What is the density (g/mL) of each of the following samples?
b. A 14.3 - cm³ sample of tin has a mass of 0.104 kg.

Verified step by step guidance

1. Step 1: Recall the formula for density: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). This formula relates the mass and volume of a substance to its density.
2. Step 2: Convert the mass from kilograms (kg) to grams (g). Since \( 1 \, \text{kg} = 1000 \, \text{g} \), multiply the given mass (0.104 kg) by 1000 to express it in grams.
3. Step 3: Ensure the volume is in cubic centimeters (cm³), which is already provided as 14.3 cm³. No conversion is needed for the volume in this case.
4. Step 4: Substitute the values for mass (in grams) and volume (in cm³) into the density formula: \( \text{Density} = \frac{\text{Mass (g)}}{\text{Volume (cm³)}} \).
5. Step 5: Perform the division to calculate the density in \( \text{g/cm³} \), which is equivalent to \( \text{g/mL} \) since \( 1 \, \text{cm³} = 1 \, \text{mL} \).

Key Concepts

Density

Density is defined as the mass of a substance divided by its volume, typically expressed in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³). It is a fundamental property that helps identify materials and understand their behavior in different contexts. The formula for density is D = m/V, where D is density, m is mass, and V is volume.

Mass and Volume

Mass is a measure of the amount of matter in an object, usually measured in grams (g) or kilograms (kg). Volume, on the other hand, is the amount of space that a substance occupies, measured in cubic centimeters (cm³) or milliliters (mL). Understanding the relationship between mass and volume is crucial for calculating density and interpreting the properties of materials.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In the context of the question, converting the mass of tin from kilograms to grams is necessary since density is typically expressed in g/mL. This involves multiplying the mass in kg by 1000 to obtain the mass in grams, ensuring consistency in units for accurate density calculation.