Required Practical: Determining Density

What the investigation must determine

In this required practical, you measure the mass and volume of regular solid objects, irregular solid objects and liquids. These measurements allow you to determine density using

$$\rho=\frac{m}{V}$$

where $\rho$ is density, $m$ is mass and $V$ is volume. Density describes how much mass is packed into each unit of volume. It is different from mass: two pieces of the same uniform material can have different masses and volumes but the same density.

The standard SI quantities are mass in kilograms, volume in cubic metres and density in kilograms per cubic metre ($\text{kg/m}^3$). Measurements may also be taken in grams and cubic centimetres, giving density in $\text{g/cm}^3$. Keep one consistent set of units throughout a calculation.

Choosing suitable apparatus

Use a balance to measure mass. The best way to measure volume depends on what is being tested:

The instrument should suit the size of the measurement and the precision required. A ruler may be suitable for a large cuboid; Vernier callipers are more precise for external dimensions, while a micrometer is useful for a small thickness or diameter.

Measuring the density of a regular solid

First check that the balance reads zero, then place the dry solid on it and record the mass, including its unit.

Measure every dimension needed to calculate the object's volume. For a cuboid,

$$V=lwh$$

Measure length, width and height without rounding them prematurely. For a cylinder, measure its radius and height and use $V=\pi r^2h$. Other regular shapes require the corresponding geometrical formula.

Use the dimensions to calculate the volume, then divide the mass by that volume. Repeating a dimension at different positions can reveal variation in an object that is not perfectly regular; an average may then provide a more representative value.

Measuring the density of an irregular solid

An irregular object has no convenient set of dimensions from which its volume can be calculated, so use displacement.

1. Put water in a measuring cylinder and record the initial volume, $V_1$.
2. Lower the object into the water until it is completely submerged.
3. Record the new volume, $V_2$.
4. Calculate the object's volume:

$$V_{\text{object}}=V_2-V_1$$

5. Measure the dry object's mass and calculate its density.

This works because a completely submerged object displaces a volume of water equal to its own volume. Make sure that no water splashes out and that no air bubbles remain attached to the object; either would make the volume result unreliable. The method is unsuitable if the object dissolves in or reacts with the liquid.

If the object is too large for a measuring cylinder, a displacement can can be used. Fill it until water has finished dripping from the spout, place a measuring cylinder beneath the spout, submerge the object and collect all the displaced water. The collected water's volume equals the object's volume.

Measuring the density of a liquid

A container is needed to hold the liquid, but its mass must not be included as though it belonged to the liquid.

1. Place an empty, dry measuring cylinder on the balance and tare it so the display returns to zero. Alternatively, record the empty cylinder's mass.
2. Add the liquid and record its volume.
3. Record the liquid's mass directly from the tared balance. If the balance was not tared, subtract the empty cylinder's mass from the combined mass.
4. Divide the liquid's mass by its volume.

The same portion of liquid must supply both the mass and volume measurements.

Reading liquid volume accurately

Put the measuring cylinder upright on a level surface. View the scale at eye level so that the line of sight is horizontal; looking from above or below causes parallax error. Water forms a concave meniscus, so read the scale at the lowest point of the curve.

Before recording a value, determine what each scale division represents. Record all measurements in a results table with headings that include the quantities and units.

Useful conversions include

$$1\ \text{ml}=1\ \text{cm}^3,\qquad 1\ \text{cm}^3=10^{-6}\ \text{m}^3$$

and therefore

$$1\ \text{g/cm}^3=1000\ \text{kg/m}^3.$$

Improving and evaluating the measurements

Zero the balance before use and check measuring instruments for a zero error. Choose apparatus with scale divisions appropriate to the measurement: using precise callipers rather than a ruler can reduce uncertainty in small dimensions. This matters because several measured dimensions are multiplied when finding the volume of a regular object.

Repeat measurements where practical and calculate a mean, checking first for anomalous results. Give the calculated density to a sensible number of significant figures based on the precision of the measurements.

For displacement, loss of water makes the measured displaced volume too small and therefore makes the calculated density too high. Trapped air increases the apparent volume and makes the calculated density too low. If a solid is weighed while wet, its measured mass—and hence its calculated density—will be too high.

Keep water away from an electronic balance and its electrical connections. Dry spills promptly and handle glass measuring cylinders carefully.

Core relationship

Recall:

$$\rho=\frac{m}{V}$$

Use kg, $\text{m}^3$ and , or use g, and consistently.