Question

A \(25.2-\mathrm{mL}\) sample of kerosene was determined to have a mass of \(20.41 \mathrm{~g}\). What is the density of kerosene?

Short answer

The density of kerosene is approximately \( 0.81 \text{ g/mL} \).

Step-by-step solution

- Understand the formula for density

Density is defined as mass per unit volume. The formula to calculate density (\rho) is given by \[ \rho = \frac{m}{V} \] where \( m \) is the mass and \( V \) is the volume.

- Identify the given values

The problem provides a volume \( V = 25.2 \text{ mL} \) and a mass \( m = 20.41 \text{ g} \).

- Substitute the given values into the formula

Substitute \( m = 20.41 \text{ g} \) and \( V = 25.2 \text{ mL} \) into the density formula: \[ \rho = \frac{20.41 \text{ g}}{25.2 \text{ mL}} \]

- Perform the calculation

Divide the mass by the volume: \[ \rho = \frac{20.41}{25.2} \approx 0.81 \text{ g/mL} \]

- State the final answer

The density of the kerosene sample is approximately \( 0.81 \text{ g/mL} \).

Key concepts

mass

Mass is a measure of the amount of matter in a substance or object. It is usually measured in grams (g) or kilograms (kg). In the given exercise, we are working with a mass of 20.41 grams. The mass is a crucial value in various calculations, including finding the density of a substance.

volume

Volume refers to the amount of space that a substance or object occupies. It is typically measured in milliliters (mL) for liquids or cubic centimeters (cm³) for solids. For the kerosene sample in our exercise, the volume is 25.2 mL. Understanding volume helps us determine how much space a particular mass occupies, which is essential in density calculations.

density formula

The density formula is a fundamental principle in physics and chemistry. Density (\rho) is calculated using the formula: \ \[ \rho = \frac{m}{V} \]
Here, \ \(\rho\) represents density, \ \(m\) represents mass, and \ \(V\) represents volume. In our example, we substitute the values we know: mass \ \(m = 20.41 \text{ g}\) and volume \ \(V = 25.2 \text{ mL}\). Performing the calculation, we get:
\ \[ \rho = \frac{20.41 \text{ g}}{25.2 \text{ mL}} \approx 0.81 \text{ g/mL} \]
The final result is approximately 0.81 g/mL, which is the density of the kerosene in the example.

unit conversion

Unit conversion is the process of converting a measurement from one unit to another. It's important because different contexts require different units. In our exercise, the volume is already in mL, and the mass is in grams, which are standard units for density calculations. However, if we needed to convert units, we might use these conversions:

• 1 milliliter (mL) = 0.001 liters (L)
• 1 gram (g) = 0.001 kilograms (kg)

Performing unit conversions ensures that all values are compatible for accurate calculations.