Question

A sterling silver spoon has a mass of \(65.5 \mathrm{~g}\) and contains \(7.50 \%\) copper. Find the mass of copper in the spoon.

Short answer

The mass of copper in the spoon is approximately 4.91 g.

Step-by-step solution

Understanding the Problem

We need to find the mass of copper in a sterling silver spoon that has a total mass of \(65.5 \mathrm{~g}\) and is composed of \(7.50\%\) copper.

Convert Percentage to Decimal

To find the mass of copper, we'll first convert the percentage of copper, \(7.50\%\), to a decimal by dividing by \(100\). Thus, \(7.50\% = \frac{7.50}{100} = 0.075\).

Calculate the Mass of Copper

Multiply the total mass of the spoon by the decimal fraction representing the copper content: \(65.5 \mathrm{~g} \times 0.075\).

Perform the Multiplication

Calculate the result of the multiplication from Step 3 to find the mass of copper: \(65.5 \times 0.075 = 4.9125 \mathrm{~g}\). Therefore, the mass of copper in the sterling silver spoon is \(4.9125 \mathrm{~g}\).

Key concepts

Metal Alloy Composition

When dealing with metal alloys like sterling silver, it's essential to understand that these materials are typically combinations of different metals. Sterling silver, for instance, is primarily composed of silver and a small percentage of another metal, usually copper. This blend enhances the properties of pure silver by improving its strength and durability. The composition of a metal alloy is often expressed in percentages, which tell us how much of each component is present. In educational problems like the one at hand, knowing the exact composition helps solve for specific quantities, like the mass of copper in a sterling silver spoon. Alloys can be designed for various characteristics such as:

• Increased hardness and strength
• Improved corrosion resistance
• Enhanced electrical conductivity

Understanding alloy compositions is crucial for many practical applications, from jewelry-making to industrial components.

Percentage Calculations

Percentage calculations are used to express the relationship between parts of a whole in a simple way. In the context of metal alloys or chemical compositions, percentages tell you how much of one component is in the mixture. Before using percentages in calculations, convert them to decimals. This involves dividing the percentage by 100. For example, if you have a spoon containing 7.50% copper, converting that to decimal means calculating \( \frac{7.50}{100} = 0.075 \). This transformation is essential because it turns a percentage into a form that can be directly used in mathematical operations like multiplication or division.Why is this useful?

• It simplifies arithmetic operations
• Enables precise calculations
• Makes it easier to find proportions of components in mixtures

Using percentage calculations efficiently helps in solving a wide range of problems, from everyday tasks to complex scientific equations.

Mass Calculation

Mass calculation is a fundamental operation in many physics and chemistry applications. In problems that involve finding the mass of a component within a mixture, this calculation is paramount. To calculate the mass of a specific element within an alloy, such as copper in a sterling silver spoon, you first need to multiply the total mass of the alloy by the decimal form of the percentage of the component you are interested in. This method isolates the mass of that single component from the whole mixture. For example:

• The spoon has a total mass: \(65.5 \, g\).
• Component percentage (as a decimal): \(0.075 \) for copper.
• Multiplying these gives us \(65.5 \, g \times 0.075 = 4.9125 \, g\).

Therefore, the mass of copper in the spoon is \(4.9125 \, g\). Mass calculations like these are used extensively in scientific experiments, engineering, and manufacturing, as they provide a way to measure and manipulate quantities accurately.