E. Solutions and Solubility · Solutions and Solubility

Concentration II: Molar Concentration (mol/L)

E2.2 E2.1 A1.12 A1.13About 70 minutes

Learning goals

I can calculate molar concentration from mass or amount of solute and volume of solution.
I can rearrange c = n/V to find the amount, mass or volume needed.
I can find the concentration of each ion in a solution of an ionic compound.
I can convert between mol/L, g/L, % m/v and ppm.

Words to know

amount concentration (molar concentration), c
The amount of solute in moles per litre of solution, c = n/V, unit mol/L.

mol/L (M)
Moles of solute per litre of solution. Some books write M ('molar'): 0.10 M = 0.10 mol/L.

square brackets [ ]
Shorthand for the molar concentration of a substance or ion: [Na⁺] means 'the concentration of sodium ions in mol/L'.

molar mass, M
The mass of one mole of a substance, in g/mol, found by adding atomic molar masses from the periodic table.

volumetric flask
Glassware with a single line that marks one exact volume, used to make solutions of accurate concentration.

Counting particles, not grams

Chemical reactions happen between particles. A gram of salt and a gram of sugar contain very different numbers of particles, so chemists prefer a concentration unit based on the mole: moles of solute per litre of solution. This is called molar concentration (or amount concentration). The hospital saline in an IV drip, the acid in a titration, and the stock solutions in every chemistry lab are labelled in mol/L.

Remember from the Quantities in Chemical Reactions unit

A mole (mol) is 6.02 × 10²³ particles. The molar mass (M, in g/mol) converts between mass and moles: n = m ÷ M. For example, M(NaCl) = 22.99 + 35.45 = 58.44 g/mol.

The formula

c = n ÷ V

c = molar concentration in mol/L
n = amount of solute in mol
V = volume of solution in litres (convert mL to L by dividing by 1000)

Rearranged: n = c × V and V = n ÷ c.

If you are given a mass, first convert it to moles with n = m ÷ M.

Notice that V is the volume of the solution, not the volume of water added. That is why chemists dissolve the solute and then add water up to the line on a volumetric flask: the final volume is known exactly.

A memory triangle for c = n ÷ V. Cover the quantity you want: n is over c × V. Always use litres for V.

Both beakers contain the same amount of solute. Spreading it through twice the volume halves the concentration.

Worked example

Example 1: Finding concentration from mass

A student dissolves 5.85 g of sodium chloride in water to make 250.0 mL of solution. Find the molar concentration.

List what you know: m = 5.85 g, M(NaCl) = 58.44 g/mol, V = 250.0 mL = 0.2500 L.
Find moles: n = m ÷ M = 5.85 g ÷ 58.44 g/mol = 0.1001 mol.
Find concentration: c = n ÷ V = 0.1001 mol ÷ 0.2500 L = 0.4004 mol/L.
Round to three significant digits (5.85 has three): c = 0.400 mol/L.

[NaCl] = 0.400 mol/L

Worked example

Example 2: Mass needed for a solution

What mass of copper(II) sulfate pentahydrate, CuSO₄·5H₂O (M = 249.72 g/mol), is needed to make 500.0 mL of a 0.100 mol/L solution?

n = c × V = 0.100 mol/L × 0.5000 L = 0.0500 mol.
m = n × M = 0.0500 mol × 249.72 g/mol = 12.486 g.
Round to three significant digits: 12.5 g.
Note: the five water molecules in the formula are part of the solid you weigh, so they are included in the molar mass.

12.5 g of CuSO₄·5H₂O

Ion concentrations

When an ionic compound dissociates, the ratio in the formula tells you each ion's concentration.

For 0.20 mol/L CaCl₂: CaCl₂(s) → Ca²⁺(aq) + 2 Cl⁻(aq)

[Ca²⁺] = 1 × 0.20 = 0.20 mol/L
[Cl⁻] = 2 × 0.20 = 0.40 mol/L

This matters because reactions in solution happen between ions, so you will need ion concentrations for solution stoichiometry.

Each CaCl₂ unit releases one Ca²⁺ and two Cl⁻ ions, so the chloride concentration is twice the calcium chloride concentration.

Converting between units

To change mol/L into mass units, multiply by molar mass: (mol/L) × (g/mol) = g/L. Then:

g/L ÷ 10 = g/100 mL = % m/v
g/L × 1000 = mg/L ≈ ppm (for dilute water solutions)

For example, 0.154 mol/L NaCl × 58.44 g/mol = 9.00 g/L = 0.900% m/v: this is exactly the "normal saline" used in hospitals.

Just for fun

Chemists' favourite way to say they made a solution too strong: "I got a little too concentrated on my work." Their favourite way to fix it: just add water and dilute the situation (the next lesson shows how).

Hands-on activity

Make a 0.10 mol/L sugar solution

You need: table sugar (sucrose, C₁₂H₂₂O₁₁, M = 342.34 g/mol), a kitchen scale that reads to 1 g, a 1 L measuring jug or a clean 1 L bottle with a known fill mark, a funnel, a spoon and water.

Calculate the mass of sugar for 1.00 L of a 0.10 mol/L solution: n = 0.10 mol, m = 0.10 × 342.34 = 34 g.
Weigh 34 g of sugar. Pour it into the jug, add about 600 mL of water and stir until all is dissolved.
Add water up to the 1 L mark, and stir again. (This is what a volumetric flask does in the lab.)
Now calculate: if you had dissolved the 34 g in exactly 1.00 L of water and then measured, would the volume be more or less than 1 L? Test it if you have a second jug.
Write two sources of error in your kitchen version compared with the lab version (scale precision, the jug's markings).

What to look for: dissolving sugar in 1 L of water gives a little more than 1 L of solution, so the concentration would be slightly below 0.10 mol/L. That is why the definition uses volume of solution. Use the sugar water for a houseplant only if very dilute; otherwise pour it down the drain.

Your turn

Find the concentration when 0.250 mol of KCl is dissolved to make 0.500 L of solution.

How many moles of HCl are in 2.00 L of 0.150 mol/L HCl(aq)?

4.00 g of NaOH (40.00 g/mol) is dissolved to make 500.0 mL of solution. Find [NaOH].

What mass of glucose (C₆H₁₂O₆, 180.18 g/mol) is needed for 250.0 mL of 0.200 mol/L solution?

What volume of 0.250 mol/L solution contains 0.0100 mol of solute?

Find [K⁺] and [SO₄²⁻] in 0.30 mol/L K₂SO₄.

Find [NO₃⁻] in 0.10 mol/L Fe(NO₃)₃.

More practice: warm-up

Write the formula for molar concentration and give its unit.

Convert 250 mL to litres.

What does [Cl⁻] mean?

1.0 mol of solute in 2.0 L of solution: concentration?

What does 0.5 M mean?

More practice: on your own

10.0 g of sucrose (342.34 g/mol) is dissolved to make 250.0 mL. Find the concentration.

What mass of silver nitrate (169.88 g/mol) is in 20.0 mL of 2.50 mol/L AgNO₃(aq)?

A 0.100 L sample contains 1.17 g of NaCl. Find [Na⁺] and [Cl⁻].

Convert 0.154 mol/L NaCl into g/L and % m/v.

Vinegar is 5.0% m/v acetic acid (CH₃COOH, 60.06 g/mol). Find its molar concentration.

Challenge

Concentrated hydrochloric acid is 37% m/m HCl with a density of 1.19 g/mL. Find its molar concentration. (M(HCl) = 36.46 g/mol)

100.0 mL of 0.20 mol/L NaCl is mixed with 200.0 mL of 0.10 mol/L CaCl₂ (no reaction). Find [Na⁺], [Ca²⁺] and [Cl⁻] in the mixture.

Fluoride in treated drinking water is about 0.7 mg/L. Convert this to mol/L (M(F) = 19.00 g/mol) and explain why ppm is the more convenient unit here.

Check your understanding

Quiz

The molar concentration of 0.40 mol of solute in 2.0 L of solution is

How many moles are in 250 mL of 0.40 mol/L solution?

In 0.25 mol/L Na₂CO₃, [Na⁺] is

In c = n/V, V must be the volume of

What mass of NaCl (58.44 g/mol) is needed for 1.00 L of 0.500 mol/L solution?

2.0 mol/L of NaOH (40.00 g/mol) equals

For parents and teachers

Big idea (E2.2): molar concentration (c = n/V) counts particles per litre, which is what matters in reactions.

How to help: Have your teen say the steps aloud: "grams to moles with molar mass; mL to L; then divide." Check that every quantity has a unit and the units cancel.

Common difficulties:

Using mL instead of L (answers 1000 times too small).
Forgetting to convert mass to moles first.
Forgetting the formula ratio for ion concentrations ([Cl⁻] in CaCl₂ is double).
Rounding mid-calculation. Keep all digits until the end, then round to the least number of significant digits in the data.

This lesson depends on mole skills from the Quantities in Chemical Reactions unit; if moles feel shaky, review n = m/M there first.