Scientific Tutor
Chem – Density Problem Solving
Author: Andrew
What sections should I know before attempting to learn this section?
—> Introduction to Problem Solving
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:
COMPLETE ANSWER: D = 0.437g/mL
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?
Answer: 0.53g/ml
What is density of something that is 36L and 97g?
Answer: 2.69g/L
What is the mass of a cube that has a density of 42g/mL and a volume of 520mL?
Answer: 21840g
An object is 34L and 369g/L. What is the mass of the object?
Answer: 12546g
What is the volume of an object that has a density of 74g/mL and a mass of 58g?
Answer: 0.78ml
If an object is 23kg and 4kg/L. What is the volume?
Answer: 5.75L
Posted in Chemistry
