Question

Copper(II) chromate, \(\mathrm{CuCrO}_{4}(s),\) dissolves in water to give a solution containing \(1.1 \times 10^{-5} \mathrm{g}\) per liter at \(23^{\circ} \mathrm{C} .\) Calculate \(K_{\mathrm{sp}}\) for \(\mathrm{CuCrO}_{4}(s)\).

Short answer

The solubility product constant (Ksp) for Copper(II) chromate is approximately \(3.93 \times 10^{-18}\).

Step-by-step solution

Convert grams per liter to moles per liter

First, we need to find the molar mass of Copper(II) chromate, \(\mathrm{CuCrO}_{4}(s)\). Use the periodic table to find the atomic masses of each element: Cu: 63.55 g/mol Cr: 52.00 g/mol O: 16.00 g/mol The molar mass of Copper(II) chromate is: Molar mass = 63.55 + 52.00 + (4 × 16.00) = 175.55 g/mol Now, convert the given solubility (in grams per liter) to moles per liter: Solubility (in moles per liter) = \(\frac{1.1 × 10^{-5}\,\text{g/L}}{175.55\,\text{g/mol}}\)

Write the balanced equilibrium equation and Ksp expression

Next, write the balanced equilibrium equation for the dissolution of Copper(II) chromate in water: \(\text{CuCrO}_{4}(s) \rightleftarrows \text{Cu}^{2+}(aq) + \text{CrO}_{4}^{2-}(aq)\) Now, write the Ksp expression for the equilibrium: Ksp = [Cu²⁺][CrO₄²⁻]

Substitute the molar solubility values and solve for Ksp

From step 1, the solubility of Copper(II) chromate in moles per liter is: Solubility (in moles per liter) = \(\frac{1.1 × 10^{-5}\,\text{g/L}}{175.55\,\text{g/mol}}\) Since there is 1 mole of Copper(II) ions and 1 mole of Chromate ions produced for each mole of Copper(II) chromate dissolved, the molar solubility of Cu²⁺ and CrO₄²⁻ are equal. Therefore, [Cu²⁺] = [CrO₄²⁻] = \(\frac{1.1 × 10^{-5}\,\text{g/L}}{175.55\,\text{g/mol}}\) Now substitute these values into the Ksp expression: Ksp = \(\left(\frac{1.1 × 10^{-5}\,\text{g/L}}{175.55\,\text{g/mol}}\right)^2\) Ksp = \(3.93 \times 10^{-18}\) The solubility product constant (Ksp) for Copper(II) chromate is approximately \(3.93 \times 10^{-18}\).

Key concepts

Molar Mass Calculation

In chemistry, calculating the molar mass is a fundamental step when dealing with reactions and solutions. The molar mass of a compound is the sum of the atomic masses of all the atoms present in a molecule. Take Copper(II) chromate, \(\text{CuCrO}_4\), as an example.

• First, identify the atomic masses using the periodic table:
  • Copper (Cu) has an atomic mass of approximately 63.55 g/mol.
  • Chromium (Cr) has an atomic mass of approximately 52.00 g/mol.
  • Oxygen (O), which appears four times in the formula, has an atomic mass of 16.00 g/mol.

By adding these together, you obtain the molar mass: \[63.55 + 52.00 + (4 \times 16.00) = 175.55 \text{ g/mol}\]
This value is crucial for converting between mass and moles, which is often a necessary step in quantifying the concentration of solutions.

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction reaches a state where the concentrations of reactants and products do not change over time. In equilibrium, the forward and backward reactions happen at the same rate.

• This concept is crucial in solutions where a solid is dissolving.
• The equilibrium expression can be written for the dissolution of Copper(II) chromate:\[\text{CuCrO}_4\,(s) \rightleftharpoons \text{Cu}^{2+}\,(aq) + \text{CrO}_4^{2-}\,(aq)\]

The equilibrium constant for this particular process, called the solubility product \(K_{sp}\), quantifies the extent of the solubility of the compound in the solution. It provides a way to predict the concentration of ions in a saturated solution.
Understanding equilibrium is important for predicting how changes in conditions (like temperature or concentration) could shift the balance of a reaction.

Dissolution Reaction

Dissolution is a type of reaction where a solute dissolves in a solvent, forming a solution. In the context of Copper(II) chromate, the dissolution process can be described by a specific chemical equation. Copper(II) chromate, when added to water, dissociates into its constituent ions:

• Solid Copper(II) chromate \(\text{CuCrO}_4\)
• Dissolves to release copper ions \(\text{Cu}^{2+}\)
• And chromate ions \(\text{CrO}_4^{2-}\).

The dissolution reaction represents an important step towards understanding the solubility and ionic form of compounds in a solvent. It is also critical for identifying how much of a compound can dissolve or how a change in conditions might affect the process.

Molar Solubility

Molar solubility is the number of moles of a solute that can dissolve in a liter of solution to form a saturated solution. Calculating molar solubility offers insight into the maximum amount of solute that can dissolve under specific conditions.

• For Copper(II) chromate, knowing the molar mass allowed us to convert its given solubility from grams per liter to moles per liter.

The calculation: \[\text{Molar Solubility} = \frac{1.1 \times 10^{-5}\,\text{g/L}}{175.55\,\text{g/mol}}\]
This conversion is essential since the solubility product \(K_{sp}\) expression requires concentrations in terms of molarity.
Understanding molar solubility can aid in predicting how different compounds will behave in solution, which is critical for many applications in chemical engineering, environmental science, and pharmaceuticals.

Chromate Compounds

Chromate compounds, such as \(\text{CuCrO}_4\), are salts containing the chromate ion \(\text{CrO}_4^{2-}\). These ions have significant industrial and chemical importance:

• Chromate ions are known for their vivid colors, often yellow, which make them useful as pigments.
• They also have applications in electroplating, printing, and as fungicides.

However, it's important to note that chromates can be toxic, and thus, handling and disposal need to be managed with care.
Understanding the chemistry of chromates, their solubility, and their reactivity is essential for safe and effective use in industries and laboratories.