OCR A-Level Chemistry

Planning an experiment

A plan starts from what has to be measured and works back to the apparatus. If the aim is the enthalpy change of a reaction in solution, the quantity needed is a temperature change, so the plan needs a thermometer or probe, an insulated container and a way of measuring the mass or volume of reactant. If the aim is a rate, the plan needs a quantity that changes steadily with time, such as the volume of gas collected, the mass lost or the intensity of a colour, and a way of timing it.

The variables come first.

• The independent variable is the one you change on purpose.
• The dependent variable is the one you measure.
• Control variables are everything else that could affect the result, and each one is held constant: temperature, volumes, concentrations, the mass or surface area of a solid, stirring and the time allowed.

A control experiment, which leaves out the thing being tested, shows that the effect comes from the independent variable and not from something else in the set-up.

A good plan gives enough detail for someone else to repeat it. That means stating the apparatus with its sizes (a 25.0 cm³ pipette, a 50 cm³ burette, a 250 cm³ volumetric flask), the quantities used, the order of steps, how often each reading is taken and how results will be processed. The range should be wide enough to show a trend and the intervals even, so five concentrations such as 0.20, 0.40, 0.60, 0.80 and 1.00 mol dm⁻³ are more useful than two. Each measurement is repeated so that a mean can be taken and an anomaly noticed.

Apparatus is chosen for the precision the question needs. A measuring cylinder is fine for a volume of reactant that is in excess, because its uncertainty does not affect the answer. A pipette or burette is needed for the volume that the calculation depends on. A balance that reads to 0.001 g is used to weigh a sample of a few tenths of a gram, since a balance reading to 0.1 g would leave a percentage uncertainty of many per cent.

Hazards and risk

Every substance in a plan has a hazard, the harm it can do, and a risk, which depends on the hazard, the amount and how it is handled. Concentrated acids and alkalis are corrosive, many organic liquids are flammable, and some solids (chromium(VI) compounds, for example) are toxic. A risk is reduced by using a smaller quantity or a lower concentration, working in a fume cupboard, wearing eye protection and gloves, heating with a water bath or electric heater rather than a naked flame when flammable vapour is present, and keeping a bath or bucket of water ready for spills.

Implementing: recording and presenting data

Results go into a table whose column headings carry the quantity and its unit, written as $\text{volume} / \text{cm}^3$ or $\text{time} / \text{s}$, so the cells hold numbers only. Every value in a column is recorded to the same number of decimal places, and that number reflects the instrument: a burette is read to 0.05 cm³, so a reading is written as 23.45, never 23.4 or 23.450.

Significant figures

Non-zero digits are always significant. Zeros between non-zero digits are significant. Leading zeros are not, since they only place the decimal point, so 0.0250 has three significant figures. Trailing zeros after a decimal point are significant, because they show the precision that was measured.

In a calculation the answer is given to the same number of significant figures as the least precise data value, and rounding happens only at the end. If intermediate values are rounded early, the error builds up.

For example, the amount of solute in 25.0 cm³ of a 0.0500 mol dm⁻³ solution is

and the answer has three significant figures, like the data.

Graphs

A graph shows how the dependent variable changes with the independent variable, so the independent variable goes on the horizontal axis. Each axis is labelled with the quantity and its unit. The scale is chosen so the plotted points fill at least half the grid in each direction, using sensible steps (1, 2, 5, 10) and not awkward ones such as 3 or 7.

A line or curve of best fit passes smoothly through the points with roughly equal scatter either side. It does not join the dots, and a point that is far off the trend is marked as an anomaly and left out of the fit.

Gradients and intercepts

A gradient is found with a large triangle drawn on the line: the change in $y$ divided by the change in $x$ between two points far apart, with units. For a curve, the gradient at a point is the gradient of a tangent drawn there. Rates of reaction are found this way from a concentration or volume against time graph. The intercept is read where the line crosses an axis, and it may need the line to be extended.

Many relationships are turned into straight lines so that a gradient can be read. Plotting $\ln k$ against $1/T$ gives a line, and plotting absorbance against concentration for a set of standards gives a calibration line that is then used to read off unknown concentrations.

Uncertainty and error

The uncertainty of a measurement is the range within which the true value is expected to lie. For an analogue scale it is half the smallest division, and for a digital display it is one unit in the last digit shown, unless the maker gives a figure. Burettes, pipettes and volumetric flasks carry their tolerance on the glass, such as $\pm 0.06\ \text{cm}^3$ for a typical 25.0 cm³ pipette.

Percentage uncertainty

A burette reading has to be taken twice, at the start and the end, so a titre measured with a burette that has a reading uncertainty of $\pm 0.05\ \text{cm}^3$ carries $\pm 0.10\ \text{cm}^3$. For a titre of 24.10 cm³:

When measurements are combined by multiplying or dividing, their percentage uncertainties add. If the same titration used a pipette of 25.0 cm³ with tolerance $\pm 0.06\ \text{cm}^3$, its percentage uncertainty is $0.06/25.0 \times 100 = 0.24\%$, and the two together give $0.41 + 0.24 = 0.65\%$ in any result that depends on both volumes.

A temperature change is a difference of two readings, so the absolute uncertainties add. A thermometer with 1 °C divisions has an uncertainty of $\pm 0.5\ ^\circ\text{C}$ per reading, so a rise of 6.0 °C has an uncertainty of $\pm 1.0\ ^\circ\text{C}$, which is 17%. That is why a calorimetry experiment is improved by using a larger quantity of reactant, which gives a bigger temperature rise, or a thermometer that reads to 0.1 °C.

Percentage error

Percentage error compares a result with a known value:

If the uncertainties in the measurements add up to less than the percentage error, then measurement uncertainty does not account for the difference, and another source of error, such as heat loss or an impure sample, must be responsible.

Accuracy and precision

An accurate result is close to the true value. A precise set of results are close to one another. Random error affects precision and is reduced by repeating and averaging, and systematic error moves every result the same way and is not removed by repeating. A balance that has not been zeroed gives precise results that are all wrong by the same amount.

Evaluating results

Evaluation starts with the data. Repeat titres within 0.10 cm³ of each other are concordant and are averaged; one far from the others is an anomaly and is excluded, and the reason is given if one is known.

Limitations are specific procedural points, each with a matching improvement, such as:

• heat lost to the surroundings in calorimetry, reduced by a lid and lagging, or a correction from a cooling curve;
• a gas that dissolves or escapes before it is collected, reduced by using a gas syringe and connecting the bung at once;
• a colour end point that is hard to judge, reduced by adding the final drops slowly over a white tile;
• a reactant that is not pure or a product that is not dry, reduced by recrystallising or drying to constant mass.

A conclusion is drawn only as far as the data supports it, and is compared with the prediction or accepted value with the percentage error as the measure.