Question

What is the molarity of an aqueous solution of potassium hydroxide if \(21.34 \mathrm{~mL}\) is exactly neutralized by \(20.78 \mathrm{~mL}\) of \(0.116 M \mathrm{HCl}\) ? Write and balance the molecular equation for the reaction.

Short answer

The molarity of the aqueous KOH solution is approximately 0.1129 M.

Step-by-step solution

Write the Balanced Chemical Equation

The reaction between potassium hydroxide (KOH) and hydrochloric acid (HCl) can be represented by the balanced chemical equation: \[ \text{KOH} + \text{HCl} \rightarrow \text{KCl} + \text{H}_2\text{O} \]This equation shows that KOH reacts with HCl in a 1:1 molar ratio.

Calculate the Moles of HCl Used

First, calculate the amount of HCl used in moles using its volume and molarity: \[ \text{moles HCl} = \text{molarity of HCl} \times \text{volume of HCl in liters} \]\[ \text{moles HCl} = 0.116 \text{ M} \times 20.78\times10^{-3} \text{ L} \]\[ \text{moles HCl} = 0.002410 \text{ moles} \] (rounded to three significant figures).

Determine the Moles of KOH Neutralized

Since the reaction between KOH and HCl proceeds in a 1:1 molar ratio, the moles of KOH will also be: \[ \text{moles KOH} = \text{moles HCl} = 0.002410 \text{ moles} \]

Calculate the Molarity of the KOH Solution

Now, calculate the molarity of the KOH solution using the moles of KOH and its volume in liters: \[ \text{Molarity of KOH} = \frac{\text{moles of KOH}}{\text{volume of KOH in liters}} \]\[ \text{Molarity of KOH} = \frac{0.002410 \text{ moles}}{21.34\times10^{-3} \text{ L}} \]\[ \text{Molarity of KOH} \rightarrow \text{Calculate for final value} \]

Calculate the Final Answer

Finishing the calculation, the molarity of the KOH solution can be found: \[ \text{Molarity of KOH} = \frac{0.002410 \text{ moles}}{21.34 \times 10^{-3} \text{ L}} \]\[ \text{Molarity of KOH} \text{ \text{}} \text{ \text{}} \text{ =0.1129 M} \] (rounded to three significant figures).

Key concepts

Chemical Equation Balancing

Understanding how to balance a chemical equation is crucial when working with chemical reactions. A balanced equation reflects the law of conservation of mass—matter cannot be created or destroyed during a chemical reaction. In the given exercise, we have the chemical reaction between potassium hydroxide (KOH) and hydrochloric acid (HCl) producing potassium chloride (KCl) and water (H₂O).

The equation before balancing looks like this: KOH + HCl → KCl + H₂O. Each side of the arrow must have the same number of atoms for each element. For this equation, the potassium (K), the chlorine (Cl), and the oxygen (O) are already balanced, with one atom of each present on both sides. Hydrogen (H), however, appears as one atom in HCl and two atoms in H₂O, but this is not cause for concern since we have hydrogen in KOH as well. We see that KOH and HCl react in a 1:1 ratio, maintaining balance. Thus, the reaction is balanced as written. Mastering this skill allows you to predict the proportions in which chemicals will react, which is a linchpin of stoichiometry.

Stoichiometry

Stoichiometry lies at the heart of the chemistry involved in calculating reactants and products in a chemical reaction. It involves using the balanced chemical equation to determine the relationship between the quantities of reactants and products. In our exercise, the reaction follows a 1:1 molar ratio between KOH and HCl. This means that one mole of KOH reacts with one mole of HCl to produce the products.

By knowing the volume and molarity of one reactant (HCl, in this case), we can calculate the moles of that reactant and , due to the fixed ratio, instantly know the moles of the other (KOH). For example, if we have 0.002410 moles of HCl, we must also have 0.002410 moles of KOH if the reaction goes to completion. Understanding stoichiometry is essential for this type of molarity calculation , which enables practitioners to figure out the composition of an unknown solution, like in the case of the KOH solution in the problem.

Aqueous Solution Concentration

Molarity is a way of expressing the concentration of a solution. It is defined as the number of moles of a solute divided by the volume of the solvent in liters. The exercise requires us to calculate the molarity of an aqueous KOH solution. Knowing the molarity is vital for predicting how substances will react in solution because it measures the active number of particles available to react.

After calculating the moles of KOH involved in the reaction (which we found to be equal to the moles of HCl), we simply need to divide this number by the volume of the KOH solution —in liters—to obtain the molarity. For instance, with 0.002410 moles of KOH and a volume of 21.34 mL (which we convert to 0.02134 L for the formula), we find that the molarity is approximately 0.1129 Manning, meaning there are 0.1129 moles of KOH in every liter of solution. This calculation is essential in many areas of chemistry and industry, like medication dosing and chemical manufacturing.