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?

Short answer

Molarity of \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) is 0.01588 M; \([\mathrm{K}^{+}]\) is 0.03176 M; \([\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}]\) is 0.01588 M.

Step-by-step solution

Determine the molar mass of potassium dichromate

To find the molar concentration, we first need the molar mass of potassium dichromate \(\left(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\right)\). The molar masses of \(\mathrm{K}\), \(\mathrm{Cr}\), and \(\mathrm{O}\) are approximately 39.1, 52, and 16 g/mol respectively. Hence, the molar mass is calculated as: \[2(39.1) + 2(52) + 7(16) = 294.2 \, \text{g/mol}.\]

Calculate moles of potassium dichromate

To determine the moles of \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\), use the formula: \[\text{moles} = \frac{\text{mass}}{\text{molar mass}}.\] Plugging in the values: \[\text{moles} = \frac{2.335 \, \text{g}}{294.2 \, \text{g/mol}} \approx 0.00794 \, \text{mol}.\]

Calculate molar concentration of potassium dichromate

To find the molar concentration, use the equation: \[\text{Concentration} = \frac{\text{moles}}{\text{volume in L}}.\] Convert 500 mL to liters: \[0.500 \, \text{L}.\] Therefore, \[\text{Concentration} = \frac{0.00794}{0.500} = 0.01588 \, \text{mol/L}.\]

Determine ions in the solution

Potassium dichromate \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) dissociates into 2 \(\mathrm{K}^{+}\) ions and 1 \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) ion per formula unit. This means every mole of \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) produces 2 moles of \(\mathrm{K}^{+}\) and 1 mole of \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\).

Calculate molar concentrations of ions

Since the molar concentration of \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) is 0.01588 mol/L, the concentration of \(\mathrm{K}^{+}\) is \(2 \times 0.01588 = 0.03176 \, \text{mol/L}\) and for \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) it is 0.01588 mol/L, because it produces one mole of \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) per mole of compound.

Key concepts

Potassium Dichromate

Potassium dichromate, known chemically as \( \text{K}_2\text{Cr}_2\text{O}_7 \), is a bright orange crystalline compound used in various applications such as a cleaning agent and an oxidizing agent in laboratories. It consists of two potassium (\( \text{K} \)) atoms, two chromium (\( \text{Cr} \)) atoms, and seven oxygen (\( \text{O} \)) atoms.

This compound is insoluble in water but can dissolve to form a vivid solution that contains potassium ions (\( \text{K}^+ \)) and dichromate ions (\( \text{Cr}_2\text{O}_7^{2-} \)). The bright color of potassium dichromate solutions is characteristic of the dichromate ions. This visibility is useful for indicating the presence of the compound when conducting experiments or chemical reactions.

Potassium dichromate is an important example for teaching and understanding molar concentration, as it visibly dissociates into ions when dissolved.

Dissociation of Compounds

Dissociation is a key concept in chemistry that describes the process where ionic compounds separate into their individual ions when dissolved in a solvent, like water. This concept is crucial for understanding how substances behave in solutions and their respective molarities.

When potassium dichromate \( \text{K}_2\text{Cr}_2\text{O}_7 \) dissolves in water, it dissociates into two \( \text{K}^+ \) ions and one \( \text{Cr}_2\text{O}_7^{2-} \) ion per molecule. Here's how it happens:

• The potassium ions (\( \text{K}^+ \)) are individually surrounded by water molecules, creating a conservation of charge balance.
• The dichromate ion (\( \text{Cr}_2\text{O}_7^{2-} \)), which gives the solution its orange color, is also surrounded by water molecules.

Each ion is separated and independent in the solution, allowing for the distinctive interaction observable in aqueous solutions, such as electrical conductivity. This dissociation allows potassium dichromate to participate in chemical reactions in its ionized form, making it a versatile chemical reagent.

Molar Mass Calculation

To determine the molar concentration of a solution, it's essential to know the molar mass of the compound in question. Molar mass is the mass of one mole of a given substance and is expressed in grams per mole (g/mol). Calculating molar mass allows us to convert between the weight of a substance and the moles of that substance.

For potassium dichromate, the molar mass is calculated by summing the atomic masses of all the atoms present in the molecule:

• Potassium (\( \text{K} \)) has an atomic mass of approximately 39.1 g/mol. Since there are two potassium atoms, this contributes \( 2 \times 39.1 = 78.2 \) g/mol.
• Chromium (\( \text{Cr} \)) has an atomic mass of about 52 g/mol. With two chromium atoms present, this contributes \( 2 \times 52 = 104 \) g/mol.
• Oxygen (\( \text{O} \)) has an atomic mass of 16 g/mol. With seven oxygen atoms, this adds up to \( 7 \times 16 = 112 \) g/mol.

Adding these allows us to find that the total molar mass of potassium dichromate is \( 294.2 \) g/mol. This value is crucial for calculating the number of moles in a sample when we know its mass, helping us determine the molar concentration of the solution.