# 3.51: Solution Concentration

Difficulty Level: At Grade Created by: CK-12
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Practice Solution Concentration

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Dante was shopping for juice and saw a bottle of juice concentrate. He read the label and learned that some of the water had been removed from the juice before it was bottled, so the concentrate had to be mixed with water before drinking. Next to the bottle of juice was a can of juice. The canned juice was ready to drink. Juice concentrate is an example of a concentrated solution. Ready-to-drink juice is an example of a dilute solution.

### Concentrated and Dilute Solutions

A solution is a mixture of two or more substances in which dissolved particles are distributed evenly throughout the solution. The substance that dissolves in a solution is called the solute, and the substance that does the dissolving is called the solvent. The concentration of a solution is the amount of solute in a given amount of solution. A solution with a lot of dissolved solute has a high concentration and is called a concentrated solution. A solution with little dissolved solute has a low concentration and is called a dilute solution.

### Calculating the Concentration of a Solution

The concentration of a solution represents the percentage of the solution that is the solute. You can calculate the concentration of a solution using this formula:

Concentration=Mass(orvolume)ofSoluteMass(orvolume)ofSolution×100%\begin{align*}\mathrm{Concentration= \frac{Mass \; (or \; volume) \; of \; Solute}{Mass \; (or \; volume) \; of \; Solution} \times 100\%}\end{align*}

For example, if a 100-gram solution of salt water contains 3 grams of salt, then its concentration is:

Concentration=3g100g×100%=3%\begin{align*}\mathrm{Concentration= \frac{3g}{100g} \times 100\%}=3\%\end{align*}

Q: A 1000 mL container of brand A juice drink contains 250 mL of juice and 750 mL of water. A 600 mL container of brand B juice drink contains 200 mL of juice and 400 mL of water. Which brand of juice drink is more concentrated, brand A or brand B?

A: Concentration(A)=250mL1000mL×100%=25%\begin{align*}\mathrm{Concentration(A)= \frac{250\; mL}{1000\; mL} \times 100\%}=25\%\end{align*}

Concentration(B)=200mL600mL×100%=33%\begin{align*}\mathrm{Concentration(B)= \frac{200\; mL}{600\; mL} \times 100\%}=33\%\end{align*}

You can conclude that brand B is more concentrated.

### Summary

• The concentration of a solution is the amount of solute in a given amount of solution. A concentrated solution has more solute in a given amount of solvent than a dilute solution.
• The concentration of a solution can be calculated with this formula:
Concentration=Mass(orvolume)ofSoluteMass(orvolume)ofSolution×100%\begin{align*}\mathrm{Concentration= \frac{Mass \; (or \; volume) \; of \; Solute}{Mass \; (or \; volume) \; of \; Solution} \times 100\%}\end{align*}

### Review

1. What is the difference between a dilute and a concentrated solution?
2. What is the concentration of a 500 mL solution that contains 5 mL of solute?
3. James mixed added 25 grams of solute with 75 grams of solvent. Then he calculated the concentration of the solution as:

Concentration(B)=25g75g×100%=33%\begin{align*}\mathrm{Concentration(B)= \frac{25\; g}{75\; g} \times 100\%}=33\%\end{align*}

What error did James make in his calculation? What is the correct concentration of this solution?

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### Vocabulary Language: English

TermDefinition
concentration Number of particles of a substance in a given volume, or ratio of solute to solution in a solution.

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