Key Points

Density is a measure of how much mass is contained in a given unit of volume. The formula to calculate density is $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$.

The volume of a regularly shaped object like a cuboid or a box is calculated by multiplying its length ($l$), width ($w$), and height ($h$). The formula is $V = l \times w \times h$.

To find the volume of an irregularly shaped object, use the water displacement method. The volume is the difference between the final water level and the initial water level in a measuring cylinder: $V_{\text{object}} = V_{\text{final}} - V_{\text{initial}}$.

If the density and volume of an object are known, its mass can be calculated by rearranging the density formula. The formula becomes $\text{Mass} = \text{Density} \times \text{Volume}$.

Similarly, if the mass and density of an object are known, its volume can be calculated. The rearranged formula is $\text{Volume} = \frac{\text{Mass}}{\text{Density}}$.

The SI unit for density is kilograms per cubic meter ($ext{kg}/ ext{m}^3$). Other common units include grams per cubic centimeter ($ext{g}/ ext{cm}^3$) and grams per milliliter ($ext{g}/ ext{mL}$).

When calculating density, it is essential to use consistent units. Remember that one milliliter is equivalent to one cubic centimeter ($1 \text{ mL} = 1 \text{ cm}^3$), and one liter is $1000 \text{ mL}$ or $1000 \text{ cm}^3$.

Relative density is a ratio that compares the density of a substance to the density of water. It has no units and is calculated using the formula: $\text{Relative density} = \frac{\text{Density of that substance}}{\text{Density of water}}$.

For water at room temperature, the mass in grams is approximately equal to the volume in milliliters. For example, $100 \text{ mL}$ of water has a mass of approximately $100 \text{ g}$, making its density about $1 \text{ g}/ ext{mL}$.

To find the value of one small division on a measuring cylinder, take the volume difference between two numbered marks and divide it by the number of divisions between them. For example, if $10 \text{ mL}$ is divided into 10 divisions, each division represents $1 \text{ mL}$.

To determine which solution is more concentrated, compare the ratio of the amount of solute to the amount of solvent. For example, comparing 4 spoons in $50 \text{ mL}$ (a ratio of $\frac{4}{50}$) with 2 spoons in $100 \text{ mL}$ (a ratio of $\frac{2}{100}$) shows the first solution is more concentrated.