Scientific Understanding

**What is Molarity?**

Molarity is by far the most common way to measure a solution concentration. So whenever you see the word concentration in a problem always immediately think molarity. The definition of molarity is moles of solute per liters of solution. I have written the equation below.

Molarity = | Moles of Solute |

Liters of Solution |

In order to think of it in a more simplistic way and help with problem solving I have simplified the formula into just units like below.

Molarity = | Moles |

Liters |

You can further shorten this into the letter representations of the units.

M = | mol |

L |

Capital M represents molarity. The mol represents moles. Capital L represents liters. When you see the M in a sentence it should usually be next to a number like 5 M. That means 5 molarity and it is a unit.

**Examples**: Solve for the molarity problems below.

If you put 0.4 mols of a solute in a beaker and then fill up with water to 3 L. What is your molarity?

Answer: 0.13 M

A 9M solution was made by filling a container up with 7L of solution. How many moles did it take?

Answer: 63 mol

If you used 2.8 moles to make a 6.3 M solution. What is the volume of that solution?

Answer: 0.44 L

**VIDEO Molarity Demonstrated Example 1**: A 15M solution was made by filling a container up with 4.2L of solution. How many moles did it take?

What information are we given?

Answer:

Molarity = 15M

Volume = 4.2L

What does the question ask for?

Answer: moles = ?

How do we set up the problem?

Answer: Start with the equation

M = | mol |

L |

What can we fill in for the equation?

Answer: The information we are given

15 M = | mol |

4.2 L |

How do we solve?

Multiply both sides by 4.2 L

4.2 L * 15 M = | mol * 4.2 L |

4.2 L |

Cross out 4.2 L on the right side

4.2 L * 15 M = | mol * 4.2 L |

4.2 L |

Simplify

4.2 L * 15 M = | mol |

11 |

Multiply the left side

4.2 L * 15 M = | mol |

11 |

Result

63 = | mol |

11 |

COMPLETE ANSWER: 63 mol

**VIDEO Molarity Demonstrated Example 2**: If you used 7.6 moles of BaCl_{2} to make a 1.2 M solution. What is the volume of that solution?

What information are we given?

Answer:

moles = 7.6 mol

molarity = 1.2 M

The BaCl_{2} does not matter.

What does the question ask for?

Answer: Volume = ? L

How do we set up the problem?

Answer: Start with the equation

M = | mol |

L |

What can we fill in for the equation?

Answer: The information we are given

1.2 M = | 7.6 mol |

L |

How do we solve?

Multiply both sides by L

L * 1.2 M = | 7.6 mol * L |

L |

Cross out L on the right side

L * 1.2 M = | 7.6 mol * L |

L |

Simplify

L * 1.2 M = | 7.6 mol |

1 |

Divide both sides by 1.2 M

L * 1.2 M = | 7.6 mol |

1.2 M | 1.2 M |

Cross out 1.2 M on the left side

L * 1.2 M = | 7.6 mol |

1.2 M | 1.2 M |

Simplify

L = | 7.6 mol |

1.2 M |

Divide the right side

L = | 6.3 |

11 |

COMPLETE ANSWER: 6.3 L

**PRACTICE PROBLEMS**: Solve for the *MOLARITY* problems below.

If you put 4.7 mols of a solute in a beaker and then fill up with water to 8.6 L. What is your molarity?

Answer: 0.55 M

A 0.58 M solution was made by filling a container up with 1.3 L of solution. How many moles did it take?

Answer: 0.75 mol

If you used 3.4 moles to make a 23 M solution. What is the volume of that solution?

Answer: 0.15 L

If you used 6.5 moles to make a 4.2 M solution. What is the volume of that solution in mL?

Answer: 155 mL