Chemical Forums
Chemistry Forums for Students => Undergraduate General Chemistry Forum => Topic started by: Luke149 on August 10, 2010, 11:09:40 AM
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Hi, im having a problem converting between two concentrations, the concentration im given is in g / 100 cm^3 and i need to convert this into kg / m^3.
My attempt at converting it so far is as follows. For the first concentration i have 0.4 g/100cm^3 which is equal to 0.004 g/cm^3, if you then multiply this by a 1000 you get 4 kg/m^3.
Ive always found it really had to get my head around conversions so if anyone can give a description of how you would do it i would be really appreciated.
Thank You
Luke
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OK i just realized i was being a bit of a fool since g/100cm^3 = g/m^3 so dividing by 1000 gives kg/m^3
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OK i just realized i was being a bit of a fool since g/100cm^3 = g/m^3 so dividing by 1000 gives kg/m^3
Not quite. 100 cm3 is not 1 m3.
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Ok im really stuck with this ive spent hours trying to understand how to convert g/100cm^3 to kg/m^3 and im just not getting anywhere. Can anyone help my understand what to do? Many Thanks
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Do it step by step using so called dimensional analysis.
Do you know how to cancel units?
Do you know that there are 1000g in 1 kg? In other words there is 1kg per 1000 g, so 1kg/1000g is our conversion factor, if you multiply
0.4 g/cm3 * 1 kg/1000g = 0.0004 kg/cm3
and that's the first correct step. Now convert cm3 to m3.
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Ah i think i understand so to convert 100cm^3 to m^3 you would do
1cm3 = 1x10-6m3
100cm3 = 1x10-4m3
So in 100cm3 there are 1x10-4m3
Therefore
0.0004 kg/cm3 * 1m3 / 0.0001cm3 = 4 kg/m3
Is this correct? Thanks for the help it was much appreciated
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Ok so ive had a go at another conversion problem to check im understanding what to do. The problem is convert 0.4 g/100cm3 to g/dm3 my solution is:
1dm3 = 1000cm3 so there is 1dm3 per 1000cm3
but since the origional units are in g/100cm3 the conversion factor is 1/(1000/100) = 0.1
therefore 0.4g/100cm3 * 0.1 = 0.04g/dm3
Is this correct? Thank You
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1cm3 = 1x10-6m3
100cm3 = 1x10-4m3
Correct.
So in 100cm3 there are 1x10-4m3
Correct, but not necessary. It is enough to know what you write earlier, there is 1m3 per 1000000cm3, so
100 cm3 = 100 cm3 * 1m3 / (1000000 cm3)
What we are doing is we multiply initial volume by the conversion factor. Conversion factor is constructed in such a way that is in fact equal 1, so multiplication doesn't change anything when it comes to the value, however, it has units selected in such a way that cm3 cancels out and we are left with m3 only:
100 cm3 = 100 cm3 * 1m3 / (1000000 cm3) = 100/1000000 m3 = 10-4 m3
1m3 / 0.0001cm3
See above, this conversion factor is incorrect. Plus, it goes in the wrong direction - check what units is your answer in (cancel units and check what is left).
but since the origional units are in g/100cm3
I would say original units are g/cm3, 100 was a volume. It is possible to proceed as you are proposing (that is assume 100 cm3 should be treated as entity) but it is easier and safer to not to.
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Ok so ive had a go at another conversion problem to check im understanding what to do. The problem is convert 0.4 g/100cm3 to g/dm3 my solution is:
1dm3 = 1000cm3 so there is 1dm3 per 1000cm3
but since the origional units are in g/100cm3 the conversion factor is 1/(1000/100) = 0.1
therefore 0.4g/100cm3 * 0.1 = 0.04g/dm3
Is this correct? Thank You
No it is wrong.
If there are 0.4g in 100cm3 and 1 dm3 = 1000cm3 will there be 10times more or less in 1dm3 compared with 100cm3? Now look at your answer.
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Ah so to convert from 100cm3 to m3 the conversion factor is 100cm3 * 1m3/1000000cm3 the cm3 cancel and you are left with 100/1000000 = x10-4m3 therefore 0.0004 kg/100cm3 would be 4x10-8kg/m3
and for the second problem, converting g/100cm3 to g/dm3 the conversion factor would be
1dm3 = 10cm3
so 100cm3 = 100cm3 * 1dm3 / 10cm3 = 10
therefor 0.4g/100cm3 = 4g/dm3
Is this correct?
Thanks for the help
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Ah so to convert from 100cm3 to m3 the conversion factor is 100cm3 * 1m3/1000000cm3 the cm3 cancel and you are left with 100/1000000 = x10-4m3 therefore 0.0004 kg/100cm3 would be 4x10-8kg/m3
No. While you are right 100 cm3 is 10-4 m3, you then multiply by the volume, instead of dividing.
0.4g
----
100cm3
We need two conversion factors, g -> kg
1kg
------
1000g
and cm3 -> m3
1m3
-------------
1000000cm3
and conversion looks like
0.4g x 1kg x 1000000cm3
--------------------------
100cm3 x 1000g x 1m3
g and cm3 cancels out. At this stage JUST CALCULATE the value, no further steps required.
1dm3 = 10cm3
No, 1 dm3 is not 10 cm3 (just like 1 m3 is not 100 cm3)
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Ok so for the conversion from 0.4g/100cm3 you get this which cancels down to
0.4g x 1kg x 1000000cm3
--------------------------
100cm3 x 1000g
Which gives 0.4 x 10 x kg / m3 or 40 kg/m3
so for the conversion of g/100cm3 to g/dm3
you only need one conversion factor which is cm3 to dm3
1dm3
---------
1000cm3
so the conversion is
0.4g x 1000cm3
---------------
100cm3 x 1dm3
giving 0.4g x 10 / dm3 or 4 g/dm3
Does this make more sense?
Sorry its taking so long for mt to grasp this, thank you for the help
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Which gives 0.4 x 10 x kg / m3 or 40 kg/m3
Sorry this should be 4kg/m3
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Twice OK.
Unless I am wrong, I am too tired to think clearly.
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Thank you so much for your help i used your method to do a couple of eample questions and got the correct answers so i think its all good :)