Mathematical Skills: Algebra, Standard Form & Accuracy

Calculate the total number of atoms in 0.25 moles of $CO_2$.

Step 1: State the core formula.

• $\text{Number of molecules} = \text{moles} \times 6.02 \times 10^{23}$

Step 2: Calculate the number of molecules.

• Calculator technique: Enter 0.25, press x, enter 6.02, press the EXP (or x10^x) button, and type 23.
• $\text{Molecules} = 0.25 \times 6.02 \times 10^{23} = 1.505 \times 10^{23}$

Step 3: Account for the atoms in the chemical formula.

• One molecule of $CO_2$ contains 3 atoms (one carbon, two oxygen).
• $\text{Total atoms} = 1.505 \times 10^{23} \times 3$

Step 4: State the final answer in standard form.

• $\text{Total atoms} = 4.515 \times 10^{23}$

Rearranging Chemistry Equations

You can memorise every formula in chemistry, but if you cannot shift the variables around, you will get stuck on the simplest questions. Changing the Subject of an Equation means isolating a single unknown variable on the left-hand side of the equals sign.

Two of the most frequently tested formulas involve mass and Concentration. Concentration measures how much Solute is dissolved in a specific volume of Solvent to form a Solution. Remember that gas or liquid volumes must always be converted to $\text{dm}^3$ by dividing the $\text{cm}^3$ value by $1000$.

$$\text{Moles} (n) = \frac{\text{Mass} (m)}{\text{Relative Formula Mass} (M_r)}$$

To make mass the subject, multiply both sides by $M_r$ to get $m = n \times M_r$.

$$\text{Concentration} (C) = \frac{\text{Moles} (n)}{\text{Volume} (V)}$$

To isolate volume, first multiply both sides by $V$ ($n = C \times V$), then divide by $C$ to get $V = \frac{n}{C}$.

Calculate the mass of $KNO_3$ ($M_r = 101$) dissolved in $250 \text{ cm}^3$ of a $0.20 \text{ mol/dm}^3$ solution.

Step 1: Convert the volume to $\text{dm}^3$.

• $V = 250 \div 1000 = 0.25 \text{ dm}^3$

Step 2: Rearrange the concentration equation to find moles.

• $n = C \times V$
• $n = 0.20 \times 0.25 = 0.05 \text{ mol}$

Step 3: Rearrange the mass equation to find mass.

• $m = n \times M_r$
• $m = 0.05 \times 101$

Step 4: Calculate the final mass.

• $m = 5.05 \text{ g}$

Significant Figures and Exam Precision

Your calculator might confidently display an answer with eight decimal places, but writing them all down in an exam will actually cost you marks. Examiners expect your final answer to reflect the precision of the data you were given. You must round your final answer to the same number of Significant Figures as the piece of question data with the lowest number of significant figures.

When counting significant figures, remember that leading zeros (like in $0.005$) are never significant, but trailing zeros after a decimal point (like in $5.00$) are significant. Edexcel mark schemes use specific codes for precision: qwrt indicates a range of acceptable rounded answers, ecf allows method marks if you use a previously incorrect calculation correctly, and cao means no variations are accepted.

Crucially, never round your numbers during intermediate steps. Keep the full number on your calculator display until the very last step to prevent accuracy loss.

Calculate the moles of $HCl$ in $15.0 \text{ cm}^3$ of a $0.025 \text{ mol/dm}^3$ solution.

Step 1: Convert volume to $\text{dm}^3$ using the exact data provided.

• $V = 15.0 \div 1000 = 0.015 \text{ dm}^3$

Step 2: Calculate moles without rounding.

• $n = 0.015 \times 0.025 = 0.000375 \text{ mol}$

Step 3: Determine the correct number of significant figures.

• The data given was $15.0$ (3 sig figs) and $0.025$ (2 sig figs).
• The lowest precision is 2 significant figures.

Step 4: Round the final answer.

• Final answer: $0.00038 \text{ mol}$ (or $3.8 \times 10^{-4} \text{ mol}$)

(Note: Burette readings follow a different rule — they must always be recorded to exactly two decimal places, ending in either .00 or .05).