1. Overview
Density is a fundamental property of matter that describes how much mass is concentrated in a specific volume. Understanding density allows us to predict whether objects will sink or float and helps in identifying unknown substances based on their physical characteristics.
Key Definitions
- Density: The mass per unit volume of a substance.
- Mass: The amount of matter in an object, measured in grams (g) or kilograms (kg).
- Volume: The amount of space an object takes up, measured in cubic centimeters ($\text{cm}^3$) or cubic meters ($\text{m}^3$).
- Displacement: The volume of fluid pushed out of the way when an object is submerged.
Core Content
The Density Formula
Density is calculated by dividing the mass of an object by its volume. $$\rho = \frac{m}{V}$$ (Note: The symbol for density is the Greek letter rho, $\rho$, which looks like a curly 'p').
Determining Density: Experimental Methods
1. Regularly Shaped Solid (e.g., a cube or cuboid)
- Measure the mass ($m$) using a digital balance.
- Measure the length, width, and height using a ruler.
- Calculate volume ($V = l \times w \times h$).
- Apply the formula $\rho = m/V$.
2. A Liquid
- Place an empty measuring cylinder on a digital balance and "tare" (zero) it, or record the mass of the empty cylinder.
- Pour the liquid into the cylinder and record the volume ($V$) from the scale.
- Record the new mass and subtract the mass of the empty cylinder to find the mass of the liquid ($m$).
- Apply the formula $\rho = m/V$.
3. Irregularly Shaped Solid (Displacement Method)
- Measure the mass ($m$) of the object using a balance.
- Fill a measuring cylinder with a known volume of water ($V_1$).
- Carefully submerge the object in the water.
- Record the new volume ($V_2$).
- Calculate the volume of the object: $V = V_2 - V_1$.
- Apply the formula $\rho = m/V$.
Floating and Sinking
- An object will float if its density is less than the density of the liquid.
- An object will sink if its density is greater than the density of the liquid.
- Example: Water has a density of $1.0 \text{ g/cm}^3$. A piece of wood with a density of $0.7 \text{ g/cm}^3$ will float, while a stone with a density of $2.5 \text{ g/cm}^3$ will sink.
Extended Content (Extended Only)
Floating Liquids (Immiscible Liquids)
When two liquids that do not mix (immiscible) are poured into the same container, they will form layers based on their densities.
- The liquid with the lowest density will float on the top.
- The liquid with the highest density will sink to the bottom.
Worked Example: A beaker contains Liquid A ($\rho = 0.8 \text{ g/cm}^3$) and Liquid B ($\rho = 1.2 \text{ g/cm}^3$). If they are immiscible, which liquid is on top?
- Answer: Liquid A will float on Liquid B because $0.8 \text{ g/cm}^3 < 1.2 \text{ g/cm}^3$.
Key Equations
| Equation | Symbols | Units |
|---|---|---|
| $\rho = \frac{m}{V}$ | $\rho$ = density, $m$ = mass, $V$ = volume | $\text{g/cm}^3$ or $\text{kg/m}^3$ |
| $V = l \times w \times h$ | $l$ = length, $w$ = width, $h$ = height | $\text{cm}^3$ or $\text{m}^3$ |
| $V_{obj} = V_2 - V_1$ | $V_2$ = final volume, $V_1$ = initial volume | $\text{cm}^3$ or $\text{ml}$ |
Unit Conversion Tip: To convert from $\text{g/cm}^3$ to $\text{kg/m}^3$, multiply by 1,000. (e.g., $1 \text{ g/cm}^3 = 1,000 \text{ kg/m}^3$)
Common Mistakes to Avoid
- ❌ Wrong: Inverting the formula (calculating Volume ÷ Mass).
- ✅ Right: Always divide Mass by Volume.
- ❌ Wrong: Forgetting to subtract the mass of the beaker when measuring a liquid.
- ✅ Right: Liquid mass = (Mass of beaker + liquid) - (Mass of empty beaker).
- ❌ Wrong: Using the total final volume ($V_2$) as the object's volume in displacement.
- ✅ Right: Subtract the initial water level from the final level ($V_2 - V_1$).
- ❌ Wrong: Miscalculating volume of a cube by only multiplying two sides.
- ✅ Right: For a 3D shape, you must multiply length × width × height.
Exam Tips
- Read the Meniscus: When measuring volume in a cylinder, always read from the bottom of the curve (the meniscus) at eye level to avoid parallax error.
- Check the Units: If the mass is in kg and volume is in $\text{m}^3$, the density must be $\text{kg/m}^3$. Do not mix grams and cubic meters in the same calculation.
- Show Your Working: Even if your final answer is wrong, you can earn marks for correctly stating the formula ($\rho = m/V$) and showing the subtraction for displacement or mass.