Question

Solid iron(III) hydroxide is added to \(625 \mathrm{~mL}\) of \(0.280 \mathrm{M} \mathrm{HCl}\). The resulting solution is acidic and titrated with \(238.2 \mathrm{~mL}\) of \(0.113 \mathrm{M} \mathrm{NaOH}\). What mass of iron(III) hydroxide was added to the HCl?

Short answer

Answer: The mass of iron(III) hydroxide added to the HCl solution is approximately 0.958 g.

Step-by-step solution

Determine the moles of HCl

We are given the initial concentration and volume of HCl. We can use the formula \(moles = (concentration)(volume)\) to find the total moles of HCl: \(moles_{HCl} = (0.280~M)(0.625~L) = 0.175~mol\)

Determine the moles of NaOH used in titration

We are given the volume and concentration of NaOH used for titration. We will use the same formula as used for the HCl: \(moles_{NaOH} = (0.113~M)(0.2382~L) = 0.02690~mol\)

Determine the remaining moles of HCl after iron(III) hydroxide addition

Knowing the moles of NaOH used in titration, we can find out how many moles of HCl remained unreacted with iron(III) hydroxide. To do that, we can use the stoichiometry of the reaction between HCl and NaOH, which is a 1:1 reaction: \(0.175~mol - 0.02690~mol = 0.1481~mol\) Hence, there were 0.1481 moles of HCl remaining unreacted after the addition of iron(III) hydroxide.

Determine moles of iron(III) hydroxide contributed to reaction

Now, we can find the moles of iron(III) hydroxide that reacted with HCl before titration. This can be done as we know that the stoichiometry of the reaction between HCl and iron(III) hydroxide: \(Fe(OH)_3 + 3HCl \rightarrow FeCl_3 + 3H_2O\). For every mole of \(Fe(OH)_3\), three moles of HCl are reacted: \(moles_{Fe(OH)_3} = (0.175~mol - 0.1481~mol) / 3 = 0.00897~mol\)

Calculate the mass of iron(III) hydroxide added

Finally, we can find the mass of iron(III) hydroxide added to HCl. We know the molar mass of \(Fe(OH)_3\), which can be calculated as follows: \(Fe(OH)_3: 1(55.845) + 3(16 + 1.008) = 106.867~g/mol\) Using the moles of iron(III) hydroxide, we can find the total mass: \(mass_{Fe(OH)_3} = moles_{Fe(OH)_3} × molar~mass = 0.00897~mol × 106.867~g/mol = 0.958~g\) Therefore, the mass of iron(III) hydroxide added to the HCl solution is approximately \(0.958~g\).

Key concepts

Iron(III) Hydroxide

Iron(III) hydroxide, represented by the chemical formula \(Fe(OH)_3\), is a sparingly soluble compound often involved in reactions with acids. This compound forms from iron in its +3 oxidation state when combined with the hydroxide ion \((OH^- )\). Due to its low solubility in water, iron(III) hydroxide tends to form as a precipitate in aqueous solutions.

When iron(III) hydroxide is introduced to an acidic solution like hydrochloric acid \((HCl)\), it reacts to form iron(III) chloride \((FeCl_3)\) and water. This process helps illustrate the principle of acid-base reactions, where the base (iron(III) hydroxide) neutralizes the acid (HCl), forming a salt and water.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It is a powerful tool in chemistry that allows us to predict how much of each substance is needed or produced in a given reaction.

In this exercise, stoichiometry helps us determine the amount of iron(III) hydroxide that reacts with hydrochloric acid. The balanced chemical equation for this reaction is:
- \(Fe(OH)_3 + 3HCl \rightarrow FeCl_3 + 3H_2O\)
This equation tells us that three moles of \(HCl\) react with one mole of \(Fe(OH)_3\). Thus, if you know how many moles of \(HCl\) were initially present and how many were left unreacted, you can find out how many moles of \(Fe(OH)_3\) have reacted by considering this 1:3 mole ratio.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole \(g/mol\). Calculating the molar mass of a compound requires adding up the atomic masses of its constituent elements, multiplied by the number of times each atom appears in the molecular formula.

For iron(III) hydroxide \((Fe(OH)_3)\), we calculate the molar mass by summing the masses of one iron atom \(55.845~g/mol\), three oxygen atoms \(3 \times 16.000~g/mol\), and three hydrogen atoms \(3 \times 1.008~g/mol\), which results in a total molar mass of \(106.867~g/mol\). This calculation is crucial for converting moles of \(Fe(OH)_3\) into grams, enabling us to find the mass of iron(III) hydroxide added in the titration.

Chemical Reactions

Chemical reactions involve the reorganization of atoms to form new substances. In the context of this acid-base titration exercise, the chemical reaction of interest occurs between iron(III) hydroxide \((Fe(OH)_3)\) and hydrochloric acid \((HCl)\).

In this specific reaction, \(Fe(OH)_3\) reacts with \(HCl\) to produce iron(III) chloride \((FeCl_3)\) and water. Such an interaction is typical of neutralization reactions, where an acid and a base react to form a salt and water, showcasing the transformative nature of chemical reactions.

Understanding the stoichiometry, molar mass, and reactivity enables us to predict the products and quantities involved in the reaction, which in this case, includes determining how much iron(III) hydroxide was added to the hydrochloric acid.