Density & Specific Gravity
Why does a 100,000-ton steel ship float, while a tiny iron pebble sinks the moment you toss it in a pond?
It’s not about weight — the ship weighs millions of times more than the pebble. It’s about how the mass is distributed through space. The ship is mostly hollow, so its average mass-per-volume is low. The pebble is solid iron, so its mass-per-volume is high.
That mass-per-volume property is density, and it’s the foundation of every fluids problem on the MCAT — floating, sinking, pressure, buoyancy, even why ice floats on water (a fact essential to aquatic life).
Density
Density tells you how much mass is packed into a given amount of space.
The density of water is the single most important reference value in fluid mechanics — memorize it and you’re ready for almost any density problem.
| Substance | Density (kg/m³) | Density (g/cm³) |
|---|---|---|
| Water (4°C) | 1000 | 1.00 |
| Ice | 917 | 0.917 |
| Air (sea level) | 1.2 | 0.0012 |
| Blood | ~1060 | ~1.06 |
| Bone | ~1900 | ~1.9 |
| Mercury | 13,600 | 13.6 |
Unit Conversions
The two density units you’ll encounter on the MCAT are kg/m³ and g/cm³. Convert between them by multiplying or dividing by 1000:
- 1 g/cm³ = 1000 kg/m³.
- g/cm³ → kg/m³: multiply by 1000.
- kg/m³ → g/cm³: divide by 1000.
Why 1000? There are 1000 g per 1 kg, and 1,000,000 cm³ per 1 m³ (100 cm per side, cubed). When you divide those out, the net factor is 1000. Don’t memorize the derivation — just remember the 1000.
Specific Gravity
Specific gravity (SG) compares an object’s density to the density of water. It’s a dimensionless ratio — no units.
Specific gravity gives you an instant float-or-sink prediction:
- SG < 1 → less dense than water → floats.
- SG = 1 → same density as water → neutrally buoyant (suspended at any depth).
- SG > 1 → denser than water → sinks.
Why Ice Floats
Ice has a density of 917 kg/m³ (SG = 0.917), making it less dense than liquid water. This is unusual — most solids are denser than their liquid form (think of how candle wax sinks when you drop a chunk into melted wax).
Water is weird because of hydrogen bonding. When water freezes, the H-bonds lock molecules into an open hexagonal lattice with more empty space than the disordered liquid arrangement. So 1 mL of liquid water becomes more than 1 mL of ice (about 9% bigger), and the ice floats.
This anomaly is critical for life on Earth: ice floats on top of lakes and oceans, insulating the liquid water below and allowing aquatic life to survive winter. If ice were denser than water, lakes would freeze from the bottom up, killing fish and disrupting global climate.
Applying Density to the MCAT
Most MCAT density problems come in one of three flavors:
- Calculate density from mass and volume (or rearrange to find mass or volume).
- Predict floating or sinking from specific gravity.
- Compare densities of layered liquids — the densest fluid always settles to the bottom.
When a passage shows you layered liquids, denser ones are always lower. Oil floats on water (oil’s SG ≈ 0.9). Mercury sits below water (SG = 13.6 — way denser). A common test setup: oil/water/mercury layers in a single tube.
Worked Example
A statue has a mass of 5400 g and a volume of 600 cm³. What’s its density? Will it float in water? In mercury?
- g/cm³.
- SG = 9.0 → much denser than water → sinks in water (it’s likely brass or copper).
- Compare to mercury (SG = 13.6) → the statue is less dense than mercury → floats in mercury.
That last result feels strange but it’s real — gold (SG ≈ 19) sinks in mercury, but most metals (steel, copper, brass) actually float on it.