Find density from the volume a sample displaces

Measure the volume of the sample, not the liquid already there

Density connects sample mass with sample volume. Write rho = m/V, where rho denotes density, m mass and V sample volume. With grams and millilitres, the result is g/mL. One millilitre equals one cubic centimetre, so g/mL and g/cm³ have the same numerical value. Background: measurements and density, OpenStax Chemistry 2e.

An irregular object may not have dimensions that make a geometric volume calculation straightforward. If a suitable sample is fully submerged without dissolving, reacting, absorbing liquid or trapping bubbles, the rise in liquid volume can measure its displaced volume. The difference matters: a cylinder initially reading 50 mL and finally reading 70 mL indicates 20 mL displacement, not 70 mL of sample.

For a 60 g sample, rho = 60 g / 20 mL = 3 g/mL. Dividing by 70 mL would include the original liquid in the denominator while using only sample mass in the numerator. That mixes two different system boundaries.

Scale a sample without changing its density

Compare 60 g occupying 20 mL with 30 g occupying 10 mL. Both have density 3 g/mL. Mass and volume scale together; density is their ratio. Under fixed conditions, two pieces of the same uniform material need not have the same mass or volume to have the same density.

Now retain 60 g but reduce sample volume to 10 mL. Density becomes 6 g/mL. That change does not represent simply cutting the original sample in half. The controls specify synthetic inventories; they do not physically compress or transform a real substance.

A volume change can also accompany a change in temperature, pressure or phase. Conditions belong with a density value. A single matching density is not a unique chemical identity: different materials, mixtures or porous samples can share similar bulk densities.

Diagnose a measurement failure

Suppose a true 20 mL sample has a 2 mL air bubble adhering to it during immersion. If the mass reading belongs to the sample alone, the apparent displaced volume becomes 22 mL. The inferred density is 60/22 ≈ 2.727 g/mL, lower than 3 g/mL. The error is in the inferred sample volume; the smaller ratio does not prove a chemical change.

A sample that floats without being fully submerged displaces only part of its volume. A sample that dissolves or reacts changes the measurement problem. Liquid entering pores may make the measured displacement differ from an external geometric volume. List these alternatives before using an uncertain displacement to identify a material.

Transfer: a 54 g specimen raises the reading from 40 to 58 mL. Compute its density. Then explain what would happen to the estimate if the final reading were mistakenly recorded as 60 mL.

Check the displacement comparison

The original displacement is 18 mL, giving 54/18 = 3 g/mL. Recording 60 mL instead gives a 20 mL displacement and 2.7 g/mL. An overestimated volume produces an underestimated density at fixed mass.

Plan evidence rather than merely naming a material

An investigation record should include sample mass, both liquid readings, units, instrument resolution, conditions and observations about immersion. Distinguish a repeated reading of the same setup from an independent preparation. Retain a discrepancy and investigate its cause rather than deleting it because a density table suggests another value.

This lab provides ideal inputs and a volume diagram, not empirical measurements or a tested physical procedure. Use its arithmetic to plan which quantities need measurement and to predict the direction of a plausible error. Practical technique needs observation and an appropriate protocol for the specific material.