Determine density for a solid and a liquid using density ρ = mass/volume. Density depends on the material and conditions, not simply on which object has the greater mass.Original labelled apparatus schematic; not to scale. Follow the stated measurements and safety instructions.
Use a balance and suitable measuring cylinders; a ruler or calipers can measure regular solid dimensions. An irregular insoluble solid can displace water to measure its volume.
Choose apparatus with an appropriate range and resolution. The object must fit without trapping air, reacting with, absorbing or dissolving in the liquid.
Clean spills promptly, support glassware and lower dense objects gently to avoid breaking a cylinder. Do not immerse the balance or place wet objects directly on it.
Solid method
Check the balance zero, then measure the dry solid's mass. Record the units and balance resolution before immersing it.
For a regular cuboid, measure length, width and height at several positions and calculate V = lwh. Use the same length units throughout; measured edges must describe the actual shape.
For an irregular object, record initial water volume V1 at eye level. Fully submerge the object with no trapped bubbles and record final volume V2. Object volume = V2 − V1, not the final cylinder reading alone.
If using an overflow can, fill to the spout, allow initial dripping to stop, then collect only water displaced by the submerged object. Measure the collected volume in a suitable cylinder.
A thin support thread can help lower the object. Its immersed volume should be negligible or allowed for; a floating object requires a suitable alternative method rather than being forced down by an unaccounted bulky weight.
Calculate the solid’s density using its dry mass and measured volume. Repeat length or water-displacement measurements to check consistency. Different pieces of the same uniform material (a homogeneous material) should have similar densities.
Liquid method and units
Measure the mass of an empty dry measuring cylinder or suitable vessel. Add a known measured liquid volume and measure the combined mass; liquid mass is the difference.
Stand the cylinder upright on a level surface and read at eye level. For water, read the bottom of the downward-curved surface (the meniscus). Follow the correct convention for the liquid used.
Calculate liquid density = liquid mass/liquid volume. A tare function can subtract the vessel mass, but verify it was zeroed with the correct empty vessel.
Measure several volumes of liquid and plot liquid mass on the vertical axis against volume on the horizontal axis. The gradient is density. If you instead plot container-plus-liquid mass, the line starts above zero by the container’s mass (its intercept), but its gradient can still give density.
State units consistently: g/cm³ or kg/m³. 1 mL = 1 cm³ and 1 g/cm³ = 1,000 kg/m³; cubing a length conversion is essential when calculating volume from SI lengths.
Precision and evaluation
A larger displaced volume reduces relative uncertainty for a given cylinder scale, but the object must fit safely. A smaller-range cylinder may improve resolution when its range is sufficient.
A difference of two cylinder readings has uncertainty from both readings. Avoid claiming the uncertainty is automatically only that of one reading.
Trapped bubbles raise the apparent displaced volume and lower calculated density. Wet mass can overestimate the dry solid's mass; remove surface water before reweighing.
Calipers can improve dimension resolution, but an irregular shape cannot be made into a cuboid just by using a more precise ruler. Select a method appropriate to shape.
Control temperature when comparing liquids, because volume and density can vary with temperature. Mix a uniform liquid sample and use clean dry apparatus to avoid contamination.
Compare calculated densities with repeat spread and justified reference values. A small spread establishes precision but not necessarily accuracy if the balance or cylinder is biased.
Exam skills: planning, precision and evaluation
State what you change (the independent variable), what you measure (the dependent variable) and what you keep the same (control variables). Explain how you keep each control variable constant, rather than just saying “make it fair”.
Accuracy means how close a result is to the true value. Precision means how close repeated measurements are to each other. Resolution is the smallest change an instrument can show. More digits on a display do not automatically mean a more accurate result.
Repeat measurements for each condition, calculate a mean and describe how spread out the results are. This helps assess and reduce the effect of random errors. Repeating cannot fix an error that pushes results consistently in one direction (a systematic error), such as a balance zero offset or unaccounted vessel mass.
Repeatability means getting similar results when the same person repeats the same method with the same equipment. Reproducibility means getting similar results when someone else, or different suitable equipment, repeats the experiment. Results can be consistent but still inaccurate.
Check that instruments read zero correctly and are calibrated where needed. Read scales at eye level: looking from an angle can give a wrong reading (parallax error). Choose suitable ranges, measurement intervals and scale divisions (resolution).
Write down the original readings straight away in a table, with units in the headings. Use decimal places that match the instrument’s resolution. Keep the original data and round only when needed. Do not discard a result just because it differs from your prediction.
An anomalous result does not fit the pattern of the other results. Repeat that measurement and check the method. Only leave it out of a mean if you have a clear reason; state which result you excluded and why.
For continuous variables, plot the independent variable on the horizontal axis and the dependent variable vertically. Use sensible scales, units and a best-fit line or curve; do not automatically join every point or force the graph through zero.
Find the gradient of a straight best-fit line using a large triangle: vertical change ÷ horizontal change. For a curve, draw a tangent to estimate the gradient at one point. Explain what the gradient shows in this experiment, include its units and use measured values to support your conclusion.
Uncertainty describes the possible range around a measurement. For one reading on a scale, half the smallest division is a useful classroom estimate unless the question says otherwise. If you subtract two readings, both have uncertainty. Percentage uncertainty = absolute uncertainty ÷ measured value × 100. Follow the method specified in the question.
Use results as evidence and then explain what they mean. A pattern linking variables (a correlation) does not prove that one causes the other. If the ranges of repeat results overlap, a claimed difference may be less convincing. Keep conclusions within the range tested and suggest an improvement that tackles a specific error.
Mr Kidman's Classroom