Molarity

Core Concept

Molarity (M) is a unit of concentration used to describe how much solute is dissolved in a given volume of solution. It is defined as the number of moles of solute per liter of solution.

Molarity is calculated using the formula:

$M = \frac{\text{moles of solute}}{\text{liters of solution}}$

Practice Tips

Confusing molarity (M) with molality (m), which is moles of solute per kilogram of solvent.
Using the mass of the solution instead of the volume in liters.
Forgetting that diluting a solution decreases molarity but does not change the number of moles of solute.
Molarity is temperature dependent! Since molarity depends on the volume of the solution, it is temperature-dependent (volume changes with temperature).

Test Yourself

Assorted Multiple Choice

A student weighs out $10.6\text{ g}$ of pure sodium carbonate ($Na_2CO_3$, molar mass = $106.0\text{ g/mol}$) and dissolves it in enough distilled water to prepare exactly $250.0\text{ mL}$ of solution. What is the molarity of the resulting sodium carbonate solution?

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Molarity

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Direct Calculation of Molarity

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Calculating Moles or Volume from Molarity

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Molarity from Mass (Single-Step Conversion)

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Conceptual and Variable Analysis

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Molarity Formula

Molarity is calculated using the formula:

$M = \frac{\text{moles of solute}}{\text{liters of solution}}$

Where:

M = Molarity of the solution (in moles per liter, or mol/L)
Moles of solute = The amount of solute in moles
Liters of solution = The total volume of the solution in liters

Brain Hack Tip

🧠 Here is a tip of how to remember how to remember molarity 🧠

Two cute mice holding onto the edge of a glass container.

Key Concepts

Solute and Solvent:

Solute: The substance that is dissolved (e.g., salt in a saltwater solution).
Solvent: The substance in which the solute is dissolved (e.g., water in a saltwater solution).
Solution: The homogeneous mixture of solute and solvent.

Dilution:

Diluting a solution reduces its molarity by adding more solvent.
Dilution formula: $M_1 V_1 = M_2 V_2$
Where:
- $M_1$ and $V_1$: Initial molarity and volume
- $M_2$ and $V_2$: Final molarity and volume

Temperature Dependence:

Since molarity depends on the volume of the solution, it is temperature-dependent (volume changes with temperature).

Steps for Calculating Molarity

Calculate Moles of Solute:
- If the amount of solute is given in grams, convert it to moles using the molar mass of the solute. $\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$
Determine Volume of Solution in Liters:
- Convert the solution volume to liters if necessary (1 L = 1000 mL).
Apply the Molarity Formula:
- Substitute the moles of solute and the liters of solution into the formula: $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

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