## How do you convert percentage concentration to molarity?

To convert percentage concentration to molarity, you need to know the **density** of the solution and the **molecular weight** of the solute. The process involves several steps:

- Calculate the mass of solute in a given volume of solution.
- Convert the mass of solute to moles.
- Calculate the volume of the solution in liters.
- Divide the number of moles by the volume in liters to get molarity.

Suppose you have a **25% (w/w)** solution of **sodium hydroxide (NaOH)** with a density of **1.28 g/mL**. To convert this to **molarity**:

- For 100 g of solution, there are 25 g of NaOH.
- The molecular weight of NaOH is 40 g/mol.
- Moles of NaOH = 25 g ÷ 40 g/mol = 0.625 mol
- Volume of solution = 100 g ÷ 1.28 g/mL = 78.125 mL = 0.078125 L
- Molarity = 0.625 mol ÷ 0.078125 L = 8 M

A 25% (w/w) solution of NaOH with a density of 1.28 g/mL is equivalent to an 8 M solution.

Converting percentage concentration to molarity is a common task in chemistry. **Percentage concentration** represents the mass of solute per 100 units of solution, while **molarity** expresses the number of moles of solute per liter of solution.

## Percentage Concentration to Molarity Conversion Chart

Percentage Concentration (w/w) | Density (g/mL) | Molecular Weight (g/mol) | Molarity (M) |
---|---|---|---|

5% | 1.05 | 58.44 (NaCl) | 0.90 |

10% | 1.10 | 58.44 (NaCl) | 1.88 |

15% | 1.15 | 58.44 (NaCl) | 2.95 |

20% | 1.20 | 58.44 (NaCl) | 4.11 |

25% | 1.25 | 58.44 (NaCl) | 5.35 |

30% | 1.30 | 58.44 (NaCl) | 6.68 |

35% | 1.35 | 58.44 (NaCl) | 8.10 |

40% | 1.40 | 58.44 (NaCl) | 9.59 |

Note: This chart uses sodium chloride (NaCl) as an example solute. The density values are approximate and may vary in real solutions.

## Percent Concentration to Molarity Formula

The formula to convert percent concentration to molarity is:

**M = (ρ × w% × 10) ÷ MW**

Where:

- M is molarity (mol/L)
- ρ (rho) is the density of the solution (g/mL)
- w% is the weight percentage of the solute
- 10 is a conversion factor (1000 mL/L ÷ 100%)
- MW is the molecular weight of the solute (g/mol)

Convert 12% (w/w) sulfuric acid (H2SO4) solution with a density of 1.08 g/mL to molarity.

- ρ = 1.08 g/mL
- w% = 12
- MW of H2SO4 = 98.08 g/mol

M = (1.08 × 12 × 10) ÷ 98.08 = 1.32 M

Convert 45% (w/w) potassium hydroxide (KOH) solution with a density of 1.45 g/mL to molarity.

- ρ = 1.45 g/mL
- w% = 45
- MW of KOH = 56.11 g/mol

M = (1.45 × 45 × 10) ÷ 56.11 = 11.63 M