## Density and Specific Gravity - Practice Problems

Calculating densities of rocks and minerals.

## Calculating Specific Gravity of Rocks and Minerals

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## Density Problems

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## Density Calculations – Worked Example Problem

Example 3 Again, we want g/mL, and our mass is in kg. Convert the mass to grams.

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## 1.7: Density and Density Problems

## Learning Objectives

## Introduction

\[ \text{Density} = \dfrac{\text{Mass}}{\text{Volume}} \label{1.5.4}\]

\[\rho = \dfrac{m}{v} \label{1.5.5}\]

\[\text{Weight} = \text{mass} \times \text{gravity} \label{1.5.6}\]

\(Weight = {m}{g} \label{1.5.7}\)

Volume = (length)(width)(height)

## Density: A Further Investigation

## Density in the Periodic Table

## Density and Temperature

## Density and Pressure

## Archimedes' Principle

## Percent Composition

If you want to know the percent composition of the elements in an compound, follow these steps:

- Find the molar mass of all the elements in the compound in grams per mole.
- Find the molecular mass of the entire compound.
- Divide the component's molar mass by the entire molecular mass.
- You will now have a number between 0 and 1. Multiply it by 100 to get percent composition!

- The compounds will always add up to 100%, so in a binary compound, you can find the % of the first element, then do 100%-(% first element) to get (% second element)
- If using a calculator, you can store the overall molar mass to a variable such as "A". This will speed up calculations, and reduce typographical errors.

These steps are outlined in the figure below.

## Percent Composition in Everyday Life

## Example \(\PageIndex{1}\): Nutritional Labels

## Example \(\PageIndex{2}\): The Lucky Penny

Following are examples of different types of percent composition and density problems.

- If you have a 2.130 mL sample of acetic acid with mass 0.002234 kg, what is the density?
- Calculate the density of a .03020 L sample of ethyl alcohol with a mass of 23.71002 g.
- Find the density of a sample that has a volume of 36.5 L and a mass of 10.0 kg.
- Find the volume in mL of an object that has a density of 10.2 g/L and a mass of 30.0 kg.
- Calculate the mass in grams of an object with a volume of 23.5 mL and density of 10.0 g/L.
- Calculate the density of a rectangular prism made of metal. The dimensions of the prism are: 5 cm by 4 cm by 5 cm. The metal has a mass of 50 grams.
- Find the density of an unknown liquid in a beaker. The beaker's mass is 165 g when there is no liquid present. With the unknown liquid, the total mass is 309 g. The volume of the unknown is 125 mL.
- Determine the density in g/L of an unknown with the following information. A 55 gallon tub weighs 137.5lb when empty and 500.0 lb when filled with the unknown.
- A ring has a mass of 5.00g and a volume of 0.476 mL. Is it pure silver?
- What is the density of the solid in the image if the mass is 40 g? Make your answer have 3 significant figures.

- Calculate the percent by mass of each element in Cesium Fluoride (CsF).
- Calculate the percent by mass of each element present in carbon tetrachloride (CCl 4 )
- A solution of salt and water is 33.0% salt by mass and has a density of 1.50 g/mL. What mass of the salt in grams is in 5.00L of this solution?
- A solution of water and HCl contains 25% HCl by mass. The density of the solution is 1.05 g/mL. If you need 1.7g of HCl for a reaction, what volume of this solution will you use?
- A solution containing 42% NaOH by mass has a density of 1.30 g/mL. What mass, in kilograms, of NaOH is in 6.00 L of this solution?

Here are the solutions to the listed practice problems.

Percent Composition Problem Solutions

- CsF is 87.5% Cs and 12.5% F by mass
- CCl 4 is 92.2% Cl and 7.8% C by mass
- AUTOR , ARQUIMEDES , and Thomas Little . The Works of Archimedes . Courier Dover Publications, 2002.
- Chande, D. and T. Fisher (2003). "Have a Penny? Need a Penny? Eliminating the One-Cent Coin from Circulation." Canadian Public Policy/Analyse de Politiques 29 (4): 511-517.
- Jefferson, T. (1999). "A Thought for Your Pennies." JAMA 281 (2): 122.
- Petrucci , Ralph , William Harwood , and Geoffrey Herring . Principles and Modern Application. ninth . New Jersey : Peason Eduation , 2007.
- Rauch, F., H. Plotkin, et al. (2003). "Bone Mass, Size, and Density in Children and Adolescents with Osteogenesis Imperfecta: Effect of Intravenous Pamidronate Therapy." Journal of Bone and Mineral Research 18 : 610-614.
- Richardson, J., S. Gwaltney-Brant, et al. (2002). "Zinc Toxicosis from Penny Ingestion in Dogs." Vet Med 97 (2): 96-99.
- Tate, J. "Archimedes’ Discoveries: A Closer Look."

## How to Calculate Density - Worked Example Problem

Finding the ratio between mass and volume.

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## Key Takeaways: How to Calculate Density

- Density is how much matter is contained within a volume. A dense object weighs more than a less dense object that is the same size. An object less dense than water will float on it; one with greater density will sink.
- The density equation is density equals mass per unit volume or D = M / V.
- The key to solving for density is to report the proper mass and volume units. If you are asked to give density in different units from the mass and volume, you will need to convert them.

Question 1: What is the density of a cube of sugar weighing 11.2 grams measuring 2 cm on a side?

Step 1: Find the mass and volume of the sugar cube.

Mass = 11.2 grams Volume = cube with 2 cm sides.

Volume of a cube = (length of side) 3 Volume = (2 cm) 3 Volume = 8 cm 3

Step 2: Plug your variables into the density formula.

density = mass/volume density = 11.2 grams/8 cm 3 density = 1.4 grams/cm 3

Answer 1: The sugar cube has a density of 1.4 grams/cm 3 .

Step 1: Find the mass and volume of the salt water.

density water = mass water /volume water

mass water = density water ·volume water mass water = 1 g/mL · 250 mL mass water = 250 grams

Now we have enough to find the mass of the salt water.

mass total = mass salt + mass water mass total = 25 g + 250 g mass total = 275 g

Volume of the salt water is 250 mL.

Step 2: Plug your values into the density formula.

density = mass/volume density = 275 g/250 mL density = 1.1 g/mL

Answer 2: The salt water has a density of 1.1 grams/mL.

## Finding Volume by Displacement

## Tips for Density Calculations

## More Homework Help

Need more examples of help with related problems?

- Worked Example Problems : Browse different types of chemistry problems.
- Density Worked Example Problem : Practice calculating density.
- Mass of Liquids From Density Example Problem : Use density to solve for mass of a liquid.

## IMAGES

## VIDEO

## COMMENTS

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