Chemistry 122 Lab 1 Notes: Density and Specific Gravity

Density and Specific Gravity

Density is the measure of how tightly matter is packed, defined as the mass per unit volume: $\rho = \frac{m}{V}$ with SI units of $\text{kg/m}^3$. Physical properties can be measured without changing composition; density depends on both mass and volume, and thus varies with temperature and pressure. Gases are light (low density) and heavy substances like lead have high density. Specific gravity (SG) indicates how dense a substance is relative to water and is unitless. It is defined as $SG = \frac{\rho}{\rho<em>{water}}$. In metric units, where the density of water is about $\rho</em>{water} \approx 1\ \text{g/cm}^3$, SG is numerically equal to the density in g/cm³.

Key concepts: density and specific gravity

Specific gravity is a comparative, unitless quantity; density is an intrinsic property with SI units. Density of a solid is determined from its mass and volume, while density of a liquid is often measured using a pycnometer for precision or a hydrometer for rapid results. The deeper a hydrometer sinks, the lower the SG of the liquid.

Densities of common metals

Key metal densities (approximate, at room temperature): Aluminum $2.70\times 10^3\ \text{kg/m}^3\,$, Brass $8.56\times 10^3\ \text{kg/m}^3\,$, Chromium $7.20\times 10^3\ \text{kg/m}^3\,$, Copper $8.92\times 10^3\ \text{kg/m}^3\,$, Iron $7.86\times 10^3\ \text{kg/m}^3\,$, Lead $1.13\times 10^4\ \text{kg/m}^3\,$, Magnesium $1.75\times 10^3\ \text{kg/m}^3\,$, Zinc $7.14\times 10^3\ \text{kg/m}^3\,$.

Density measurement methods

Density measurements are performed by combining mass and volume. For solids, determine mass with a balance and volume by either geometric measurements (regular solids) or water displacement (irregular shapes). For liquids, density is measured with a pycnometer for precision or with a hydrometer for speed; the deeper the hydrometer bulb sinks, the lower the SG.

Battery context and SG values

In automotive batteries, sulfuric acid density correlates with charge state. A fully charged battery has SG about $1.30$; when SG drops below $1.20$, recharge is needed. This illustrates SG as a practical density indicator in solutions.

Experimental setup and procedures (overview)

The experiment investigates density measurements for solids and SG measurements for liquids. Solids: three metal cylinders are weighed with an electronic balance (tare first), dimensions are measured with a vernier caliper, and volumes are obtained by water displacement using a graduated cylinder. Repeat for the remaining cylinders. Liquids: determine SG of sulfuric acid solutions using a hydrometer and relate the results to the battery state of charge.

Experimental procedure details (solids)

For each metal cylinder, obtain the mass with the electronic balance to the nearest 0.01 g. Measure height and diameter with a vernier caliper to the nearest 0.001 cm, ensuring the caliper reads mm and closes at zero. Determine the volume by water displacement: fill a 25–50 mL graduated cylinder about half full with tap water and read the initial volume to the nearest 0.1 mL; gently submerge the cylinder and read the final volume to the same precision.

Experimental procedure details (solids, continued)

Repeat the mass, dimension, and displacement measurements for the two additional cylinders.

Experimental procedure details (liquids)

Use a hydrometer to determine the SG of the sulfuric acid solutions. Record the results and associate them with the battery state of charge.

Equations and data interpretation

Key equations include $\rho = \frac{m}{V}$ for density and $SG =\frac{\rho}{\rho_{water}}$ for specific gravity. The percent error is given by
$\%\ \text{error} = \left|\frac{\text{actual} - \text{experimental}}{\text{actual}}\right| \times 100.$