Practice question • Everyday Chemistry Foundations: Matter, Atoms, and Reactions

Density is like a material’s “fingerprint.” Two objects can look the same size, but if one feels weirdly heavy, density is usually the reason. Even better: density helps you identify substances and predict things like floating vs. sinking.

What density means (in plain language)

Density tells you how much mass is packed into a certain amount of space (volume).

High density → lots of mass in a small volume (often feels heavy for its size)
Low density → less mass in the same volume (often feels light)

The density formula

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

$\rho$ (rho) = density
$m$ = mass
$V$ = volume

Units: the “language” of density

You’ll commonly see density in:

g/mL (grams per milliliter) — super common for liquids
g/cm³ (grams per cubic centimeter) — super common for solids

Key unit fact (very handy!)

$1\ \text{mL} = 1\ \text{cm}^3$

So:

g/mL and g/cm³ are numerically equivalent.

Measuring mass and volume (the real-lab way)

Mass: use a balance

A balance gives mass directly (often in grams).

Volume: use a graduated cylinder (especially for irregular solids)

If the object doesn’t have an easy geometric shape, you can find its volume by water displacement:

Put water in the graduated cylinder.
Record the initial volume.
Carefully add the object.
Record the final volume.
The object’s volume is the difference.

Worked example (step-by-step, with realistic measurements)

Let’s say you found a small metal nugget and want to identify it.

1) Measure mass on a balance

Balance reads:

$m = 26.42\ \text{g}$

2) Measure volume by water displacement

You read the graduated cylinder at eye level (more on the meniscus soon):

Initial water level: $V_i = 15.2\ \text{mL}$
Final water level after adding the nugget: $V_f = 18.6\ \text{mL}$

Compute the object’s volume:
$V = V_f - V_i = 18.6\ \text{mL} - 15.2\ \text{mL} = 3.4\ \text{mL}$

3) Compute density using $\rho = m/V$

Substitute:
$\rho = \frac{26.42\ \text{g}}{3.4\ \text{mL}}$

Calculator-ready division:
$\rho = 7.770588\dots\ \text{g/mL}$

4) Significant figures (final rounding)

Mass: 26.42 g has 4 significant figures
Volume: 3.4 mL has 2 significant figures

For multiplication/division, your final answer should match the fewest sig figs, so 2 sig figs.

Final density:
$\rho = 7.8\ \text{g/mL}$

5) Quick units check (so you know it makes sense)

You started with:

grams on top
milliliters on bottom

So the result must be g/mL. Perfect.

A quick note on uncertainty + reading the meniscus

Measurements are never perfectly exact—so we report them in a smart, consistent way.

Reading the meniscus (liquids curve!)

Water forms a curve in a glass cylinder called a meniscus.

For water, read the volume at the bottom of the curve.
Read at eye level to avoid parallax (the “looking from an angle” mistake).

Why you report one estimated digit

A graduated cylinder has marked lines (certain digits are “certain”). You’re allowed to estimate one more digit beyond the smallest marking.

Example:

If the cylinder is marked every 1 mL, you can often estimate to the nearest 0.1 mL.
That’s why readings like 15.2 mL and 18.6 mL make sense: the 0.1 mL place is the “estimated digit.”

Matching sig figs in final density

In our example, volume came out to 3.4 mL (2 sig figs), so the density must also be reported with 2 sig figs:
$7.8\ \text{g/mL}$
This keeps your reported precision honest—no pretending you know more than you measured.

Compare densities: predicting floating vs. sinking

Here’s a super practical way to interpret density.

Density of water is about $1.0\ \text{g/mL}$ .

If an object’s density is:

less than 1.0 g/mL → it tends to float
greater than 1.0 g/mL → it tends to sink

Example interpretation

Our nugget had:
$\rho = 7.8\ \text{g/mL}$
That’s way bigger than $1.0\ \text{g/mL}$ , so it would sink fast in water.

(That big density is also a clue it might be a metal—many metals have densities several times higher than water.)

Takeaway (you’ve got this)

Density is a powerful “ID tool” because it stays the same for a material no matter how big the sample is. Measure mass, measure volume, divide, and report with sensible units and sig figs: