frac {gm}{cc}} = gm \cdot \frac {cc}{gm} \, = \, cc$

$\displaystyle Volume \, = \, \frac{123 \, gm}{11.4 \, \frac{gm}{cc}} \, = 10.78947368 \, cc \, = \, 10.8 \, cc$

 

[Ladybug]

Thanks for answering, Mr. Khan. I think I get the reasoning although a bit complicated till I studied it. I'm writing that number down in my notebook and see if it matches the correction when I get my test back. Nice to know early that I got it completely wrong! :roll:

 

[Deleted member 4993]

I'm writing that number down in my notebook ...

Instead, write the process down - internelize it. You'll use it many many times.

You have used the process many times - I am sure - with different units.

You are looking at pants that cost 40 dollars/pant (equivalent to density). You have 200 dollars (equivalne to mass). How many pants (equivalent to volume) can you buy with that money?

See --- no difference....

 

[Ladybug]

Thank you! Yes, the answer was right, AND especially after I figured it out (looking at your answer for the g/cc, at which I got stuck - wanting to write 11.4g / cc) instead of writing it all out in my notebook.

In doing my homework, I'm solving for the volume of a sphere in liters. Is there any direct way to convert from meters to liters? Each measure different things, so I didn't think there was. But apparently there is, as I have to convert from meters to get the volume in liters in the steps. How would I go about doing this?

 

[Deleted member 4993]

Thank you! Yes, the answer was right, AND especially after I figured it out (looking at your answer for the g/cc, at which I got stuck - wanting to write 11.4g / cc) instead of writing it all out in my notebook.

In doing my homework, I'm solving for the volume of a sphere in liters. Is there any direct way to convert from meters to liters?

No ... meters is LENGTH and Liters is VOLUME ... two different animals

You can go from Cubic meters (Volume) to liters.

1 cu m (or M[sup:25iyxrn5]3[/sup:25iyxrn5]) = 10[sup:25iyxrn5]6[/sup:25iyxrn5] cu cm (cc or cm[sup:25iyxrn5]3[/sup:25iyxrn5]) = 1000 liters



Each measure different things, so I didn't think there was. But apparently there is, as I have to convert from meters to get the volume in liters in the steps. How would I go about doing this?

 

[Ladybug]

1 cu m (or M3) = 10^6 cu cm (cc or cm3) = 1000 liters

That's where I messed up my test. I hadn't seen cubed meters before and had no idea how to get from that to mL and from that to L, which is easy once the relationships are known. Maybe I can memorize it along with the other things I memorized (deca, kilos, centi etc etc). Thanks for pointing out!