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

A 5-gallon 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. In this case, the specific gravity of gold is 20, which means gold is 20 times denser than water.

Calculate Water Density in the Bucket

A 5-gallon bucket of water weighs 40 pounds. Therefore, the density of water, when translated into pounds per 5 gallons, is 40 pounds.

Determine Gold Weight from Specific Gravity

Since gold is 20 times denser than water, we can find the weight of a 5-gallon bucket of gold by multiplying the weight of the 5-gallon bucket of water by the specific gravity of gold. So, the weight of the bucket of gold is \( 40 \text{ pounds} \times 20 = 800 \text{ pounds} \).

Key concepts

Density of Gold

Gold is renowned for its exceptional density. Density is a measure of how much mass exists in a given volume, which in turn is a critical part of calculating weight in physical materials.
Gold has a much higher density compared to many other metals, making it significantly heavier in the same volume.
When we say that gold has a density of nearly 20 times that of water, we mean that a set volume of gold will weigh 20 times more than the exact same volume of water.
This higher density contributes to gold's profound weight when gathered in large quantities, such as a bucket full.

Density of Water

Water is often used as a baseline reference due to its simple and uniform density, especially at standard temperature and pressure.
The density of water is approximately 1 gram per cubic centimeter or equivalently 8.34 pounds per gallon. A 5-gallon bucket of water, therefore, weighs approximately 40 pounds, giving us a straightforward metric for reference.
Understanding the density of water is essential because it serves as a point of comparison to measure the specific gravity of other substances, like gold.

Weight Calculation

Calculating weight using density involves the concept of mass over a given volume and how specific gravity factors in as a multiplier.
To find out how much a different material with known specific gravity will weigh in a similar scenario, multiply the weight of the reference substance by the specific gravity value.
For instance, with gold having a specific gravity of 20, a 5-gallon bucket that holds 40 pounds of water would correspondingly hold 800 pounds of gold \( (40 \text{ pounds} \times 20 = 800 \text{ pounds}) \).
This simple calculation shows how denser substances like gold pack more weight in the same space.

Reference Substance

When calculating densities and specific gravities, using a reference substance is key to ensuring consistent and comparable results.
Water is the most commonly used reference due to its known density properties. It provides a reliable constant that other materials can be easily compared against.
Using water as the base measurement, substances with higher specific gravities are denser and will weigh more in the same volume, as shown with gold's specific gravity in this scenario.

• Reference substances act as benchmarks in scientific calculations.
• They ensure that density measurements are standardized across various materials.