One mole is both a count of particles and a mass

1. Counting atoms one at a time is impossible, so chemists count them in moles instead.
2. One mole of any substance contains $6.02\times 10^{23}$ particles.
3. The particles are whichever the formula represents: atoms for an element such as aluminium, molecules for $O_2$, formula units for $NaCl$, or ions when the question names an ion.
4. One mole of a substance has a mass in grams equal to its relative particle mass.
5. The relative particle mass is the $A_r$ for an element made of single atoms, and the $M_r$ for a compound.
6. One mole of water therefore has a mass of $18g$, and one mole of aluminium a mass of $27g$.

Converting between mass and amount

1. Divide a mass by the relative particle mass to get the amount: $$n=\frac{m}{M_r}$$
2. Multiply an amount by the relative particle mass to get the mass: $$m=n\times M_r$$
3. The mass is in $g$, the amount in $mol$, and the relative particle mass carries no unit.
4. So $36g$ of water is $36÷18=2.0mol$.
5. And $0.25mol$ of carbon dioxide has a mass of $0.25\times 44=11g$.

Converting between amount and number of particles

1. Multiply an amount by the Avogadro constant to get the number of particles: $$N=n\times 6.02\times 10^{23}$$
2. Divide a number of particles by the Avogadro constant to get the amount: $$n=\frac{N}{6.02\times 10^{23}}$$
3. So $0.50mol$ of oxygen contains $0.50\times 6.02\times 10^{23}=3.01\times 10^{23}$ molecules.
4. And $1.204\times 10^{24}$ chloride ions is $1.204\times 10^{24}÷(6.02\times 10^{23})=2.00mol$.
5. A number of particles carries no unit, although the particle itself has to be named.

Going from mass straight to particles

1. Mass and particle number are linked through the amount in moles.
2. From a mass, divide by the relative particle mass and then multiply by the Avogadro constant: $$N=\frac{m}{M_r}\times 6.02\times 10^{23}$$
3. From a number of particles, divide by the Avogadro constant and then multiply by the relative particle mass: $$m=\frac{N}{6.02\times 10^{23}}\times M_r$$
4. For $9.0g$ of aluminium, with $A_r=27$, the amount is $0.3333mol$ and the count is $2.0\times 10^{23}$ atoms.
5. For $3.01\times 10^{23}$ molecules of ${CO}_2$, the amount is $0.500mol$ and the mass is $0.500\times 44=22g$.

Choosing the right quantity

1. A mass in the question and a mass in the answer means the relative particle mass is used twice.
2. A particle count anywhere in the question means the Avogadro constant appears in the working.
3. The amount in moles sits in the middle of every one of these conversions.
4. Units settle most slips: $g$ for a mass, $mol$ for an amount, and no unit for a particle count.
5. The relative particle mass always comes from the substance named, never from a neighbouring one.