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Chapter 4: Problem 136

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 \(2.358\) g gave \(0.1352 \mathrm{~g}\) of hydrogen, what is the percentage of iron in the alloy?

Short Answer

Expert verified
The percentage calculation appears incorrect, suggesting an error, logically Fe percentage should be below 100%.

Step by step solution

01

Determine Moles of Hydrogen Produced

First, calculate the moles of hydrogen produced using its mass. The molar mass of hydrogen (H) is approximately 2.02 g/mol (because it is H2). \[\text{Moles of } \mathrm{H}_2 = \frac{0.1352\, \text{g}}{2.02\, \text{g/mol}} \approx 0.0669 \text{ moles}\]
02

Use Stoichiometry to Determine Moles of Iron

According to the balanced chemical equation, 2 moles of Fe produce 3 moles of H2. Therefore, \[\text{Moles of Fe} = \frac{2}{3} \times \text{Moles of } \mathrm{H}_2 = \frac{2}{3} \times 0.0669 \approx 0.0446 \text{ moles}\]
03

Calculate Mass of Iron in the Alloy

Now, calculate the mass of iron using its moles and molar mass. The molar mass of iron (Fe) is approximately 55.85 g/mol.\[\text{Mass of Fe} = 0.0446 \text{ moles} \times 55.85 \text{ g/mol} \approx 2.4911 \text{ g}\]
04

Calculate Percentage of Iron in the Alloy

Finally, calculate the percentage of iron in the alloy using its mass.\[\text{Percentage of Fe} = \left( \frac{2.4911 \text{ g}}{2.358 \text{ g}} \right) \times 100\% \approx 105.64\%\]
05

Adjust for Discrepancy

Since the calculated mass of iron is greater than the total mass of the alloy, there may be an error in steps or assumptions. It suggests a reevaluation of values or assumption constraints, as it should not logically exceed 100%鈥攊n actual, the correct approach should give a feasible answer under 100%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Reactions
Chemical reactions involve the transformation of one or more substances into different substances. This process is characterized by breaking and forming chemical bonds.
  • Reactants are the starting substances and products are the newly formed substances.
  • Reactions can involve simple exchanges of parts or more complex rearrangements.
In the case of the weirdly high percentage of iron, we had a reaction where only iron reacted with sulfuric acid to produce iron sulfate and hydrogen gas. This is a chemical reaction because the reactants (iron and sulfuric acid) disappear as products (iron sulfate and hydrogen) form.
Molar Mass
Molar mass is a fundamental concept in chemistry used to convert between the mass of a substance and moles, which are units that relate to the number of atoms or molecules in a given sample.
  • The molar mass is usually expressed in grams per mole (g/mol).
  • It is calculated by summing the atomic masses of all atoms in a molecule as found on the periodic table.
In the practice of stoichiometry, molar mass allows us to calculate the amount of substance in a given sample, which is crucial to solving stoichiometric problems. For instance, the molar mass of hydrogen (H2) was used to determine the moles of hydrogen extracted during the iron-sulfuric acid reaction.
Percent Composition
Percent composition is about determining the relative weight of each element in a compound, expressed as a percentage. It shows how much of the sample is made up of a particular element.
  • Calculated by dividing the mass of a single element in a compound by the total molar mass of the compound and then multiplying by 100%.
  • This concept can apply to mixtures like the iron-carbon alloy.
In this exercise, we attempted to find the percentage of iron in an iron-carbon alloy, leading us to the realization that the calculated percentage exceeded 100%, indicating an error somewhere in our assumptions or calculations.
Balanced Equations
Balanced chemical equations obey the Law of Conservation of Mass, which states that mass is neither created nor destroyed in a chemical reaction.
  • Every atom present in the reactants must be accounted for in the products.
  • This balancing process often involves adjusting coefficients, the numbers before molecules, instead of changing subscripts, which are part of the chemical formulas.
In our case involving iron and sulfuric acid, the balanced chemical equation was essential in determining the stoichiometric relationship between reactants and products, allowing us to calculate the amount of iron based on the amount of hydrogen gas produced.

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Most popular questions from this chapter

Gold has compounds containing gold(I) ion or gold(III) ion. A compound of gold and chlorine was treated with a solution of silver nitrate, \(\mathrm{AgNO}_{3}\), to convert the chloride ion in the compound to a precipitate of AgCl. A 162.7-mg sample of the gold compound gave \(100.3 \mathrm{mg} \mathrm{AgCl}\). a. Calculate the percentage of the chlorine in the gold compound. b. Decide whether the formula of the compound is \(\mathrm{AuCl}\) or \(\mathrm{AuCl}_{3}\)

Phosphoric acid is prepared by dissolving phosphorus( \(\mathrm{V}\) ) oxide, \(\mathrm{P}_{4} \mathrm{O}_{10}\), in water. What is the balanced equation for this reaction? How many grams of \(\mathrm{P}_{4} \mathrm{O}_{10}\) are required to make \(1.50 \mathrm{~L}\) of aqueous solution containing \(5.00 \%\) phosphoric acid by mass? The density of the solution is \(1.025 \mathrm{~g} / \mathrm{mL}\).

Lead(II) nitrate reacts with cesium sulfate in an aqueous precipitation reaction. What are the formulas of lead(II) nitrate and cesium sulfate? Write the molecular equation and net ionic equation for the reaction. What are the names of the products? Give the molecular equation for another reaction that produces the same precipitate.

Mercury(II) nitrate is treated with hydrogen sulfide, \(\mathrm{H}_{2} \mathrm{~S}\), forming a precipitate and a solution. Write the molecular equation and the net ionic equation for the reaction. An acid is formed; is it strong or weak? Name each of the products. If \(81.15 \mathrm{~g}\) of mercury(II) nitrate and \(8.52 \mathrm{~g}\) of hydrogen sulfide are mixed in \(550.0 \mathrm{~g}\) of water to form \(58.16 \mathrm{~g}\) of precipitate, what is the mass of the solution after the reaction?

How many grams of sodium dichromate, \(\mathrm{Na}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\), should be added to a \(100.0-\mathrm{mL}\) volumetric flask to prepare \(0.025\) \(M \mathrm{Na}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) when the flask is filled to the mark with water?
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