## Chem – Density Problem Solving

What sections should I know before attempting to learn this section?

How do you solve density word problems?

To help further your problem solving skills, I will introduce you to the concept of density. Density is the mass per unit volume. Another way to state that is the mass divided by the volume. See equation below:

 Density = mass volume 1 D = m V

The letter D represents Density, the letter m represents mass, and the letter V represents volume. The density equation has 3 variables. That means in a problem where you have to use density, you will be given 2 variables and asked to solve for the 3rd. Density can have different units like (g/mL) or (g/L) or (kg/L) or (mg/mL) just to name a few. How do we use it to solve some equations? Look to the demonstrated examples below.

VIDEO Density Problem Solving Demonstrated Example 1: What is the density for a mass that is 345g and 789mL?

Step 1:  highlight number and units

What is the density for a mass that is 345g and 789mL?

Step 2:  write numbers and units

mass = 345g

volume = 789mL

Step 3:  restate the question

density = ?

Step 4

Now what is a formula or concept that relates together mass, volume, and density?

Answer: the density formula (so write down the density formula below)

 D = m V

Step 5:

What next?

Answer: fill in the numbers and units from your steps 1 through 3.

 D = 345g 789mL

Step 6:

Solve for density (D)

Answer: 245g / 789mL = 0.437g/mL

Step 7:

VIDEO Density Problem Solving Demonstrated Example 2: What is the volume of an object that is 154g and has a density of 67g/L?

Step 1:  highlight numbers and units

What is the volume of an object that is 154g and has a density of 67g/L?

Step 2:  write numbers and units

mass = 154g

density = 67g/L

Step 3:  restate question

volume = ?

Step 4:

Now what is a formula or concept that relates together mass, volume, and density?

Answer: the density formula (so write down the density formula below)

 D = m V

Step 5:

What next?

Answer: fill in the numbers and units from your steps 1 through 3.

 67g/L = 154g V

Step 6:

How do you solve for volume?

Answer: First multiply both sides by V

 V * 67g/L = 154g * V V

Step 7:

Cross out V on the right side

 V * 67g/L = 154g * V V

Step 8:

Simplify

 V * 67g/L = 154g 1

Step 9:

Now divide both sides by 67g/L (red)

 V * 67g/L = 154g 67g/L 67g/L

Step 10:

Cross out 67g/L on the left side

 V * 67g/L = 154g 67g/L 67g/L

Step 11:

Simplify

 V = 154g 67g/L

Step 12:

Solve for V

Answer: 154 / 67 = 2.30 L

Step 13:

COMPLETE ANSWER: V = 2.30 L

PRACTICE PROBLEMS: Solve for the missing variable in the word problem.

What is the density of an object with a mass of 25g and a volume of 47mL?

What is density of something that is 36L and 97g?

What is the mass of a cube that has a density of 42g/mL and a volume of 520mL?

An object is 34L and 369g/L. What is the mass of the object?

What is the volume of an object that has a density of 74g/mL and a mass of 58g?  