Question

How many grams of cobalt(II) chloride are needed to react completely with \(60.0 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{KOH}\) solution? The net ionic equation for the reaction is $$ \mathrm{Co}^{2+}(a q)+2 \mathrm{OH}^{-}(a q) \longrightarrow \mathrm{Co}(\mathrm{OH})_{2}(s) $$

Short answer

0.7790 grams of CoCl2 are needed.

Step-by-step solution

Calculate the moles of KOH

To find out how many grams of cobalt(II) chloride are needed, first determine the moles of KOH. Use the volume and concentration of the KOH solution to calculate this. The number of moles can be found using the formula: moles = concentration (M) × volume (L). Given that we have 60.0 mL of 0.200 M KOH, first convert the volume from mL to L (60.0 mL = 0.0600 L). Then calculate the moles of KOH: (0.200 mol/L) × (0.0600 L) = 0.0120 mol.

Determine the moles of CoCl2 needed

According to the balanced net ionic equation, 1 mole of Co^2+ reacts with 2 moles of OH-. Therefore, the moles of CoCl2, which provides the Co^2+, are half the moles of OH- because of the 1:2 molar ratio. Since we have 0.0120 mol of OH-, the moles of CoCl2 needed are 0.0120 mol ÷ 2 = 0.0060 mol.

Calculate the mass of CoCl2

To find the mass of CoCl2 required, use its molar mass. The molar mass of CoCl2 (Co = 58.93 g/mol, Cl = 35.45 g/mol) is calculated to be: 58.93 g/mol + 2(35.45 g/mol) = 129.83 g/mol. Now, multiply the moles of CoCl2 by the molar mass to get the mass: 0.0060 mol × 129.83 g/mol = 0.7790 g. Therefore, 0.7790 grams of CoCl2 are needed.

Key concepts

Moles Calculation

Understanding moles calculation is crucial for solving stoichiometry problems involving chemical equations. A mole is a unit used in chemistry to express amounts of a chemical substance, and it is equivalent to Avogadro's number (\(6.022 \times 10^{23}\) particles). To calculate moles from volume and molarity, as in the provided exercise, you use the formula: \[ \text{moles} = \text{concentration (M)} \times \text{volume (L)} \] By converting milliliters to liters (since 1000 mL = 1 L) and applying this formula, students can find the amount of substance involved in a reaction. When dealing with solid substances, moles are calculated by dividing the mass of the substance by its molar mass. The molar mass is the sum of the atomic masses of all atoms in a molecule, measured in grams per mole (g/mol).

Molarity

Molarity, denoted as M, is a measure of the concentration of a solution, describing the amount of solute present in a given volume of solution. It is calculated as the number of moles of solute divided by the volume of the solution in liters. This concept is key when you are mixing solutions in chemistry to get the desired reaction or concentration.

The formula for molarity is given by: \[ \text{M} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \] In the context of our problem, the molarity of KOH is 0.200 M, which means there are 0.200 moles of KOH per liter of solution. Since stoichiometry requires precise measurements, understanding and using molarity allows students to accurately determine how much of each substance is used and created in chemical reactions.

Limiting Reactant

The limiting reactant concept is paramount in stoichiometry as it tells us which reactant will run out first, thus halting the reaction and determining the maximum amount of product that can be formed. It is the substance that is completely consumed in a chemical reaction.

To identify the limiting reactant, compare the mole ratio of the reactants used in the reaction to the mole ratio presented in the balanced chemical equation. The reactant that provides less than or exactly the required stoichiometric amount is the limiting reactant. In the exercise, once you calculate the moles of each reactant, you can compare them to the ratios in the net ionic equation and find which reactant will be exhausted first, guiding you to understand the progression of the reaction.

Net Ionic Equations

Net ionic equations represent the ions that participate directly in a chemical reaction, omitting the spectator ions which do not change during the process. These equations provide a simplified way to see the actual chemical changes taking place.

To write a net ionic equation:

• Begin with a balanced molecular equation.
• Dissociate all strong electrolytes into their ions.
• Identify and cancel out the spectator ions on both sides of the equation.
• What remains is the net ionic equation, which shows only the species that undergo a change.

The provided solution demonstrates this by showing the net ionic equation for the reaction between cobalt(II) ions and hydroxide ions to form solid cobalt(II) hydroxide. Understanding this concept allows students to focus on the reaction's essentials, making calculations more straightforward.