Question

What volume of \(0.250 \mathrm{M} \mathrm{HCl}\) is required to neutralize each of the following solutions? a. \(25.0 \mathrm{mL}\) of \(0.103 \mathrm{M}\) sodium hydroxide, \(\mathrm{NaOH}\) b. \(50.0 \mathrm{mL}\) of \(0.00501 \mathrm{M}\) calcium hydroxide, \(\mathrm{Ca}(\mathrm{OH})_{2}\) c. \(20.0 \mathrm{mL}\) of \(0.226 \mathrm{M}\) ammonia, \(\mathrm{NH}_{3}\) d. \(15.0 \mathrm{mL}\) of \(0.0991 \mathrm{M}\) potassium hydroxide, \(\mathrm{KOH}\)

Short answer

The volume of 0.250M HCl required to neutralize the solutions are as follows: a. 10.3 mL of HCl for 25.0 mL of 0.103M NaOH b. 100.2 mL of HCl for 50.0 mL of 0.00501M Ca(OH)₂ c. 18.1 mL of HCl for 20.0 mL of 0.226M NH₃ d. 5.96 mL of HCl for 15.0 mL of 0.0991M KOH

Step-by-step solution

Calculate moles of sodium hydroxide

Firstly, calculate the moles of sodium hydroxide by multiplying volume by molarity. Using the formula: moles = Molarity * Volume This gives \(0.103 \mathrm{M} * 25.0 \mathrm{mL} * \frac{1 \mathrm{L}}{1000 \mathrm{mL}} = 0.002575 \mathrm{mol}\)

Use stoichiometry for HCl

The reaction between NaOH and HCl is a 1:1 reaction, so the moles of HCl will be equal to the moles of NaOH. Hence, 0.002575 mol of HCl is required.

Calculate the volume

Use this mole number to figure out the volume of 0.250M HCl needed to neutralize the sodium hydroxide. As \(Volume = \frac{moles}{Molarity} = \frac{0.002575 \mathrm{mol}}{0.250 \mathrm{M}} = 0.0103 \mathrm{L} = 10.3 \mathrm{mL}\).

Repeat steps for others

The same process is carried out for the other compounds. For Ca(OH)2, remember that it reacts in a 1:2 ratio with HCl, and the volume of HCl required will be twice that of NaOH. For NH3 and KOH, the process is the same as for NaOH because they each react in a 1:1 ratio with HCl. So, the volume of HCl required will be the same as that for NaOH.

Key concepts

Neutralization Reactions

Neutralization reactions are a type of chemical reaction where an acid reacts with a base to produce water and a salt. These reactions are fundamental in understanding how substances react to form different compounds.

In our exercise, hydrochloric acid (\( ext{HCl} \)) acts as the acid, and bases such as sodium hydroxide (\( ext{NaOH} \)), potassium hydroxide (\( ext{KOH} \)), calcium hydroxide (\( ext{Ca(OH)}_{2} \)), and ammonia (\( ext{NH}_3 \)) neutralize it.

• NaOH + HCl → NaCl + H\(_{2}\)O
• KOH + HCl → KCl + H\(_{2}\)O
• Ca(OH)\(_{2}\) + 2HCl → CaCl\(_2\) + 2H\(_{2}\)O
• NH\(_3\) + HCl → NH\(_4\)Cl

Understanding these reactions helps you gauge how bases and acids can be used to neutralize each other in real-world applications and lab settings.

Stoichiometry

In the realm of chemistry, stoichiometry allows us to calculate the precise amounts of substances involved in chemical reactions.

This involves balancing chemical equations to ensure that the same number of atoms of each element are present on both sides of the equation. This principle ensures the law of conservation of mass is met. In a neutralization reaction, stoichiometry plays a key role.

• For NaOH and KOH reacting with HCl: One mole of base reacts with one mole of HCl.
• For Ca(OH)\(_{2}\) and HCl: One mole of Ca(OH)\(_{2}\) reacts with two moles of HCl.
• For NH\(_3\) and HCl: One mole of NH\(_3\) reacts with one mole of HCl.

To solve problems like those in the exercise, understanding stoichiometry lets you figure out how much of each reactant is needed or produced in a reaction.

Molarity

Molarity is a key concept in chemistry that is used to express the concentration of a solution. It is defined as the number of moles of solute per liter of solution and is expressed as \( ext{M} \).

For example, when dealing with our exercise, the molarity helps us identify how concentrated the solutions of \( ext{HCl} \), \( ext{NaOH} \), \( ext{Ca(OH)}_2 \), \( ext{NH}_3 \), and \( ext{KOH} \) are.

• \(0.250 ext{M} ext{HCl} \) means there are 0.250 moles of HCl in every 1 liter of the solution.
• \(0.103 ext{M} ext{NaOH} \) means 0.103 moles of NaOH per liter, and so on for other solutions.

Understanding molarity is crucial for calculating how much solution is required to completely react with or neutralize another solution, making it essential for performing accurate lab work and experiments.

Consumption of Reagents

The consumption of reagents refers to the amount of a reactant used up during a chemical reaction. Knowing how much reagent is consumed helps in determining how much product is formed and whether the reaction will be complete or leave excess unreacted materials.

Let's see how this applies to our exercise problems. In a reaction:

• We know how much \( ext{NaOH} \) and other bases are present, so we calculate the volume of \( ext{HCl} \) needed to neutralize it completely.
• This is important for efficiency, as it prevents the wastage of reagents and ensures that the reaction proceeds to completion.

By understanding how much of each reagent is consumed, chemists can plan reactions better, ensuring that all reactants are used as needed, and estimate costs or resource allocation effectively in laboratories and industrial processes.