Question

What volume of a \(0.500 \mathrm{M} \mathrm{HCl}\) solution is needed to neutralize each of the following: a) \(10.0 \mathrm{~mL}\) of a \(0.300 \mathrm{M} \mathrm{NaOH}\) solution b) \(10.0 \mathrm{~mL}\) of a \(0.200 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) solution

Short answer

a) 6.00 mL of 0.500 M HCl; b) 8.00 mL of 0.500 M HCl.

Step-by-step solution

Write the neutralization reaction

For part (a), the reaction between HCl and NaOH is \(\text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O}\). For part (b), the reaction between HCl and Ba(OH)\(_2\) is \(2\text{HCl} + \text{Ba(OH)}_2 \rightarrow \text{BaCl}_2 + 2\text{H}_2\text{O}\).

Calculate moles of base

For part (a), use the formula \(\text{moles} = \text{concentration} \times \text{volume}\). Convert the volume from mL to L: \(10.0\, \text{mL} = 0.0100\, \text{L}\). \[\text{Moles of NaOH} = 0.300\, \text{M} \times 0.0100\, \text{L} = 0.00300 \text{ moles}\] For part (b), \[\text{Moles of Ba(OH)}_2 = 0.200\, \text{M} \times 0.0100\, \text{L} = 0.00200 \text{ moles}\]

Determine moles of HCl required

For part (a), 1 mole of HCl reacts with 1 mole of NaOH, so 0.00300 moles of HCl are required. For part (b), 2 moles of HCl are needed for every 1 mole of Ba(OH)\(_2\), so \[0.00200\, \text{moles Ba(OH)}_2 \times 2 = 0.00400\, \text{moles HCl}\]

Calculate volume of HCl solution needed

For part (a), use \(\text{volume} = \frac{\text{moles}}{\text{concentration}}\) to find the volume of HCl: \[\text{Volume} = \frac{0.00300\, \text{moles}}{0.500\, \text{M}} = 0.00600\, \text{L} = 6.00\, \text{mL}\] For part (b), \[\text{Volume} = \frac{0.00400\, \text{moles}}{0.500\, \text{M}} = 0.00800\, \text{L} = 8.00\, \text{mL}\]

Key concepts

Molarity Calculations

Molarity is a crucial concept in solution chemistry, representing the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution and is expressed in moles per liter (M). Understanding molarity is vital in performing calculations for chemical reactions that occur in solutions, like neutralization reactions.

To calculate molarity, use the formula:

• Molarity (M) = moles of solute / liters of solution

Converting volumes from milliliters to liters is necessary because molarity is defined per liter of solution.

For instance, if you have a 0.300 M NaOH solution and need to find the moles of NaOH in a given volume, you convert the volume to liters (10.0 mL to 0.0100 L) and multiply by the molarity:

• Moles of NaOH = 0.300 M × 0.0100 L = 0.00300 moles

Such calculations enable you to determine how much reagent is needed in a chemical reaction.

Stoichiometry

In chemistry, stoichiometry involves calculating the relationships between the reactants and products in a chemical reaction. It is a vital part of understanding how different substances interact and react with each other.

Stoichiometry relies heavily on the balanced chemical equation, which shows the proportion of reactants to products. For example, in the reaction between HCl and NaOH:

• HCl + NaOH → NaCl + H₂O

Each mole of HCl reacts with one mole of NaOH. This one-to-one ratio simplifies calculations since the amount of acid needed equals the amount of base available.

Conversely, in the reaction between HCl and Ba(OH)₂:

• 2 HCl + Ba(OH)₂ → BaCl₂ + 2 H₂O

Two moles of HCl are required for each mole of Ba(OH)₂. Understanding the stoichiometry of these reactions is crucial to performing accurate calculations in acid-base reactions.

Acid-Base Reactions

Acid-base reactions are a type of chemical reaction that involves the transfer of protons (H⁺ ions) from the acid to the base. This reaction results in the formation of water and a salt. Understanding these reactions are fundamental to solving neutralization problems.

During an acid-base reaction:

• An acid donates hydrogen ions (H⁺).
• A base accepts hydrogen ions.

For instance, in the reaction between HCl and NaOH, HCl (the acid) donates a proton to NaOH (the base), producing water and sodium chloride (a salt).

The process of neutralization is complete when the acid and base have reacted in stoichiometric proportions, such that no excess of either reactant remains. Mastering this concept is essential to understanding broader chemical processes and interactions.

Solution Chemistry

Solution chemistry focuses on understanding the principles of solutes, solvents, and the interactions between them in a solution. It forms the foundation for understanding how substances mix, dissolve, and react.

A solution is a homogeneous mixture, which means that its composition is uniform throughout. It consists of a solute, the substance that is dissolved, and a solvent, the substance in which the solute is dissolved. In many cases, water is the solvent, making the solution aqueous.

Key points in solution chemistry include:

• Concentration: How much solute is present in a given quantity of solvent.
• Solubility: The maximum amount of solute that can dissolve in a particular solvent at a given temperature.

Understanding these principles is critical for predicting and calculating the behavior of substances in solution, which is especially important in neutralization reactions where precise concentrations determine the outcome.