Determine the density (g/mL) for each of the following:
c. A gem has a mass of 4.50 g. When the gem is placed in a graduated cylinder containing 12.00 mL of water, the water level rises to 13.45 mL.

Verified step by step guidance

1. Step 1: Recall the formula for density, which is \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). This formula relates the mass of an object to the volume it occupies.
2. Step 2: Identify the mass of the gem from the problem. The mass is given as 4.50 g.
3. Step 3: Determine the volume of the gem. The volume can be calculated by finding the difference in water levels before and after the gem is placed in the graduated cylinder. Use the formula \( \text{Volume of gem} = \text{Final water level} - \text{Initial water level} \). Substitute the values: \( \text{Volume of gem} = 13.45 \text{ mL} - 12.00 \text{ mL} \).
4. Step 4: Substitute the mass and calculated volume into the density formula. \( \text{Density} = \frac{4.50 \text{ g}}{\text{Volume of gem}} \).
5. Step 5: Perform the division to calculate the density. Ensure the units are consistent (g/mL) and interpret the result as the density of the gem.

Key Concepts

Density

Density is defined as the mass of an object divided by its volume, typically expressed in grams per milliliter (g/mL) for liquids and solids. It is a crucial property that helps identify substances and understand their behavior in different environments. In this context, density can be calculated using the formula: Density = Mass/Volume.

Volume Displacement

Volume displacement is a method used to measure the volume of an irregularly shaped object by observing the change in liquid level when the object is submerged. In this scenario, the initial water level is 12.00 mL, and it rises to 13.45 mL when the gem is added, indicating that the volume of the gem is the difference, which is 1.45 mL.

Measurement Units

Measurement units are standardized quantities used to express physical properties. In this problem, mass is measured in grams (g) and volume in milliliters (mL). Understanding these units is essential for accurately calculating density and interpreting the results, as they ensure consistency and clarity in scientific communication.