Density & Specific Gravity Reference Cheat Sheet

Density and specific gravity help chemists identify substances, compare materials, and predict whether objects or liquids will float, sink, or form layers. This cheat sheet summarizes the formulas, units, and comparison rules students need for lab work and problem solving. It is especially useful when measuring mass and volume, converting units, or interpreting results from common chemistry experiments.

The main density formula is $D = \frac{m}{V}$ , where $D$ is density, $m$ is mass, and $V$ is volume. Specific gravity compares a substance’s density to the density of water, so it has no units. Temperature can change density by changing volume, and gases require special attention because their density depends strongly on pressure, temperature, and molar mass.

Key Facts

Density is calculated with $D = \frac{m}{V}$ , where mass is usually measured in $\mathrm{g}$ and volume in $\mathrm{mL}$ or $\mathrm{cm^3}$ .
Mass can be found from density using $m = D V$ when density and volume are known.
Volume can be found from density using $V = \frac{m}{D}$ when mass and density are known.
Specific gravity is calculated with $SG = \frac{D_{\text{substance}}}{D_{\text{water}}}$ and has no units because the density units cancel.
For most chemistry problems, water has density $D_{\text{water}} = 1.00\,\mathrm{g/mL}$ at about $4\,^{\circ}\mathrm{C}$ , so $SG \approx D$ when density is in $\mathrm{g/mL}$ .
An object floats in a liquid if $D_{\text{object}} < D_{\text{liquid}}$ and sinks if $D_{\text{object}} > D_{\text{liquid}}$ .
Immiscible liquids form layers with the least dense liquid on top and the most dense liquid on bottom.
Gas density can be calculated from molar mass using $D = \frac{PM}{RT}$ , where $P$ is pressure, $M$ is molar mass, $R$ is the gas constant, and $T$ is temperature in kelvin.

Vocabulary

Density: Density is the amount of mass in a given volume, calculated with $D = \frac{m}{V}$ .
Mass: Mass is the amount of matter in a sample, commonly measured in $\mathrm{g}$ or $\mathrm{kg}$ .
Volume: Volume is the amount of space a substance occupies, commonly measured in $\mathrm{mL}$ , $\mathrm{L}$ , or $\mathrm{cm^3}$ .
Specific Gravity: Specific gravity is the ratio of a substance’s density to the density of water, calculated with $SG = \frac{D_{\text{substance}}}{D_{\text{water}}}$ .
Buoyancy: Buoyancy is the upward force a fluid exerts on an object, which helps determine whether the object floats or sinks.
Miscible: Miscible substances mix evenly with each other, while immiscible substances separate into layers.

Common Mistakes to Avoid

Using the wrong density formula, such as $D = mV$ , is wrong because density is mass divided by volume, $D = \frac{m}{V}$ .
Forgetting to match units is wrong because $\mathrm{g/mL}$ , $\mathrm{g/cm^3}$ , and $\mathrm{kg/L}$ can only be compared directly after proper conversion.
Putting the densest liquid on top is wrong because immiscible liquids layer from lowest density on top to highest density on bottom.
Giving specific gravity units is wrong because $SG = \frac{D_{\text{substance}}}{D_{\text{water}}}$ is a ratio and the density units cancel.
Using Celsius in gas density calculations is wrong because $D = \frac{PM}{RT}$ requires absolute temperature in kelvin, so use $T_{\mathrm{K}} = T_{^{\circ}\mathrm{C}} + 273.15$ .

Practice Questions

1 A metal sample has mass $78.6\,\mathrm{g}$ and volume $10.0\,\mathrm{mL}$ . What is its density in $\mathrm{g/mL}$ ?
2 A liquid has density $0.82\,\mathrm{g/mL}$ . What is its specific gravity if $D_{\text{water}} = 1.00\,\mathrm{g/mL}$ ?
3 A gas has pressure $1.00\,\mathrm{atm}$ , molar mass $44.0\,\mathrm{g/mol}$ , and temperature $298\,\mathrm{K}$ . Using $R = 0.0821\,\mathrm{L\cdot atm/(mol\cdot K)}$ , find its density with $D = \frac{PM}{RT}$ .
4 Three immiscible liquids have densities $0.90\,\mathrm{g/mL}$ , $1.10\,\mathrm{g/mL}$ , and $0.75\,\mathrm{g/mL}$ . Explain the order of the layers from top to bottom and why.

Understanding Density & Specific Gravity Reference

Reliable density work begins with careful measurement. A balance measures mass, while a graduated cylinder, pipette, or volumetric flask measures volume. Read liquid volume at eye level from the bottom of the curved surface called the meniscus.

A small volume error can cause a large density error, especially when the sample volume is small. For an irregular solid, volume is often found by water displacement. The rise in water level shows the volume of the solid.

The object must be fully submerged, free of air bubbles, and unable to absorb water. One millilitre has the same volume as one cubic centimetre, which makes these units easy to connect in lab calculations.

Buoyancy is the upward push a fluid exerts on an object placed in it. This push happens because fluid pressure is greater at the bottom of the object than at the top. An object floats when the buoyant push can support its weight.

A floating object displaces enough liquid to have the same mass as the object. This explains why a large steel ship can float even though solid steel sinks in water. The ship contains much empty space, so its average density is lower than water.

A steel nail has little empty space, so its average density remains high. Shape matters through average density, not because shape changes the density of the material itself.

Temperature changes many density results because most substances expand when heated. The same mass then occupies more space, so density decreases. This is why accurate tables list a temperature with the density value.

Water has an important exception near four degrees Celsius. It becomes less dense when cooled below that temperature, which is why ice floats and lakes freeze from the top downward. Liquid layers stay separate only when the liquids are immiscible.

Oil and water can form layers, but alcohol and water mix into one solution. In a mixture, the final density depends on the amount of each substance and can help track concentration.

Hydrometers use this idea. They sink farther in less dense liquids and rise higher in denser ones.

Gas density needs extra care because gases compress easily. Increasing pressure squeezes gas particles into a smaller space, raising density. Heating a gas spreads particles farther apart when pressure is allowed to stay constant, lowering density.

This helps explain why warm air rises in the atmosphere and why hot air balloons lift. Gas density is useful for comparing gases, predicting collection methods, and understanding ventilation safety. A gas with a greater molar mass is usually denser than air under the same conditions.

When solving any density problem, check that units match before calculating. Convert litres to millilitres or kilograms to grams when needed. Keep reasonable significant figures, since a calculator cannot fix an imprecise mass or volume measurement.

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