Question

Given that the density of gold and sand are 19. 3 g/cm^3 and 2. 95 g/cm^3, respectively, and that the density of the mixture is 4. 17g/cm^3, calculate the percent by mass of gold in the mixture.

Answer 1

The percent by mass of gold in the mixture will be 34.5%.

How to calculate the percentage?

The following information can be deduced based on the information given:

Density of gold = 19.3 g/cm³.

Density of sand = 2.94 g/cm³

Density of mixture = 4.17 g/cm³

It should be noted that when we find the volume fo gold on a 1cm³ sample, then we can be able to find that mass. The volume of gold will be calculated thus:

4.17 = [(19.3x + 2.95(1 - x)]

4.17 = 19.3x + 2.95 - 2.95x

4.17 = 16.35x + 2.95

x = 0.0746cm³

The mass of gold will be:

= 0.0746 × 19.3

= 1.44

The percent by mass of gold in the mixture will be:

= 1.44/4.17 × 100

= 34.5%

In conclusion, the percent by mass of gold in the mixture will be 34.5%.

What is Mass?

Mass is a physical body's total amount of matter. It also serves as a gauge for the body's inertia, or resistance to acceleration (change in velocity) in the presence of a net force. The strength of an object's gravitational pull to other bodies is also influenced by its mass.

The kilogram is the primary mass unit in the SI (kg). Even though weight is frequently measured using a spring scale rather than a balancing scale and directly compared with known masses, mass is not the same as weight in physics. Due to the lower gravity on the Moon, an object would weigh less than it does on Earth while maintaining the same mass. Given that weight is a force.

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