Problem 40 - Chemistry and Chemical Reactivity

Question

Some potassium dichromate \(\left(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\right), 2.335 \mathrm{g}\) is dissolved in enough water to make exactly \(500 .\) mL of solution. What is the molar concentration of the potassium dichromate? What are the molar concentrations of the \(\mathrm{K}^{+}\) and \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) ions?

Step-by-Step Solution

Answer

The molar concentration of K2Cr2O7 is 0.015872 M, K+ is 0.031744 M, and Cr2O7^2- is 0.015872 M.

Step 1: Calculate the Moles of Potassium Dichromate

First, determine the molar mass of \(\mathrm{K}_{2} \mathrm{Cr}_{2}\mathrm{O}_{7}\). The atomic masses are approximately \(\mathrm{K}: 39.1\, \mathrm{g/mol}\), \(\mathrm{Cr}: 51.9961\, \mathrm{g/mol}\), and \(\mathrm{O}: 16.00\, \mathrm{g/mol}\). Therefore, the molar mass is: \[2 (39.1) + 2 (51.9961) + 7 (16.00) = 294.18\, \mathrm{g/mol}\] Next, use the mass of the compound to find the moles: \[\text{Moles of } \mathrm{K}_2\mathrm{Cr}_2\mathrm{O}_7 = \frac{2.335\, \mathrm{g}}{294.18\, \mathrm{g/mol}} = 0.007936\, \text{mol}\]

Step 2: Calculate Molar Concentration of Potassium Dichromate

The molar concentration is calculated by dividing the number of moles by the volume of the solution in liters: \[\text{Molar concentration of } \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} = \frac{0.007936\, \text{mol}}{0.500\, \text{L}} = 0.015872\, \text{M}\]

Step 3: Determine Molar Concentration of Ions

Potassium dichromate dissociates in water as follows: \[\mathrm{K}_2\mathrm{Cr}_2\mathrm{O}_7 \rightarrow 2 \mathrm{K}^+ + \mathrm{Cr}_2\mathrm{O}_7^{2-}\]Thus, each mole of \(\mathrm{K}_2\mathrm{Cr}_2\mathrm{O}_7\) produces 2 moles of \(\mathrm{K}^+\) ions and 1 mole of \(\mathrm{Cr}_2\mathrm{O}_7^{2-}\) ions. Using this relationship:- The molar concentration of \(\mathrm{K}^+\) is \(2 \times 0.015872\, \text{M} = 0.031744\, \text{M}\).- The molar concentration of \(\mathrm{Cr}_2\mathrm{O}_7^{2-}\) is \(0.015872\, \text{M}\).

Key Concepts

Potassium Dichromate

Potassium dichromate, with the chemical formula \(\mathrm{K}_2\mathrm{Cr}_2\mathrm{O}_7\), is a common laboratory reagent that appears as an orange crystalline solid. It is an inorganic salt composed of two potassium ions attached to a dichromate ion. This compound is widely used in analytical chemistry due to its strong oxidizing properties. It can affect various reactions by facilitating the transfer of electrons, which makes it valuable for identifying chemical changes.

When dissolved in water, potassium dichromate forms a brightly colored solution, enabling easy visualization for experiments. Due to its toxicity and strong oxidative characteristics, exercising care and proper safety measures when handling it is crucial.

• The color change of its solutions can be utilized in volumetric analysis.
• Potassium dichromate can also be used in photographic processes and as a cleaning agent for laboratory glassware.

Ion Dissociation

When potassium dichromate dissolves in water, it separates into ions in a process known as ion dissociation. During this transformation, each mole of \(\mathrm{K}_2\mathrm{Cr}_2\mathrm{O}_7\) dissociates to yield two moles of potassium ions \((\mathrm{K}^+)\) and one mole of dichromate ions \((\mathrm{Cr}_2\mathrm{O}_7^{2-})\). Understanding this dissociation is essential for calculating the resulting ion concentrations in a solution.

This phenomenon occurs because the ionic bonds between the ions in the solid break, allowing them to move freely in the aqueous solution. As a result, the ions become solvated, meaning that water molecules surround each ion.

• Ion dissociation contributes to the conductivity of a solution, as free ions allow electric current to flow.
• The extent of ion dissociation can be influenced by factors such as temperature and the nature of the solvent.

Molar Mass Calculation

Calculating the molar mass of a compound is a fundamental step in any stoichiometric calculation involving solutions. It involves summing the atomic masses of all the atoms in a molecule. For potassium dichromate, the molar mass is determined by adding up the atomic masses of its elements: 2 potassium (\(\mathrm{K}\)), 2 chromium (\(\mathrm{Cr}\)), and 7 oxygen (\(\mathrm{O}\)) atoms. The approximate atomic masses are:

• Potassium \(\rightarrow 39.1\, \mathrm{g/mol}\)
• Chromium \(\rightarrow 51.9961\, \mathrm{g/mol}\)
• Oxygen \(\rightarrow 16.00\, \mathrm{g/mol}\)

Thus, the molar mass of \(\mathrm{K}_2\mathrm{Cr}_2\mathrm{O}_7\) is: \[2(39.1) + 2(51.9961) + 7(16.00) = 294.18\, \mathrm{g/mol}\] This calculation allows you to convert from grams of potassium dichromate to moles, which is crucial for determining concentrations in solution. Knowing the accurate molar mass aids in rigorous chemical analysis and ensures precise measurement in experimental setups.