A 10.0 g block of gold is hammered into a thin gold sheet which has an area of 150 cm2. Given the density of gold is 19.3 g/cm3, what is the approximate thickness of the gold sheet in millimeters?

Verified step by step guidance

1. Calculate the volume of the gold block using its mass and the density of gold. Use the formula: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).
2. Substitute the given values into the formula: Mass = 10.0 g and Density = 19.3 g/cm^3 to find the volume in cm^3.
3. Use the formula for volume of a rectangular prism (or sheet): \( \text{Volume} = \text{Area} \times \text{Thickness} \). Rearrange this to solve for thickness: \( \text{Thickness} = \frac{\text{Volume}}{\text{Area}} \).
4. Substitute the calculated volume and the given area (150 cm^2) into the rearranged formula to find the thickness in cm.
5. Convert the thickness from cm to mm by multiplying by 10, since 1 cm = 10 mm.

Key Concepts

Density

Density is defined as mass per unit volume and is a crucial property of materials. For gold, the density is given as 19.3 g/cm³, meaning that one cubic centimeter of gold weighs 19.3 grams. Understanding density allows us to relate the mass of the gold block to its volume, which is essential for calculating the thickness of the gold sheet.

Volume Calculation

To find the thickness of the gold sheet, we first need to calculate its volume. The volume can be determined using the formula: Volume = Mass / Density. In this case, the mass of the gold block is 10.0 g, and using the density of gold, we can find the volume of the gold that has been transformed into the sheet.

Area and Thickness Relationship

The relationship between area, thickness, and volume is fundamental in this problem. The volume of the gold sheet can also be expressed as Volume = Area × Thickness. By rearranging this formula, we can solve for thickness once we have the volume from the previous calculations, allowing us to determine how thick the gold sheet is in millimeters.