Question

A mixture contains only \(\mathrm{NaCl}\) and \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3} .\) A \(0.456-\mathrm{g}\) sample of the mixture is dissolved in water, and an excess of \(\mathrm{NaOH}\) is added. producing a precipitate of \(\mathrm{Fe}(\mathrm{OH})_{3} .\) The precipitate is filtered. dried, and weighed. Its mass is \(0.107 \mathrm{~g}\). Calculate the following. a. the mass of iron in the sample b. the mass of \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\) in the sample c. the mass percent of \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\) in the sample.,

Short answer

a. Mass of Iron in the sample can be calculated as: Moles of Fe(OH)₃ = \(\frac{0.107 g}{106.87 \frac{g}{mol}} = 0.001 \: mol\) Mass of Iron = Moles of Iron × molar mass of Iron = \(0.001 \: mol \times 55.85 \frac{g}{mol} = 0.05585 g\) b. Mass of Fe(NO₃)₃ in the sample: Mass of Fe(NO₃)₃ = Moles of Iron × Molar mass of Fe(NO₃)₃ = \(0.001 \: mol \times 241.85 \frac{g}{mol} = 0.24185 g\) c. Mass percent of Fe(NO₃)₃ in the sample: Mass percent of Fe(NO₃)₃ = \(\frac{0.24185 g}{0.456\:g}\) × 100 = 53.04%

Step-by-step solution

Find the moles of Fe(OH)₃ precipitate

Firstly, we need to find the moles of Fe(OH)₃ precipitate. We can do this by dividing the given mass of Fe(OH)₃ by the molar mass of Fe(OH)₃. The molar mass of Fe(OH)₃ is: \(1\times(55.85 \frac{g}{mol})+3\times(15.999 \frac{g}{mol}+1.007 \frac{g}{mol}) = 106.87 \frac{g}{mol}\). Calculate the moles of Fe(OH)₃ precipitate: Moles of Fe(OH)₃ = \(\frac{0.107 g}{106.87 \frac{g}{mol}}\)

Find the moles of Iron in the sample

Since there is one mole of Iron in each mole of Fe(OH)₃, the moles of Fe(OH)₃ precipitate are equal to the moles of Iron in the sample. Moles of Iron = Moles of Fe(OH)₃

Calculate the mass of Iron in the sample

Now that we have the moles of Iron, we can find the mass of Iron in the sample by multiplying the moles of Iron by the molar mass of Iron. The molar mass of Iron is 55.85 g/mol. Mass of Iron = Moles of Iron × molar mass of Iron

Calculate the mass of Fe(NO₃)₃ in the sample

Knowing that the mass of Iron found is from Fe(NO₃)₃, we can calculate the mass of Fe(NO₃)₃ in the sample by using stoichiometry. Calculate the molar mass of Fe(NO₃)₃: \(1 \times (55.85 \frac{g}{mol}) + 3 \times (14.0067 \frac{g}{mol} + 3 \times (15.999 \frac{g}{mol}) = 241.85 \frac{g}{mol}\). Mass of Fe(NO₃)₃ = Moles of Iron × Molar mass of Fe(NO₃)₃

Calculate the mass percent of Fe(NO₃)₃ in the sample

Finally, we can calculate the mass percent of Fe(NO₃)₃ in the sample by dividing the mass of Fe(NO₃)₃ by the total mass of the sample (0.456 g) and then multiplying by 100. Mass percent of Fe(NO₃)₃ = \(\frac{Mass\:of\:Fe(NO_{3})_{3}}{0.456\:g}\) × 100 Following these steps, we can calculate the mass of Iron, the mass of Fe(NO₃)₃, and the mass percent of Fe(NO₃)₃ in the sample.

Key concepts

Precipitate Formation

When we mix chemical solutions, a solid can form, called a precipitate. This happens when ions in the solutions combine to make an insoluble compound, which separates from the liquid. In this exercise, an excess of sodium hydroxide (NaOH) was added to a solution containing iron(III) nitrate and sodium chloride. The reaction between the iron(III) ions and hydroxide ions produces iron(III) hydroxide, written as \( \mathrm{Fe(OH)}_3 \). This is the precipitate that forms, and it can be filtered out of the solution. The mass of the precipitate is crucial for further calculations, as it provides a way to determine the amount of iron present in the original sample. Understanding the role of precipitates helps in separating and identifying substances in mixtures.

Molar Mass Calculation

Molar mass is a critical concept in chemistry, used to convert between grams and moles of a substance. It is the mass of one mole of a given substance, composed of the atomic masses of its constituent elements. It's typically expressed in grams per mole (g/mol). Let's look at iron(III) hydroxide, \( \mathrm{Fe(OH)}_3 \). To find its molar mass, you need to add up the masses of its elements. Iron (Fe) has a molar mass of approximately 55.85 g/mol. Oxygen (O) is about 15.999 g/mol, and hydrogen (H) is roughly 1.007 g/mol. Since \( \mathrm{Fe(OH)}_3 \) contains one Fe, three O, and three H atoms, you can calculate the molar mass as:**Molar mass of \( \mathrm{Fe(OH)}_3 \)** \[1 \times 55.85 + 3 \times (15.999 + 1.007) = 106.87 \, \text{g/mol}.\] This molar mass lets you convert the mass of \( \mathrm{Fe(OH)}_3 \) precipitate into moles, which is essential for stoichiometric calculations.

Mass Percent

Mass percent measures the concentration of a component in a mixture. It tells you the proportion of a particular substance relative to the total mass of the mixture, usually given as a percentage by mass. Calculating the mass percent involves dividing the mass of the component by the total mass, then multiplying by 100. In this example, we find the mass percent of iron(III) nitrate, \( \mathrm{Fe(NO}_3)_3 \), in a sample. First, you calculate the mass of \( \mathrm{Fe(NO}_3)_3 \) using the mass of the iron measured from the precipitate. Then, the mass percent is:**Mass percent formula** \[\frac{\text{mass of } \mathrm{Fe(NO}_3)_3}{\text{total mass of the sample}} \times 100.\] Knowing the mass percent helps in understanding the composition of mixtures and is a common method for expressing concentration in chemistry.