# How do you measure density with the greatest precision?

Sep 30, 2016

There are two definitions of precision: reproducibility, and number of decimal places.

DECIMAL PLACES

Since density is $\frac{m}{V}$, we must be able to measure mass and volume to high precision.

Measuring mass to high precision is generally easier to accomplish in lab; my lab has a typical scale that measures to a precision (uncertainty) of $\pm \text{0.0002 g}$ and approximately a max load of $\text{150 g}$. Four decimal places is pretty sufficient for many intents and purposes.

Volume, on the other hand, is often measured to two decimal places, maybe three. I would use a volumetric flask, which for example can be $\pm \text{0.02 mL}$ for a Type A (to-contain) $\text{100.00 mL}$ volumetric flask.

Using common mass (5.0000~"100.0000 g") and volume (10.00~"500.00 mL") values, that would give roughly 4 significant figures of precision for the density overall.

So if you have a density less than $1$, you get 4 decimal places. If your density is between $1$ and $10$, you have 2 or 3 decimal places.

REPRODUCIBILITY

If we define precision as reproducibility of data, the issue is in using balances and glassware properly. So the experimental conditions must be controlled to make the equipment consistent. That means we must at least control:

• Temperature
• Pressure
• Mass Drift
• Our technique

Temperature and pressure are pretty easy. Pressure tends to be constant in real life in lab anyways. Temperature is typically constant in lab as well. So now it's up to us.

Mass drift is just the mass changing on the scale we use due to the static electricity around the scale messing up the display consistency. Reduce the static electricity with a static gun (fire it a few times and the mass stops changing around), and the mass becomes more consistent.

Technique with measuring volume and mass also helps. Measuring the mass would require that we are delicate in our placement of substances onto the scale. Finally, measuring the volume consistently requires that we delicately add the substance into a container to find that volume by displacement.

Once we refine all of those, density can be measured pretty consistently.