Calculations With Density

Calculations: Density

Now, let's move on to the last objective for the lesson and work with density again. You have experience in making the necessary measurements (or you will when you have completed the lab work) and calculating the density of materials. One use of density is to help identify materials. It can also be used to determine the concentration of certain mixtures such as battery acid, antifreeze, urine and blood.

Another use for density is as a conversion factor between mass and volume. It can be used as a conversion factor because it relates the two proportional properties of mass and volume. I should point out that mass and volume are proportional for a given material under given conditions. If you change materials or conditions, such as temperature or pressure, the density will change.

In this section we will look at the use of density as a conversion factor and also at the algebraic approach that can be used to accomplish the same things.

Density as a Conversion Factor

Suppose you wanted to know how much space a particular mass of a certain substance would occupy. To convert mass to volume (or vice versa), you must know the relationship between the mass and volume and that relationship is density.

First, let's review how to find the density of an object with a mass of 5.0 g and a volume of 2.0 g. The density is mass divided by volume.

d = 5.0 g/2.0 mL = 2.5 g/mL

Now that we know the density for this material, we can calculate how much 6.0 milliliters of it would weigh as asked for here. Take the 6.0 milliliters and then use the density 2.5 grams per milliliter as a conversion factor. The 2.5 goes on top with the grams and the one milliliter goes on the bottom because you want to cancel out milliliters and end up with grams. The result is 15 grams.

6.0 mL * 2.5 g/1 mL = 15 g

Next we can find how much volume four grams of this material would occupy? You start with 4.0 grams and multiply by one milliliter over 2.5 grams and you come up with the answer of 1.6 milliliters.

4.0 g * 1 mL/2.5 g = 1.6 mL

The Algebraic Approach

An algebraic approach can be used for density calculations also. If you are familiar with algebra you know that it involves representing a relationship with an equation and using symbols to represent quantities.

You know that density equals mass divided by volume. That relationship can then be expressed in many ways by carefully rearranging the equation. Mass equals volume times density. Volume equals mass divided by density. Which form of the equation is used depends on what you are trying to figure out.

d = m/V m = V*d V = m/d

This example asks the same question as before, but the approach to the answer is different. First write down the appropriate form of the equation--or write down the standard form and then rearrange it. Next substitute the known values into the equation and carry out the calculations.

m = d*V

m = 2.5 g/mL * 6.0 mL

m = 15 g

Next, answer the questions in the following study check using whichever method you prefer.

Study Check: Density Conversions

Select the correct answer for each of the following questions. (These are also shown in your workbook as Exercise 41.) Answers follow at the bottom of this page.

1. If an object weighs 43.3 g and it has a volume of 11.2 mL, what is the density of the material of which it is made?

a. 485 g/mL

b. 4.85 g/mL

c. 3.87 g/mL

d. 2.59 g/mL

e. 0.259 g/mL

2. If a material has density if 3.50 g/mL, how much space would 7.0 g of it take up?

a. 24.5 mL

b. 10.5 mL

c. 2.45 mL

d. 2.0 mL

e. 0.50 mL

3. If a material has a density of 7.25 g/mL, how much would 15.5 mL of it weigh?

a. 214 g

b. 112 g

c. 22.8 g

d. 2.14 g

e. 0.468 g

4. Will 85 g of lead fit into a 50 mL container? The density of lead is 11.4 g/mL.

a. yes

b. no

Answers