Quantitative Chemistry: Moles and Calculations

The bridge you cannot see across

Quantitative chemistry frightens people because it looks like a pile of separate formulae, one for moles, one for concentration, one for yield. It is not. It is one idea used over and over, and once you see the idea the formulae stop being a list to memorise. The idea is the mole, and the mole is a bridge. On one side is mass, which you can actually weigh out in grams. On the other side is the number of particles, atoms and molecules, which you can never count because they are far too small and too many. You cannot get from one side to the other directly. Relative formula mass is what lets you cross. The relative formula mass of a substance is the grams in one mole of it, so it is the exchange rate between grams and moles. Weigh a mass, divide by the relative formula mass, and you have the number of moles, which stands in for the number of particles. That is why almost every calculation is the same three moves. Turn the mass you are given into moles. Use the ratio from the balanced equation to find the moles of the substance you want. Then turn those moles back into a mass, or a concentration, or compare them as a yield. Conservation of mass sits underneath all of it. In a reaction no atoms are made or destroyed, so the total mass of the reactants equals the total mass of the products. Nothing vanishes; it is only rearranged. Show your working, because this strand carries a lot of the maths marks. A wrong final number with clear working still earns method marks; a bare wrong answer earns nothing. Carry one question through everything that follows: have I gone to moles, used the ratio, and come back?

Words for the calculations

Five terms, each defined by what it is. They are the whole toolkit for this unit.

Work out a relative formula mass

Calcium carbonate has the formula CaCO3. Using the relative atomic masses calcium 40, carbon 12 and oxygen 16, work out its relative formula mass. Remember there are three oxygen atoms.

What the mole lets you do

Why is the mole so useful in chemistry calculations?

• It links a mass you can weigh to a number of particles you cannot count, using the relative formula mass as the exchange rate
• It lets you weigh a single atom directly on a balance
• It lets you count the particles one by one
• It tells you the colour a substance will be

Two things you cannot compare directly

The mole exists to connect these two, because on their own they do not meet.

Match each quantity to what it is

Two that follow from the bridge

Select the TWO statements that follow from the mole being the bridge between mass and number of particles.

• The ratio in a balanced equation is a ratio of moles, so you must convert to moles before using it
• To find a reacting mass you go from grams to moles and then back to grams
• You can use the equation ratio directly on the masses in grams
• A balance counts the number of particles for you

Turn a mass into moles

Water has the formula H2O and a relative formula mass of 18. How many moles are there in 36 grams of water?

The three-move calculation

A method for almost any reacting-mass or yield question. Write the balanced equation and the masses you know. The equation gives you the ratio you will need, and it must be balanced first or the ratio is wrong. Move one: turn the known mass into moles. Divide the mass in grams by the relative formula mass of that substance. Now you have moles, which is what the equation actually deals in. Move two: use the ratio. Read the balanced equation for how many moles of what you want are made from, or react with, the moles you have. Multiply across the ratio. Move three: turn the moles back. Multiply the moles of the substance you want by its relative formula mass to get a mass, or divide by a volume to get a concentration. Then sanity-check. A percentage yield above a hundred, or a product heavier than all the reactants together, means an error, because mass is conserved. Two habits lose marks. The first is using the equation ratio on grams instead of moles. The second is not showing the working, so a small slip costs every mark instead of just one.

Order a reacting-mass calculation

Put the steps of a reacting-mass calculation into the order you would do them.

• Write and balance the equation
• Turn the known mass into moles by dividing by its relative formula mass
• Use the equation ratio to find the moles of the substance you want
• Turn those moles back into a mass by multiplying by the relative formula mass
• Check the answer against conservation of mass

Build the three-move rule

This is the routine behind almost every calculation in this unit. Assemble it.

The calculations quick-fire

Five questions on the quantities and how they connect. Three lives.

One reaction, worked all the way

Here is the three-move routine on one reaction. Magnesium burns in oxygen to give magnesium oxide, and the balanced equation is 2Mg plus O2 gives 2MgO. Suppose you start with 48 grams of magnesium and want to know the mass of magnesium oxide made. The relative atomic mass of magnesium is 24 and of oxygen is 16. Move one, turn the known mass into moles. The relative formula mass of magnesium is 24, so 48 grams divided by 24 is 2 moles of magnesium. Move two, use the ratio. The balanced equation shows 2 magnesium give 2 magnesium oxide, a ratio of one to one, so 2 moles of magnesium give 2 moles of magnesium oxide. Move three, turn the moles back into a mass. The relative formula mass of magnesium oxide is 24 plus 16, which is 40. So 2 moles is 2 times 40, which is 80 grams of magnesium oxide. Now the sanity check. The magnesium weighed 48 grams and the oxygen it joined with makes up the rest, so the 80 grams of product is heavier than the magnesium alone but not more than the magnesium and the oxygen together. Mass is conserved, so the answer is believable. Notice that no step needed a new formula. Mass to moles, ratio, moles to mass, then check. That one routine, written out with the working shown, is what earns the marks whatever the reaction.

Complete the calculation facts

The sum of the relative atomic masses of all the atoms in a formula is the _____. The amount of a substance whose mass in grams equals that number is one _____. You find the number of them by dividing the mass by the relative formula mass. How much of a substance is dissolved in a given volume, in moles per cubic decimetre, is its _____.

Three calculations to put right

Three students make a calculation slip. In each case pick what went wrong and how to fix it.

• A student finds the number of moles by multiplying the mass by the relative formula mass, and gets a huge number. What is the fix?
• A student uses the balanced-equation ratio directly on the masses in grams, not on moles. What is the problem?
• A student calculates a percentage yield of a hundred and thirty. What should they conclude?

Explain how to do a reacting-mass sum

A student in the year below can balance equations but freezes when a question asks for a reacting mass. Explain the method you would teach them so it works for any reaction.

• Explain what the mole is and why relative formula mass is the link to mass
• Explain move one, turning a known mass into moles
• Explain move two, using the balanced-equation ratio, and why it must be moles not grams
• Explain move three, turning the moles back into a mass
• Explain how conservation of mass lets you sanity-check the answer
• Finish with why showing the working matters for the marks