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

In the finished steel, the mass percent of carbon is approximately \(4.7\%\), the mass percent of nickel is approximately \(1.4\%\), and the mass percent of iron is approximately \(93.9\%\).

Step-by-step solution

Find the total mass of steel

To find the total mass of the steel, we need to add the mass of each component: carbon (C), nickel (Ni), and molten iron (Fe). Total Mass (Steel) = Mass of C + Mass of Ni + Mass of Fe We know that there are \(5.0 \mathrm{g}\) of carbon and \(1.5 \mathrm{g}\) of nickel per \(100 . \mathrm{g}\) of molten iron. So, Total Mass (Steel) = \(5.0 \mathrm{g} + 1.5 \mathrm{g} + 100 . \mathrm{g} = 106.5 \mathrm{g}\)

Calculate the mass percent of each component.

Now, we can find the mass percent of each component. To do that, we divide the mass of the component by the total mass of steel and then multiply by 100. Mass Percent of C = \(\frac{Mass \hspace{2mm} of \hspace{2mm} C}{Total \hspace{2mm} Mass \hspace{2mm} (Steel)} \cdot 100\) Mass Percent of Ni = \(\frac{Mass \hspace{2mm} of \hspace{2mm} Ni}{Total \hspace{2mm} Mass \hspace{2mm} (Steel)} \cdot 100\) Mass Percent of Fe = \(\frac{Mass \hspace{2mm} of \hspace{2mm} Fe}{Total \hspace{2mm} Mass \hspace{2mm} (Steel)} \cdot 100\) Now we can plug in the values and find the mass percent of each component: Mass Percent of C = \(\frac{5.0 \mathrm{g}}{106.5 \mathrm{g}} \cdot 100 \approx 4.7\%\) Mass Percent of Ni = \(\frac{1.5 \mathrm{g}}{106.5 \mathrm{g}} \cdot 100 \approx 1.4\%\) Mass Percent of Fe = \(\frac{100 . \mathrm{g}}{106.5 \mathrm{g}} \cdot 100 \approx 93.9\%\) In the finished steel, the mass percent of carbon is approximately \(4.7\%\), the mass percent of nickel is approximately \(1.4\%\), and the mass percent of iron is approximately \(93.9\%\).

Key concepts

Alloy Composition

Understanding the composition of alloys is crucial in industries like construction and transportation. An alloy is a mixture of two or more elements, where at least one of them is a metal. The resulting material has improved properties that are beneficial in various applications. Alloys often have enhanced strength, resistance to corrosion, or better electrical conductivity compared to their component elements. For example, stainless steel is an alloy made primarily of iron, carbon, and other elements such as nickel or chromium. By altering the composition, manufacturers can tailor the properties of the alloy to suit specific needs. In this exercise, the alloy is steel, composed of carbon, nickel, and molten iron. Each element contributes to the overall strength and usability of the steel. As you calculate the percentages of each element, you gain insights into how the alloy's composition affects its characteristics.

Mass Percent

Mass percent is a useful way to express the concentration of a component in a mixture or solution. To calculate mass percent, you need to divide the mass of a single component by the total mass of the mixture and multiply by 100 to convert it to a percentage. This measurement helps in understanding the proportion of each element in an alloy. For example, in our steel alloy, the mass percent of carbon is calculated as

• Mass Percent of C = \(\frac{5.0 \mathrm{g}}{106.5 \mathrm{g}} \times 100 \approx 4.7\%\)

Conducting these calculations allows engineers to precisely mix components to achieve desirable properties in the finished product. Mass percent simplifies complex mixture descriptions into easier terms to grasp and work with, especially in manufacturing processes where consistency is key.

Chemical Engineering

Chemical engineering involves designing and managing processes that transform raw materials into valuable products. This field applies principles from chemistry, physics, and biology to develop efficient production methods. One fundamental task within chemical engineering is to ensure the correct composition of alloys like steel. Engineers must calculate and control the amounts of each component to deliver a product that meets all structural and functional requirements.
Mass percent calculations, as seen in the steel example, are a typical task for chemical engineers. These professionals need to understand how altering one component can impact the quality and properties of the entire product. Through accurate calculations and deep knowledge of material behaviors, chemical engineers innovate, improve, and optimize material production to meet industrial standards and economic constraints.