Question

Consider the titration of 150.0 \(\mathrm{mL}\) of 0.100 \(\mathrm{M} \mathrm{HI}\) by 0.250 \(\mathrm{M}\) \(\mathrm{NaOH}\) . a. Calculate the pH after 20.0 \(\mathrm{mL}\) of NaOH has been added. b. What volume of NaOH must be added so that the \(\mathrm{pH}=7.00 ?\)

Short answer

a. After adding 20.0 mL of NaOH, the pH is 1.33. b. To achieve a pH of 7.00, 60.0 mL of NaOH must be added.

Step-by-step solution

Calculate moles of reactants present initially

First, we need to calculate the initial moles of both reactants using the concentration and volume given. Moles = Molarity × Volume Initial moles of HI = \(0.100\textrm{ M} \times 150.0\textrm{ mL}\) Initial moles of NaOH = \(0.250\textrm{ M} \times 20.0\textrm{ mL}\) Note that we need to convert mL to L (by dividing by 1000) to correctly calculate the moles. a. Calculate the pH after 20.0 mL of NaOH has been added.

Determine the remaining moles of acid and base after the reaction

The stoichiometry of the reaction between HI and NaOH is 1:1, so we have to subtract the moles of the reactants consumed during the reaction. Remaining moles of HI = Initial moles of HI - Initial moles of NaOH

Calculate the concentration of H+ ions

Since HI is a strong acid, it completely dissociates in water, so the concentration of H+ ions is equal to the concentration of remaining HI. [H+] = (Remaining moles of HI) / (Total titration volume) Total titration volume = Initial volume of HI + volume of NaOH added

Calculate the pH

Use the formula to calculate pH: pH = -log10([H+]) Now for part b. b. What volume of NaOH must be added so that the pH=7.00?

Calculate the [H+] for a pH of 7.00

Use the formula: [H+] = 10^(-pH)

Calculate the moles of NaOH required to neutralize the acid

At pH=7, the moles of the remaining acid and the added NaOH should be equal. Moles of NaOH required = Initial moles of HI - moles of remaining acid

Calculate the volume of NaOH needed to achieve a pH of 7.00

To find the volume of NaOH needed, divide the moles of NaOH required by its molarity. Volume of NaOH = (moles of NaOH required) / (molarity of NaOH)

Key concepts

Molarity in Titration

Molarity, often denoted as "M," plays a crucial role in titration processes. It is defined as the number of moles of solute per liter of solution. In titrations, molarity helps us determine the amount of one solution needed to react with a given amount of another. For instance, consider the { ext {original exercise}}, where the molarity of hydroiodic acid (HI) and sodium hydroxide (NaOH) are utilized to find their initial moles. To do this conversion:

• Convert the volume from milliliters to liters.
• Use the formula: \[\text{Moles} = \text{Molarity} \times \text{Volume (L)}\]

By calculating moles in this way, we can accurately predict how one solution will neutralize the other. This understanding of molarity is vital for determining how much of a titrant is needed to reach a desired pH level in the solution.

pH Calculation Essentials

Understanding pH is key in titration because it indicates the acidity or basicity of a solution. pH is calculated as follows:

• The pH scale ranges from 0 to 14, with 7 being neutral.
• To find pH, use the formula:\[pH = -\log_{10}[H^+]\]where \([H^+]\) is the concentration of hydrogen ions in moles per liter.
• In titrations with strong acids like HI, which fully dissociate, the concentration of \([H^+]\) directly corresponds to the moles of acid present.

As we add NaOH, a strong base, it reacts with HI to alter the \([H^+]\) concentration, thus changing the pH. By calculating the remaining moles after each addition of NaOH, you can determine the new \([H^+]\) and therefore, the updated pH of the solution.

Neutralization Reaction Dynamics

A neutralization reaction occurs when an acid and a base react to form water and a salt. It's the essence of titration experiments, especially when the aim is to find the point of complete neutralization where pH equals 7.

• In the reaction between HI and NaOH, the equation is straightforward:\[\text{HI (aq) + NaOH (aq) } \rightarrow \text{ H}_2\text{O (l) }+ \text{ NaI (aq) }\]
• This is a one-to-one stoichiometric relationship, meaning one mole of HI reacts with one mole of NaOH.
• During titration, the addition of NaOH neutralizes HI until all hydrogen ions are reacted, moving the solution toward neutrality (pH 7).

This understanding is crucial when estimating the amount of base needed to completely neutralize the acid present in the solution to achieve the desired pH level.

Stoichiometry in Action

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the relative quantities of substances involved. During the titration process, stoichiometry helps:

• Determine how many moles of NaOH are necessary to neutralize the given moles of HI.
• Calculate the exact volume of a titrant solution required to reach the end point of the titration.
• Predict pH changes by considering the stoichiometric relationship in the neutralization reaction.

In the original problem, stoichiometry helps calculate both the amount of NaOH needed to begin affecting the pH (20.0 mL), and the precise volume required to make the pH equal to 7.0. By understanding these calculations, you can effectively manage both the process and results of a titration experiment.