Question

A stainless steel spoon has a mass of \(55.5 \mathrm{~g}\) and contains \(10.5 \%\) chromium. Find the mass of chromium in the spoon.

Short answer

The mass of chromium in the spoon is 5.8275 grams.

Step-by-step solution

Identify Given Values

We are given the total mass of the spoon as 55.5 grams and the percentage of chromium in the spoon as 10.5%. Let's identify these values. Mass of spoon = 55.5 grams, Chromium percentage = 10.5%.

Understand the Problem

The problem asks for the mass of chromium contained in the spoon. We have the percentage of chromium, so we need to calculate how much this percentage represents in terms of the actual mass from the total spoon mass.

Convert Percentage to Decimal

Since percentages are parts per 100, we convert 10.5% to a decimal by dividing by 100. This gives us 0.105 as the decimal representation of the chromium content.

Calculate Chromium Mass

Using the formula: Mass of chromium = Total mass of spoon  Chromium percentage in decimal form, we have: Mass of chromium = 55.5  0.105 = 5.8275 grams.

Key concepts

Mass Percentage

Mass percentage is a term used in chemistry to describe the concentration of a certain element or compound in a mixture. It tells us how much of one specific component (like a metal) is present in a combination (such as an alloy), compared to the whole mixture. To calculate the mass percentage, we follow a simple formula:

• First, identify the mass of the component of interest.
• Then, find the total mass of the mixture.
• Finally, divide the mass of the component by the total mass and multiply by 100 to get the percentage.

For example, if a stainless steel spoon weighs 55.5 grams and chromium accounts for 10.5% of that, we calculate the mass percentage by adapting this general process. This method is highly useful in industries that require specific proportions of elements, such as metallurgy and material science.

Metal Alloys

Metal alloys are combinations of two or more elements where at least one of them is a metal. Alloys are created to enhance properties like strength, durability, resistance to corrosion, and more, beyond what is achievable with pure metals. Common examples include steel, brass, and bronze.

In the case of stainless steel, which is a popular alloy, chromium is a crucial component. By adding chromium, the steel gains better resistance to rust and tarnish. When you look at metal alloys from a chemist's perspective, you can see how each part influences the overall makeup and properties of the alloy.

This understanding of metal alloys is crucial for fields like engineering and manufacturing, where specific material characteristics are necessary for functionality and safety. Knowing the mass percentage of each component in an alloy helps in designing and creating materials that meet these precise requirements.

Basic Chemistry Calculations

Basic chemistry calculations are foundational tools that help us figure out quantities and proportions within chemical substances. Common calculations include finding the mass of components within mixtures, determining reactant or product masses in reactions, and more.

To make these calculations, you follow these general steps:

• Identify the data you are given and what you need to find out.
• Convert percentages to decimals if necessary for calculations.
• Use algebraic formulas to solve for the unknown, such as when multiplying the total mass by the decimal percentage.

These steps are not only applied when dealing with mixtures like metal alloys but are also vital in everyday chemistry labs for solution preparations, analyzing material compositions, and understanding reaction stoichiometry.

By practicing these basic chemistry calculations, students and professionals alike can solve both simple and complex chemistry problems efficiently, helping them gain a better grasp of both theoretical and practical chemical processes.