A simple unit conversion problem that I don't get.

[JerusalemLuver]

The question is a enthalopy problem where the enthalopy has to be caluculated per mole at the end. I understand how to calculate the enthalopy change, but I can't seem to calculate the number of moles in the question to be able to calculate the change in enthalapy per mole. I'm given 50.0 cm^3 of 1.00 mol dm^-3 of a substance. The answer is given so I know it's 0.05 moles but how was that calculated? And also why is it dm^-3 and not dm^3?

I know that a cm is a hundreth of a meter and a dm is 10cm/meter or is it? I'm really confused about my units (especially the cubed parts) so if someone can clarify all this it would be greatly appreciated.

 

[mrjeffy321]

You are given a molar “density” (moles per unit volume) of your substance as well as the volume of the substance used in the reaction.

Your molar density is given as,
1.00 mol dm^-3

Now you asked why it is dm^-3 and not dm^3….maybe it is because of this fact that you did not realize you were given a density.
Remember the ‘rules of exponents’…a negative exponent in the numerator of a fraction can be re-written as a positive exponent in the denominator of a fraction. So if you were to move the dm term to the denominator of the fraction you would get,
1.00 mole / dm^3
And of course dm^3 is a unit of volume equal to 1000 cubic centimeters (10 cm * 10 cm * 10 cm = 1000 cm^3 = 1 dm^3).

So now you know how many moles of your substance are in a given volume, and you also know the volume (50.0 cm^3), so you should be able to calculate the number of moles.

 

[JerusalemLuver]

Still a bit confused...

You're right I forgot about the rule of exponents, but I'm still a bit confused about "And of course dm^3 is a unit of volume equal to 1000 cubic centimeters (10 cm * 10 cm * 10 cm = 1000 cm^3 = 1 dm^3)." can anyone simplify this concept any further?
P.S. Is 1dm = 10cm ?

 

[chemisttree]

The prefix "deci-" (abbreviated "d" here) means one tenth. Deciliter is 100 mL and decimeter is 10 cm.