Calculating Density

Question

Calculate the density g/ml of a solid if it has a mass of .0019kg and a volume of 0.00303 L

Answer 1

I prefer not just "multiplying by numbers" to get new units. If I am converting from kg to g, I would rather use a conversion factor. A conversion factor is essentially a fraction that is equal to a 1, because the top is equal to the bottom. So you really aren't changing the amount of anything, because multiplying by "1" gives you the same thing! You are only changing the unit or the way it "looks". Since 1000 g = 1 kg, I would write:

0.0019 kg x (1000 g / 1 kg) = 1.9 g

Notice the units of kg cancel out, if you set up conversion factors based on known definitions or true relationships, these will help you solve all sorts of problems! If I multiply 0.0019 kg by 1000 then I get 1.9 kg, which is really not what you are trying to do. You are trying to keep the same quantity or amount, but only change the units you are using to describe it! 0.0019 kg is the same thing as 1.9 g, we just changed the units.

Using this same method, and knowing 1000 mL = 1 L (this is true!) then we can convert the L to mL

0.00303 L x (1000 mL / 1 L) = 3.03 mL

Notice the units of Liters cancel out here, and your new unit is mL. Now to find density, the definition of density is mass per unit of volume, and the formula is D = m / V. So we need to divide the mass in grams by the volume in mL to get density in g/mL (grams per milliliter).

1.9 g / 3.03 mL = 0.627062706 g/mL on my calculator, BUT we need to decide how many digits to report! There are only 2 significant digits (or "sig figs" as some say) in the mass, so we should only report 2 sig figs in our answer. So the final answer should be rounded to 2 sig figs: 0.63 g/mL

Hope that helps, good luck with your class!

Answer 2

1. What information am I given?
2. Mass = 0.0019 kg of Solid
3. Let's convert this to grams
4. 0.0019kg * (1000 g / 1 kg) = 1.9 g
5. Volume = 0.00303 L
6. Let's convert this to mL
7. 0.00303 L * (1000 mL/ 1 L) = 3.03 mL
8. How am I supposed to use this information?
9. The formula I am given is: Density = g / mL = mass / volume
10. Let's plug in our mass and volume
11. 1.9g/ 3.03 mL =______ g/mL
12. Do my units in my answer match my units in the question?

Answer 3

Density equation is Density=Mass (g)/ Volume (mL)

SO, we need to divide .0019kg by .00303L, but first we need the right units.

There are 1000 kg in 1 gram, so you multiply .0019 kg by 1000 and you get 1.9g.

There are 1000mL in 1 L so you multiply .00303 by 1000 and you get 3.03 mL

to find density, divide 1.9/3.03 and you get .627 g/mL

Hope this helped!