Question

A certain grade of steel is made by dissolving \(5.0 \mathrm{~g}\) of carbon and \(1.5 \mathrm{~g}\) of nickel per \(100 . \mathrm{g}\) of molten iron. What is the mass percent of each component in the finished steel?

Short answer

Mass percent of carbon = \(\frac{5.0}{106.5}\) × 100 ≈ 4.69% Mass percent of nickel = \(\frac{1.5}{106.5}\) × 100 ≈ 1.41% Mass percent of iron = \(\frac{100}{106.5}\) × 100 ≈ 93.90%

Step-by-step solution

Calculate total mass of the finished steel

We are given that there are 5.0 g of carbon, 1.5 g of nickel, and 100 g of iron in the finished steel. To find the total mass, we add the mass of each component: Total mass = mass of carbon + mass of nickel + mass of iron

Calculate the mass percent of each component

To find the mass percent of each component, we divide the mass of that component by the total mass and multiply by 100: Mass percent of carbon = \(\frac{mass\_of\_carbon}{total\_mass}\) × 100 Mass percent of nickel = \(\frac{mass\_of\_nickel}{total\_mass}\) × 100 Mass percent of iron = \(\frac{mass\_of\_iron}{total\_mass}\) × 100

Substitute values and calculate mass percent of each component

Now we just substitute the values of mass for each component and the total mass in the above formulas to find the mass percent: Mass percent of carbon = \(\frac{5.0}{100+5.0+1.5}\) × 100 Mass percent of nickel = \(\frac{1.5}{100+5.0+1.5}\) × 100 Mass percent of iron = \(\frac{100}{100+5.0+1.5}\) × 100 Calculating these values, we find the mass percentage of each component in the finished steel.

Key concepts

Stoichiometry

Stoichiometry is a foundational principle in chemistry that deals with the quantitative relationships of the reactants and products in a chemical reaction. In education, it's a critical topic because it forms the basis for understanding how different chemicals interact. At its core, stoichiometry involves balancing chemical equations, predicting the yields of reactions, and using mole ratios to calculate the amounts of substances consumed or produced in a reaction.

For instance, when dissolving carbon and nickel in molten iron to make steel, as in the exercise example, stoichiometry allows us to predict the proportions needed to achieve the desired chemical properties of steel. Additionally, by understanding the stoichiometric principles, students can grasp why certain amounts of each component are necessary and how they contribute to the final product's characteristics, like its strength or durability.

Percent Composition

Percent composition is an essential concept in stoichiometry that describes the percentage by mass of each element in a compound. This measurement is fundamental for chemists to understand the makeup of a substance and thus its potential reactions and properties. For educational purposes, teaching percent composition supports the student's ability to visualize and conceptualize the molecular proportions within substances.

Applying Percent Composition

In chemistry practice, when students are asked to determine the mass percent of elements in a compound, like calculating the percentages of carbon, nickel, and iron in steel, they learn to combine theoretical knowledge with practical problems. This enhances their problem-solving skills alongside their chemistry knowledge. As shown in the exercise, the mass percent is calculated by taking the individual mass of each element, dividing it by the total mass, and then multiplying by 100 to get a percentage. This concept is crucial when it comes to quality control in material science and formulation of mixtures in industries.

Chemistry Education

Chemistry education plays an instrumental role in developing analytical thinking, problem-solving, and decision-making skills among students. It not only provides the understanding of basic chemical principles like stoichiometry and percent composition but also prepares students to tackle real-world challenges. By translating complex concepts into simpler forms, educators empower students to grasp intricate ideas, leading to innovations and advancements in various fields such as medicine, engineering, and environmental science.

The focus in chemistry education is to transition from rote memorization to active problem-solving, which is exemplified in exercises that involve mass percent calculations. Such exercises require synthesizing information and applying mathematical skills, demonstrating the practical relevance of the subject matter.