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Chapter 12: Problem 196

A student dilutes \(75.0 \mathrm{~mL}\) of a \(2.00 \mathrm{M}\) solution of iron(III) nitrate with sufficient water to prepare \(2.00 \mathrm{~L}\) of solution. (a) What is the molar concentration of iron(III) nitrate in the diluted solution? Once in solution, the iron(III) nitrate exists not intact but rather as dissociated ions. What are the molar concentrations (b) of \(\mathrm{Fe}^{3+}(a q)\) in the diluted solution and (c) of \(\mathrm{NO}^{3-}(a q)\) in the diluted solution?

Short Answer

Expert verified
The molar concentrations in the diluted solution are: (a) Iron(III) nitrate: 0.075 M, (b) Fe鲁鈦�: 0.075 M, and (c) NO鈧冣伝: 0.225 M.

Step by step solution

01

Use the dilution formula to find the molar concentration of the diluted solution.

The dilution formula is given by: \[ M_1V_1 = M_2V_2 \] Where: - \(M_1\) is the initial concentration of the solution. - \(V_1\) is the initial volume of the solution. - \(M_2\) is the final concentration of the solution after dilution. - \(V_2\) is the final volume of the solution after dilution. Given that the initial concentration is 2.00 M and the initial volume is 75.0 mL, we can plug these values into the dilution formula, keeping in mind that the final volume is 2.00 L. We want to find \(M_2\), the molar concentration of iron(III) nitrate after dilution, so let's rearrange the equation: \[ M_2 = \frac{M_1V_1}{V_2} \] Then plug in the known values and solve for \(M_2\).
02

Calculate the molar concentration of iron(III) nitrate after dilution.

Substituting the values: \[ M_2 = \frac{(2.00 \mathrm{~M})(75.0 \mathrm{~mL})}{2.00 \mathrm{~L}} \] Convert 75.0 mL to L: \[ 75.0 \mathrm{~mL} \times \frac{1 \mathrm{~L}}{1000 \mathrm{~mL}} = 0.075 \mathrm{~L} \] Now, calculate \(M_2\): \[ M_2 = \frac{(2.00 \mathrm{~M})(0.075 \mathrm{~L})}{2.00 \mathrm{~L}} = 0.075 \mathrm{~M} \] The molar concentration of iron(III) nitrate in the diluted solution is 0.075 M.
03

Write the dissociation equation for iron(III) nitrate in water.

To find the molar concentrations of Fe鲁鈦� and NO鈧冣伝, we must first understand how iron(III) nitrate dissociates in water: \[ \mathrm{Fe(NO_3)_3} (aq) \rightarrow \mathrm{Fe^{3+}}(aq) + 3\mathrm{NO_3^-}(aq) \] From the stoichiometry of the equation, for every 1 mole of iron(III) nitrate that dissociates, 1 mole of Fe鲁鈦� and 3 moles of NO鈧冣伝 are produced.
04

Calculate the molar concentration of Fe鲁鈦� in the diluted solution.

Since the dissociation produces 1 mole of Fe鲁鈦� for every 1 mole of iron(III) nitrate, the molar concentration of Fe鲁鈦� in the diluted solution is equal to the molar concentration of iron(III) nitrate: \[ [\mathrm{Fe^{3+}}] = 0.075 \mathrm{~M} \]
05

Calculate the molar concentration of NO鈧冣伝 in the diluted solution.

Since the dissociation produces 3 moles of NO鈧冣伝 for every 1 mole of iron(III) nitrate, the molar concentration of NO鈧冣伝 in the diluted solution is three times the molar concentration of iron(III) nitrate: \[ [\mathrm{NO_3^-}] = 3 \times 0.075 \mathrm{~M} = 0.225 \mathrm{~M} \] So, the molar concentrations in the diluted solution are: a) Iron(III) nitrate: 0.075 M b) Fe鲁鈦�: 0.075 M c) NO鈧冣伝: 0.225 M

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Key Concepts

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

Molar Concentration
Molar concentration, often referred to as molarity, measures the concentration of a substance in a solution. It is defined as the number of moles of a solute per liter of solution. The formula is given by:
  • \( M = \frac{n}{V} \)
Where:
  • \( M \) is the molarity in moles per liter (M).
  • \( n \) is the number of moles of solute.
  • \( V \) is the volume of the solution in liters.

To determine the molarity of a diluted solution, we use the dilution formula:
  • \( M_1V_1 = M_2V_2 \)
Here, \( M_1 \) and \( V_1 \) are the initial concentration and volume, and \( M_2 \) and \( V_2 \) are the final concentration and volume, respectively.
In our exercise, iron(III) nitrate's initial molarity is 2.00 M, and its initial volume is converted to 0.075 L. After dilution to 2.00 L, we calculate the final molarity as 0.075 M.
Dissociation Equation
A dissociation equation represents how a compound separates into its ions in an aqueous solution. Understanding this process is key to calculating the concentrations of individual ions.
For iron(III) nitrate, the dissociation equation in water is:
  • \( \mathrm{Fe(NO_3)_3} (aq) \rightarrow \mathrm{Fe^{3+}}(aq) + 3\mathrm{NO_3^-}(aq) \)
This equation shows that one mole of iron(III) nitrate produces one mole of \( \mathrm{Fe^{3+}} \) and three moles of \( \mathrm{NO_3^-} \).
By interpreting this reaction, we can deduce that the molarity of \( \mathrm{Fe^{3+}} \) ions will be equal to the molarity of the original iron(III) nitrate solution, while the \( \mathrm{NO_3^-} \) ions will be three times more concentrated.
Ions in Solution
In a solution, compounds like salts disassociate into their respective ions. Knowing how ions behave and interact in a solution is fundamental to chemistry.
For iron(III) nitrate, once it is dissolved, it separates into individual \( \mathrm{Fe^{3+}} \) and \( \mathrm{NO_3^-} \) ions.
After calculating the molar concentration of the diluted solution:
  • The concentration of \( \mathrm{Fe^{3+}} \) ions is the same as the dissolved iron(III) nitrate, which is 0.075 M.
  • The concentration of \( \mathrm{NO_3^-} \) ions is three times that of \( \mathrm{Fe^{3+}} \), resulting in 0.225 M.
Understanding these ion concentrations helps predict how solutions will react chemically and physically, which is crucial for experiments and industrial applications.

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Most popular questions from this chapter

The dissolving of a solute into a solvent can be thought of as a three-step process. The drinking alcohol, ethanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2}-\mathrm{OH}\right)\), is infinitely soluble in water. However, another alcohol called pentanol, with the molecular formula \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2}-\mathrm{OH}\), is nearly insoluble in water. (a) Which of the three steps in the solubility model is most responsible for this difference in solubility? Describe the step you choose (specify its name). (b) Give a BRIEF explanation for your choice.

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