Molarity (HSC SSCE Chemistry): Revision Notes

Molarity

What is molarity?

When working with chemical reactions, chemists need a practical way to measure how much of a substance is dissolved in a solution. While we could use mass or percentage concentration, these measures don't directly connect to the number of particles involved in reactions. Since chemical reactions occur between specific numbers of particles (measured in moles), we need a concentration measure that uses moles.

Molarity is a measure of concentration that tells us how many moles of a dissolved substance (called the solute) are present in each litre of solution. This makes it extremely useful for chemical calculations because it directly connects the volume of solution we use to the number of moles participating in reactions.

For example, a solution with a molarity of $0.020 \text{ mol L}^{-1}$ contains exactly 0.020 moles of solute dissolved in one litre of solution. We read this as "zero point zero two zero molar" or "zero point zero two zero moles per litre."

The molarity formula

The basic formula for molarity connects three important quantities:

$c = \frac{n}{V}$

Where:

• $c$ represents molarity (measured in $\text{mol L}^{-1}$)
• $n$ represents the number of moles of solute
• $V$ represents the volume of solution in litres

We can also write this formula in words as:

$\text{Molarity} = \frac{\text{number of moles of solute}}{\text{volume of solution in litres}}$

Working with millilitres

Since laboratory glassware often measures volumes in millilitres rather than litres, we have an alternative form of the molarity formula:

$\text{Molarity} = \frac{\text{number of moles of solute} \times 1000}{\text{volume of solution in millilitres}}$

The multiplication by 1000 converts from millilitres to litres. This means that $500$ mL is the same as $0.500$ L, and we must use the correct form of the equation depending on which volume unit we're working with.

Calculating moles from molarity

If we know the molarity of a solution and the volume we're using, we can calculate how many moles of solute are present. By rearranging the molarity formula, we get:

$n = cV$

This can be written as:

$\text{Number of moles of solute} = \text{molarity} \times \text{volume in litres}$

Alternatively, when working with volumes in millilitres:

$\text{Number of moles} = \frac{\text{molarity} \times \text{volume in millilitres}}{1000}$

This formula is essential when you need to know exactly how much of a substance you're using in a reaction. For instance, if you use $25$ mL of a $0.1 \text{ mol L}^{-1}$ solution, you're using $\frac{0.1 \times 25}{1000} = 0.0025$ moles of solute.

The relationship between mass, moles, and molar mass

To connect molarity calculations with actual masses of substances we weigh in the laboratory, we use another fundamental equation:

$n = \frac{m}{MM}$

Where:

• $n$ represents the number of moles
• $m$ represents the mass (in grams)
• $MM$ represents the molar mass (in $\text{g mol}^{-1}$)

This can be written as:

$\text{Number of moles} = \frac{\text{mass}}{\text{molar mass}}$

Standard solutions

A standard solution is a solution whose concentration has been determined very accurately. These solutions are essential in analytical chemistry because we need to know their exact concentration to perform precise measurements and calculations.

Real-world examples of molarity

Many common household and laboratory chemicals can be described using molarity. Here are some examples that demonstrate the practical range of concentrations:

• Sea water: $\text{NaCl}$ concentration of approximately 0.60 mol L$^{-1}$
• Household ammonia: approximately 1.1 mol L$^{-1}$
• Laboratory hydrochloric acid: typically 8.2 mol L$^{-1}$
• Vinegar: acetic acid concentration of approximately 0.67 mol L$^{-1}$
• Bleach: chlorine concentration of approximately 0.56 mol L$^{-1}$
• Wine: ethanol concentration of approximately 2.4 mol L$^{-1}$

These examples show that molarity is a practical way to describe the strength of solutions we encounter in everyday life and in the laboratory.

Worked examples

Let's work through three different types of molarity calculations to see how these formulas are applied in practice.

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