Question

Gold has a specific gravity of almost \(20 .\) A 5 -gallon bucket of water weighs 40 pounds. How much would a 5 -gallon bucket of gold weigh?

Short answer

The bucket of gold would weigh 800 pounds.

Step-by-step solution

Understanding Specific Gravity

Specific gravity is the ratio of the density of a substance to the density of a reference substance, typically water for liquids and solids. Thus, if gold has a specific gravity of 20, it means it is 20 times denser than water.

Converting Gallons to Weight of Water

First, recognize that 1 gallon of water weighs approximately 8 pounds. Therefore, a 5-gallon bucket of water weighs \(5 \times 8 = 40\) pounds, as given in the problem.

Calculating Weight of Gold

Since gold has a specific gravity of 20, a bucket of gold would weigh 20 times that of a similar bucket of water. So, the weight of a 5-gallon bucket of gold would be \(40 \times 20 = 800\) pounds.

Key concepts

Understanding Density

The concept of density is important in understanding specific gravity. Density is defined as the mass of a substance per unit volume. It is often expressed in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).
When you think about density, consider how tightly packed the particles of a substance are. The denser a material, the more mass it has in a given volume. Water, which is used as a reference point for measuring density and specific gravity, has a density of approximately 1 g/cm³.
Gold's density is significantly higher than water's, making it much heavier for the same volume. This heaviness is due to the tightly packed arrangement of its atomic structure. Understanding density helps us grasp why materials like gold with high specific gravities are so much heavier than water.

Weight Calculation in Context of Specific Gravity

Calculating the weight of substances using specific gravity involves understanding how much heavier a substance is compared to water. In our exercise, water has a weight of about 8 pounds per gallon.
Your task is to determine how much heavier gold is for the same volume by using its specific gravity. Given that specific gravity is simply the ratio of densities, to find the weight of another substance like gold in the same volume, you multiply the weight of water by the specific gravity of the substance.
For example, if gold has a specific gravity of 20, and a bucket of water weighs 40 pounds, then a similar bucket of gold would weigh 20 times 40 pounds, equating to 800 pounds.

Using Conversion Factors

Conversion factors help us translate measurements between different units. Here, we are tasked with converting the volume measure in gallons to a weight measure in pounds.
Knowing that 1 gallon of water weighs approximately 8 pounds provides us with the necessary conversion factor. This conversion allows us to translate a 5-gallon volume of a substance into its respective weight.

• 5 gallons of water = 5 x 8 pounds = 40 pounds
• 5 gallons of gold = 5 gallons of water x specific gravity of gold
• Thus, 5 gallons of gold equals 40 pounds (water) x 20 (specific gravity) = 800 pounds

These conversion calculations simplify the complex interaction of weight, volume, and specific gravity into manageable math.

Gold and Its Properties

Gold is a precious metal well-known for its appealing qualities including its luster, malleability, and conductivity. However, one of its defining characteristics is its high density.
Gold's density contributes to its significant weight compared to other substances with an equivalent volume.
Since gold is denser than water by 20 times, this attribute is vital in determining the weight of gold when given its volume. Understanding this heavyweight nature of gold is crucial when relating it to specific gravity calculations.

• Gold's high density implies high weight in small volumes
• Useful in industries needing high-density materials
• Important when assessing the economic value of gold

Gold's unique properties make calculations involving its specific gravity a critical skill in fields like metallurgy and jewelry making.