Chem conversion questions...?

Question

1.) What is the mass in grams, or a cork having a volume of 72cm^3. Given the density of the cork is 240 kg/m^3? What happens to the units do I have to covert them?

2.) A 100 gram sample of iron ore was found to contain 44 g of iron, how many grams of iron are in a 450 gram smaple of the ore?

Thanks!

Answer 1

1) Yes, you will need to be converting units before you can complete the problem. It can be seen that the density uses cubic meters, but the volume is in units of cubic centimeters. Let's convert the cubic centimeters to meters, but it can also be done vice-versa.

(72 cm^3) * (.01 m / cm) * (.01 m / cm) * (.01 m / cm) = 0.00072 m^3

Now, we can do direct multiplication to find the mass, as the density is the ratio of mass to volume.

(240 kg / m^3) * (0.00072 m^3) = 0.01728 kg

Now, we need to convert that to grams, as that is what the problem asks us to do.

(0.01728 kg) * (1000 g / kg) = 17.28 grams

2) This problem is a simple ratio. Since 100 grams of a sample contains 44 g of iron, there is a percentage that can be obtained for the content of iron in the sample.

44 g iron / 100 g sample = 0.44 g iron / g sample

Now, we can use that ratio to obtain our answer.

(0.44 g iron / g sample) * (450 g sample) = 198 grams iron

Answer 2

(72 cm^3)*(1 m^3/ 1000 cm^3) * (240 kg/m^3) = 17.28 Kg

44 gm Fe / 100 gm sample = 0.44 gm Fe / gm sample

(450 gm sample)*(0.44 gm Fe / gm sample) = 198 grams Fe

BTW" "Fe" is the atomic symbol of Iron. Is cork really 2.40 kg/m^3? A two inch cube of cork should not weigh 43 pounds.

Answer 3

This is just bookkeeping.  

240 kg/m^3 x 1000g/1kg x (1m/100 cm)^3 = 0.240 g/cm^3

Now you have got your data in the same units, you can go ahead and use

Mass = density x volume

Principle: use conversion factors such that the thing on top is worth the same as the thing on the bottom, and the conversion takes you out of the units you are in to start with, into the units you want to finish with.

2) is just a matter of scaling up.