Problem 42 - 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 \(\mathbf{K}^{+}\) and \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) ions?

Step-by-Step Solution

Answer

The molarity of potassium dichromate is 0.015874 M. Molarity of \( \mathbf{K}^+ \) is 0.031748 M, and \( \mathrm{Cr}_2 \mathrm{O}_7^{2-} \) is 0.015874 M.

Step 1: Calculate Moles of Potassium Dichromate

First, determine the molar mass of potassium dichromate, \( \mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7 \). The molar masses are approx:- \( \mathrm{K} = 39.10 \text{ g/mol} \)- \( \mathrm{Cr} = 51.996 \text{ g/mol} \)- \( \mathrm{O} = 16.00 \text{ g/mol} \)The molar mass of \( \mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7 \) is:\[ 2(39.10) + 2(51.996) + 7(16.00) = 294.18 \text{ g/mol} \]Next, calculate the moles of the substance:\[ \text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}} = \frac{2.335}{294.18} \approx 0.007937 \text{ mol} \]

Step 2: Calculate Molarity of Potassium Dichromate

Molarity is calculated as the moles of solute divided by the volume of solution in liters.Convert 500 mL to liters:\[ 500 \text{ mL} = 0.500 \text{ L} \]Now, calculate the molarity:\[ \text{Molarity of } \mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7 = \frac{0.007937 \text{ mol}}{0.500 \text{ L}} = 0.015874 \text{ M} \]

Step 3: Calculate Molarity of Potassium Ions \( \mathbf{K}^+ \)

Each formula unit of \( \mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7 \) dissociates to form 2 potassium ions \( \mathbf{K}^+ \).Thus, the molarity of \( \mathbf{K}^+ \) ions is:\[ \text{Molarity of } \mathbf{K}^+ = 2 \times 0.015874 \text{ M} = 0.031748 \text{ M} \]

Step 4: Calculate Molarity of Dichromate Ions \( \mathrm{Cr}_2 \mathrm{O}_7^{2-} \)

Each formula unit of \( \mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7 \) forms one dichromate ion \( \mathrm{Cr}_2 \mathrm{O}_7^{2-} \).Therefore, the molarity remains the same as that of the original compound:\[ \text{Molarity of } \mathrm{Cr}_2 \mathrm{O}_7^{2-} = 0.015874 \text{ M} \]

Key Concepts

Potassium Dichromate

Potassium dichromate, represented by the chemical formula \( \mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7 \), is a bright orange-red crystalline compound used in various applications, including in laboratories as an oxidizing agent.
It is composed of potassium (\( \mathrm{K} \)), chromium (\( \mathrm{Cr} \)), and oxygen (\( \mathrm{O} \)) elements in the ratios that ensure each formula unit contains two potassium ions and one dichromate ion (\( \mathrm{Cr}_2 \mathrm{O}_7^{2-} \)).
When dissolved in water, it dissociates to form these ions, which can have various interactions in solution chemistry.

Ion Concentration

Understanding ion concentration is crucial when dealing with solutions like potassium dichromate. Ion concentration refers to the amount of a particular ion in a solution and is typically expressed in molarity (M), which is moles per liter.
For every formula unit of potassium dichromate dissolved, the solution contains ion concentrations of two \( \mathrm{K}^+ \) ions and one \( \mathrm{Cr}_2 \mathrm{O}_7^{2-} \) ion.
To find the concentration of each ion, we consider the dissociation process and the initial concentration of the compound. Here, the potassium ion concentration is double that of the dichromate ion due to the stoichiometry of the compound.

Molar Mass

The molar mass of a substance plays a pivotal role in chemistry to relate the mass of a substance to the amount in moles. To find it, sum the atomic masses of all atoms in the compound's formula.
For potassium dichromate (\( \mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7 \)), calculate as follows:

• Two potassium (\( \mathrm{K} \)): \( 2 \times 39.10 = 78.20 \text{ g/mol} \)
• Two chromium (\( \mathrm{Cr} \)): \( 2 \times 51.996 = 103.992 \text{ g/mol} \)
• Seven oxygen (\( \mathrm{O} \)): \( 7 \times 16.00 = 112.00 \text{ g/mol} \)

Making the molar mass total \( 294.18 \text{ g/mol} \).
This information helps convert the mass of potassium dichromate into moles, vital for calculating concentrations.

Solution Chemistry

Solution chemistry explores how substances dissolve, interact, and react in solvents like water, forming homogeneous mixtures or solutions.
When potassium dichromate dissolves in water, it separates into \( \mathrm{K}^+ \) and \( \mathrm{Cr}_2 \mathrm{O}_7^{2-} \) ions.
This dissolution process results in a uniform mixture, allowing for consistent reactions and activities throughout the solution.
Solution chemistry principles, like molarity, guide the quantification of dissolved substances, aiding in predicting reactions, creating buffers, and understanding dynamic chemical environments.