# Moles and molar concentration

### Moles and molar concentration

#### Lessons

In this lesson, we will learn:
• To apply our understanding of moles calculations to solutions.
• To understand the difference between molarity, moles, and mass.
• To be able to calculate molarity of chemicals dissolved in solution.
• To be able to calculate amounts of substance from titration problems.

Notes:

• You cannot use the molar volume of gas constant (22.4 L / mol at STP) if your question is about a solution or is not at standard temperature and pressure (STP). It is only used when dealing with gases at STP.
$\circ$ The same goes for RTP molar volume if not at RTP.

• Molarity means concentration, for chemists - it means the amount of moles of a chemical per amount of volume. For example, in a given volume of solution.
$\circ$ Units of concentration are abbreviated “M”. It means moles per litre, written mol / L or mol L$^{-1}$ or moles per cubic decimeters, written mol / dm$^3$ or mol dm$^{-3}$.
$\circ$ Square brackets, e.g. [HCl] are used to show that the concentration of a chemical is being referred to.

• You can use the formula $c=\frac{n}{V}$ to find concentration, where $n$ = number of moles and $V$ is volume (in liters, L, or cubic decimeters, written dm$^3$). You can re-arrange for $n = c * V$.

• A titration is an experiment used to find out the unknown concentration of an acid by reacting it with a base of known concentration, or vice versa (unknown base with known acid). This lesson covers titration calculations, not the titration method or procedure.

• When answering molar concentration questions, make sure you convert your units properly – volume is often given in mL but concentration is measured in moles per litre!

• Introduction
Expanding our moles calculations
a)
Previous examples – calculating moles using molar mass, and molar volume of gas.

b)
Expansion – concentration of solution.

c)
Expansion – calculating moles in solution.

d)
Titration, an introduction.

• 1.
Find the number of moles and concentration of substances used in chemical reactions.
a)
Calculate the number of moles in 100 mL of 0.2M HCl $_{(aq)}$

b)
Calculate the concentration of a solution of 1.7 litres of water with 0.75 moles of HCl dissolved in it.

c)
Calculate the new concentration of this solution when 3.4 extra litres of water are added to the solution.

• 2.
Find the number of moles and use it to find the volume of substances used in chemical reactions.
a)
Calculate the number of moles in 120mL of 0.05M H$_2$SO$_{4\; (aq)}$ solution.

b)
When H$_2$SO$_4$ and CaCO$_3$ are reacted, CO$_2$ gas is produced. What is the volume of CO$_{2\; (g)}$ produced when 120 mL of 0.1M H$_2$SO$_{4\; (aq)}$ is reacted with an excess amount of CaCO$_3$?

c)
What volume of 0.04M HCl $_{(aq)}$ is required to react completely to neutralise 6 g of Mg(OH)$_2$?

• 3.
Find the number of moles and use it to find the molarity of substances used in chemical reactions.
a)
In a titration reaction, 32 mL HCl $_{(aq)}$ of unknown concentration reacts with 25 mL of 0.5M NaOH $_{(aq)}$. Calculate the molarity of the hydrochloric acid being analysed.

b)
In another titration reaction, it took 14mL of NaOH $_{(aq)}$ of unknown concentration to react with 39 mL of 0.1M H$_3$PO$_{4\; (aq)}$. Calculate the molarity of the NaOH solution used.

• 4.
Find the number of moles and use it to find the quantities of substances used in chemical reactions.
Consider the reaction:
2 Al$_{\;(s)} +$2 NaON$_{\;(aq)} +$2 H$_2$O$_{\;(l)}$→2 NaAlO$_{2\;(aq)} +$3 H$_{2\;(g)}$
a)
A student needs to produce 20L of H$_2$ at STP using this reaction. Excess water and aluminium is available to react with 1.5M sodium hydroxide solution. How much sodium hydroxide solution will be required?

b)
When repeating the experiment, only 500 mL of 2.2M sodium hydroxide solution is available. How many litres of hydrogen gas can be produced given this limit?