Unit 3 Properties of Substances and Mixtures

AP Chemistry Density

Density of solids and liquids, using it to convert between mass and volume, and the gas density equation d = PM/RT, in four worked examples.

Density links a mass you weigh to a volume you measure. In AP Chemistry it appears in two forms: as a conversion factor for liquids and solids, often on the way to moles, and as a property of gases that the ideal gas law predicts and that can identify an unknown gas by its molar mass. This page covers both, ending with the gas case that most general density guides skip.

The Density Formulas for Solids, Liquids, and Gases

Any substance: d = m/V, so m = dV and V = m/d.
Units: g/cm³ or g/mL for solids and liquids (1 cm³ = 1 mL), and g/L for gases.
Gases: substituting n = m/M into PV = nRT gives d = PM/RT, and rearranging gives M = dRT/P.

The gas equation shows that, at the same temperature and pressure, a gas's density is proportional to its molar mass. The chart compares six common gases at 1.00 atm and 25°C.

Fig. 1 · Gas density at 1.00 atm, 25°C

Worked Example 1: Finding the Density of a Metal Block

A metal block has a mass of 27.0 g and a volume of 10.0 cm³. Find its density and suggest which metal it could be.

Density: d = 27.0 g ÷ 10.0 cm³ = 2.70 g/cm³.
Identity: 2.70 g/cm³ matches aluminum.

Density is an intensive property: a larger block of the same metal has the same density, which is why it can help identify a substance. Report it with the significant figures of the data; see significant figures. Comparing a measured density with an accepted value is a classic percent error calculation.

Worked Example 2: Using Density to Get From Volume to Moles

How many moles of ethanol (C₂H₅OH, density 0.789 g/mL, molar mass 46.07 g/mol) are in 25.0 mL?

Mass: m = dV = (0.789 g/mL)(25.0 mL) = 19.7 g.
Moles: 19.7 g ÷ 46.07 g/mol = 0.428 mol.

Density turns a measured volume of a pure liquid into a mass, and molar mass turns that mass into moles. This is the usual way to handle a liquid reactant in a stoichiometry problem. It is different from molarity, which describes a solute dissolved in a solution; the molar mass value comes from molar mass.

Worked Example 3: Calculating the Density of a Gas

Find the density of CO₂ (M = 44.01 g/mol) at 1.00 atm and 0°C, and again at 25°C.

At 273 K: d = PM/RT = (1.00)(44.01) ÷ [(0.08206)(273.15)] = 1.96 g/L.
At 298 K: d = (1.00)(44.01) ÷ [(0.08206)(298.15)] = 1.80 g/L.

Warming the gas spreads the same mass over a larger volume, so the density falls. CO₂ is denser than air, which is mostly N₂ and O₂, which is why it collects in low places. Keep temperatures in kelvins, as in temperature conversions.

Worked Example 4: Identifying an Unknown Gas From Its Density

A gas has a density of 1.25 g/L at 1.00 atm and 273 K. Find its molar mass and suggest what it could be.

Rearrange: M = dRT/P.
Substitute: M = (1.25 g/L)(0.08206 L·atm/mol·K)(273 K) ÷ 1.00 atm = 28.0 g/mol.
Identity: 28.0 g/mol matches N₂ (28.02) or CO (28.01).

The density alone cannot tell N₂ from CO, since their molar masses are nearly the same; another test would be needed. This route from a measured density to a molar mass is a common lab-based free-response setup, and it is one more use of the relationships in the gas laws.

Five Density Practice Questions With Answers

A 15.0 mL sample of a liquid has a mass of 11.8 g. What is its density?
Show answer
11.8 ÷ 15.0 = 0.787 g/mL.
What is the mass of 50.0 mL of a liquid with density 1.26 g/mL?
Show answer
(1.26)(50.0) = 63.0 g.
Find the density of O₂ at 2.00 atm and 300. K.
Show answer
d = (2.00)(32.00) ÷ [(0.08206)(300.)] = 2.60 g/L.
A gas has a density of 3.17 g/L at 1.00 atm and 273 K. Find its molar mass and suggest what it is.
Show answer
M = (3.17)(0.08206)(273) ÷ 1.00 ≈ 71.0 g/mol, consistent with Cl₂ (70.90 g/mol).
If the pressure of a gas is doubled at constant temperature, what happens to its density?
Show answer
It doubles, since d = PM/RT is proportional to P.

Common Density Mistakes

Inverting the formula. Density is mass divided by volume, not volume divided by mass.
Mixing units. g/mL for liquids and g/L for gases differ by a factor of 1000.
Using Celsius in d = PM/RT. Temperature must be in kelvins.
Confusing density with molarity. Density is mass per volume of the whole substance; molarity is moles of solute per liter of solution.
Treating density as extensive. It does not change with the amount of sample.
Forgetting that gas density changes with conditions. Quote the temperature and pressure with any gas density.

Density problems are short but often sit inside a longer gas or stoichiometry question. To see how a stronger Unit 3 would shift your overall estimate, the AP Chem Score Calculator turns section scores into a 1–5 range.

Frequently Asked Questions

What is the formula for density?

Density = mass ÷ volume (d = m/V). Solids and liquids are usually reported in g/cm³ or g/mL, and gases in g/L.

How do you find the density of a gas?

Use d = PM/RT, which comes from the ideal gas law by replacing n with m/M. With P in atm, M in g/mol, R = 0.08206 L·atm/(mol·K), and T in kelvins, the density is in g/L.

How do you find the molar mass of a gas from its density?

Rearrange to M = dRT/P. For example, a gas with a density of 1.25 g/L at 1.00 atm and 273 K has M = (1.25)(0.08206)(273)/1.00 ≈ 28.0 g/mol, consistent with N₂ or CO.

Why are gas densities so much smaller than liquid densities?

Gas particles are far apart, so a liter of gas holds far fewer particles than a liter of liquid. Most gases at room conditions are between about 0.1 and 3 g/L, while water is about 1000 g/L.

Does gas density depend on temperature and pressure?

Yes. From d = PM/RT, density rises with pressure and falls with temperature. Solids and liquids change only slightly.

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