Question

Would the volume of a \(0.10 \mathrm{M} \mathrm{NaOH}\) solution needed to titrate \(25.0 \mathrm{~mL}\) of a \(0.10 \mathrm{M} \mathrm{HNO}_{2}\) (a weak acid) solution be different from that needed to titrate \(25.0 \mathrm{~mL}\) of a \(0.10 \mathrm{M} \mathrm{HCl}\) (a strong acid) solution?

Short answer

The required volume of NaOH for both acids is the same, 25.0 mL.

Step-by-step solution

Understanding the Problem

We need to determine if the volumes of a sodium hydroxide (NaOH) solution needed to titrate equal concentrations and volumes of weak acid (HNO₂) and strong acid (HCl) solutions are different.

Acid and Base Reactions

In a titration, the acid reacts with the base to form water and a salt. The balanced chemical equation for the reaction of each acid with NaOH is essential to determine the stoichiometry and thus the required volume of NaOH.

Write Reaction Equations

1. For the weak acid HNO₂: \[ \mathrm{HNO}_{2} + \mathrm{NaOH} \rightarrow \mathrm{NaNO}_{2} + \mathrm{H}_{2} \mathrm{O} \]2. For the strong acid HCl: \[ \mathrm{HCl} + \mathrm{NaOH} \rightarrow \mathrm{NaCl} + \mathrm{H}_{2} \mathrm{O} \]

Assess Stoichiometry

Both reactions have a 1:1 stoichiometric ratio, meaning it takes one mole of NaOH to neutralize one mole of either HNO₂ or HCl.

Calculate Moles of Acid

Use the formula \( M \times V = n \) to find moles:- For HNO₂: \( 0.10 \mathrm{M} \times 0.025 \mathrm{L} = 0.0025 \) moles- For HCl: \( 0.10 \mathrm{M} \times 0.025 \mathrm{L} = 0.0025 \) moles

Calculate Volume of NaOH Needed

Since both reactions require the neutralization of 0.0025 moles of acid, and both acids have the same molarity and volume, you need the same moles of NaOH:- Required moles of NaOH \( = 0.0025 \) moles.- Use the formula \( V = \frac{n}{M} \) to find volume: - Volume of NaOH \( = \frac{0.0025}{0.10} = 0.025 \mathrm{L} \) or \( 25.0 \mathrm{mL} \)

Conclusion

Both the weak acid (HNO₂) and the strong acid (HCl) require the same volume of 0.10 M NaOH for titration, given that their concentrations and initial volumes are the same.

Key concepts

Weak acid

A weak acid is an acid that only partially dissociates in solution, meaning not all of its molecules release hydrogen ions (H⁺) into the solution. Because of this, weak acids exist in an equilibrium between the undissociated acid molecules and the ions they produce. Examples of weak acids include acetic acid (found in vinegar) and nitrous acid (HNO₂).

Here are some characteristics of weak acids:

• They have higher pH values compared to strong acids at the same concentration because fewer H⁺ ions are present.
• Their reactions with bases, like NaOH, occur more slowly compared to strong acids.
• They are often not completely ionized even at higher concentrations.

Understanding the behavior of weak acids is crucial in titrations because the equilibrium must be established before determining the endpoint.

Strong acid

A strong acid is an acid that completely dissociates in solution, meaning all of its molecules release hydrogen ions (H⁺). Strong acids, therefore, easily break into their constituent ions. Hydrochloric acid (HCl) is a common example of a strong acid and is completely ionized in aqueous solutions.

Key features of strong acids include:

• They produce a large concentration of H⁺ ions, which leads to a lower pH compared to weak acids at the same concentration.
• Their reactions with bases are typically more vigorous and immediate than those involving weak acids.
• No equilibrium is present between ionized and non-ionized forms since all molecules are ionized in solution.

In a titration, a strong acid reacts swiftly with a base, making the endpoint easier to determine.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It tells us how much of each substance is consumed or produced. In the context of acid-base titrations, stoichiometry helps determine the exact amount of titrant needed to completely react with the analyte.

The general steps to consider in stoichiometry during titration are:

• Writing a balanced chemical equation to understand the mole relationship between reactants.
• Using the equation to find out the moles of acid and base involved, which will give the ratio required for neutralization.
• Calculating the volume needed for the neutralization based on molarity and volume relationships.

For instance, in the reactions provided (both for HNO₂ and HCl), a 1:1 stoichiometric ratio means one mole of NaOH is needed to react with one mole of acid, allowing for straightforward calculations using molarity and volume.

Chemical reaction equation

A chemical reaction equation represents the substances involved in a reaction and their transformations. It's essential for understanding the specifics of what happens during a titration.

A balanced chemical equation shows:

• The reactants, which in acid-base titrations commonly include the acid and the base.
• The products, usually a salt and water.
• The stoichiometric coefficients that indicate the relative amounts of each substance.

For the reaction between nitrous acid and sodium hydroxide, the equation is:
\[ \mathrm{HNO}_{2} + \mathrm{NaOH} \rightarrow \mathrm{NaNO}_{2} + \mathrm{H}_{2} \mathrm{O} \]
While for hydrochloric acid, it is:
\[ \mathrm{HCl} + \mathrm{NaOH} \rightarrow \mathrm{NaCl} + \mathrm{H}_{2} \mathrm{O} \]
Both equations demonstrate a 1:1 reaction stoichiometry, meaning each acid molecule reacts with one molecule of NaOH to produce water and a salt. Balancing these equations is crucial for understanding the amount of reactants needed and ensuring the calculation of the titration volume is accurate.