Calculate The Molarity M of The Following Solutions

Molarity (M) is a measure of the concentration of a solution, defined as the number of moles of solute per liter of solution. This calculator helps you determine the molarity of a solution when you know the amount of solute and the total volume of the solution.

What is Molarity?

Molarity is a fundamental concept in chemistry that describes how much of a particular substance is dissolved in a given volume of solvent. It's commonly used in chemistry, biochemistry, and pharmaceutical applications to quantify the concentration of solutions.

The term "molar" refers to the number of moles of solute, while "ity" indicates the concentration. Molarity is different from molality, which measures moles of solute per kilogram of solvent, and from mole fraction, which measures moles of solute per total moles of solution.

Molarity Formula

Molarity (M) = Moles of Solute (n) / Volume of Solution (V)

Where:

M = Molarity (moles per liter, mol/L)
n = Number of moles of solute
V = Volume of the solution in liters (L)

To calculate molarity, you need to know the number of moles of solute and the total volume of the solution in liters. The formula is straightforward once these values are known.

How to Calculate Molarity

Step 1: Determine the Moles of Solute

First, calculate the number of moles of solute using the formula:

n = mass of solute (g) / molar mass of solute (g/mol)

For example, if you have 5 grams of sodium chloride (NaCl) with a molar mass of 58.44 g/mol:

n = 5 g / 58.44 g/mol ≈ 0.0856 mol

Step 2: Measure the Solution Volume

Next, measure the total volume of the solution in liters. For example, if you dissolve the sodium chloride in 250 milliliters of water:

V = 250 mL = 0.25 L

Step 3: Apply the Molarity Formula

Finally, plug the values into the molarity formula:

M = n / V = 0.0856 mol / 0.25 L ≈ 0.3424 M

This means the solution has a molarity of approximately 0.3424 moles per liter.

Molarity Units

Molarity is typically expressed in moles per liter (mol/L), often written as "M". Other common units include:

Millimolar (mM) = 1/1000 M (0.001 M)
Micromolar (µM) = 1/1,000,000 M (0.000001 M)
Normality (N) = Equivalent weight per liter (used for acids and bases)

Understanding these units helps in interpreting concentration values across different scientific fields.

Molarity Examples

Example 1: Diluting a Solution

You have a 1 M solution of hydrochloric acid (HCl). You want to prepare 500 mL of a 0.5 M solution. How many milliliters of the 1 M solution do you need?

M₁V₁ = M₂V₂

1 M × V₁ = 0.5 M × 0.5 L

V₁ = (0.5 × 0.5) / 1 = 0.25 L = 250 mL

You need 250 mL of the 1 M solution to make 500 mL of 0.5 M solution.

Example 2: Calculating Moles from Molarity

You have 250 mL of a 0.2 M sodium hydroxide (NaOH) solution. How many moles of NaOH are present?

n = M × V = 0.2 M × 0.25 L = 0.05 mol

The solution contains 0.05 moles of NaOH.

FAQ

What is the difference between molarity and molality?

Molarity measures moles of solute per liter of solution, while molality measures moles of solute per kilogram of solvent. Molarity changes with temperature because the volume of the solution changes, whereas molality remains constant.

How do I convert molarity to molality?

To convert molarity to molality, you need to know the density of the solution. The formula is:

Molality (m) = Molarity (M) × Density (ρ) / 1000

What is the difference between molarity and normality?

Molarity measures moles of solute per liter of solution, while normality measures equivalents of solute per liter of solution. Normality is commonly used for acids and bases where the equivalent weight is different from the molar mass.

How do I dilute a solution to a specific molarity?

Use the dilution formula:

M₁V₁ = M₂V₂

Where M₁ and V₁ are the initial molarity and volume, and M₂ and V₂ are the final molarity and volume.