Question

An alloy of iron and carbon was treated with sulfuric acid, in which only iron reacts. $$ 2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}(a q)+3 \mathrm{H}_{2}(g) $$ If a sample of alloy weighing \(2.358 \mathrm{~g}\) gave \(0.1067 \mathrm{~g}\) of hydrogen, what is the percentage of iron in the alloy?

Short answer

The percentage of iron in the alloy is approximately 83.33%.

Step-by-step solution

Calculate Moles of Hydrogen Produced

First, we need to determine how many moles of hydrogen were produced. The molar mass of hydrogen (H₂) is 2.02 g/mol. Thus, the number of moles of hydrogen can be calculated as \( \text{Moles of H}_2 = \frac{0.1067 \text{ g}}{2.02 \text{ g/mol}} \approx 0.0528 \text{ mol} \).

Determine Moles of Iron Reacted

From the balanced chemical equation, we know that 3 moles of H₂ are produced for every 2 moles of Fe. Therefore, the moles of iron reacted is \( \text{Moles of Fe} = \frac{2}{3} \times 0.0528 \text{ mol} \approx 0.0352 \text{ mol} \).

Calculate Mass of Iron Reacted

Now, calculate the mass of iron that reacted using its molar mass. The molar mass of Fe is 55.85 g/mol. Thus, the mass of Fe is \( \text{Mass of Fe} = 0.0352 \text{ mol} \times 55.85 \text{ g/mol} \approx 1.965 g \).

Calculate Percentage of Iron in the Alloy

Finally, to find the percentage of iron in the alloy, use the formula \( \text{Percentage of Fe} = \left( \frac{1.965 \text{ g}}{2.358 \text{ g}} \right) \times 100 \approx 83.33\% \).

Key concepts

Alloys

An alloy is a mixture of two or more elements, where at least one is metal. Alloys like the one mentioned in the exercise are often stronger or more resistant than the pure metals they're made from. Alloys are common in everyday items and industrial applications.

Understanding how the composition of an alloy affects its properties is crucial. For example, adding carbon to iron can make steel, which is much harder than pure iron.
- Alloys can combine metallic and non-metallic elements.
- Adjusting the amounts of each component can alter the physical and chemical characteristics.

The exercise above deals with an iron-carbon alloy. Here, only the iron component reacts with sulfuric acid, which allows us to isolate and calculate the amount of iron based on the chemical reaction.

Stoichiometry

Stoichiometry is the method of calculating the amounts of reactants or products involved in a chemical reaction. It relies on the balanced chemical equation to provide concepts such as molar relationships and proportional quantities.

In the reaction of iron with sulfuric acid, stoichiometry allows us to understand how much iron reacts by using the amount of hydrogen gas produced.
- The balanced equation indicates the molar ratio: for every 2 moles of iron, 3 moles of hydrogen are produced. - Through stoichiometry, we can determine the exact moles of each reactant and product, crucial for calculating quantities in industrial processes.

Using the stoichiometric calculations described in the step-by-step solution, we see how 0.0528 moles of hydrogen correlate to 0.0352 moles of iron.

Chemical Reactions

Chemical reactions involve changing the arrangement of atoms to form new substances. In the example, iron reacts with sulfuric acid to form iron(III) sulfate and hydrogen gas.

Chemical equations offer vital insights:
- Reactants are on the left, products on the right.
- Subscripts and coefficients indicate the quantity of atoms and molecules involved.

In our exercise, the chemical equation:
\( 2 \mathrm{Fe}(s) + 3 \mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}(a q) + 3 \mathrm{H}_{2}(g) \)
shows how iron molecules react quantitatively with sulfuric acid. Analyzing this allows us to determine how much of each substance is consumed and produced. Understanding these principles is crucial for explaining both simple and complex chemical processes.