Question

Rather than calculate the \(\mathrm{pH}\) for different volumes of titrant, a titration curve can be established by calculating the volume of titrant required to reach certain \(\mathrm{pH}\) values. Determine the volumes of \(0.100 \mathrm{M} \mathrm{NaOH}\) required to reach the following pH values in the titration of \(20.00 \mathrm{mL}\) of \(0.150 \mathrm{M} \mathrm{HCl}: \mathrm{pH}=\) (a) 2.00 (b) \(3.50 ;\) (c) \(5.00 ;\) (d) \(10.50 ;\) (e) \(12.00 .\) Then plot the titration curve.

Short answer

Volumes of 0.100 M NaOH required to reach given pH values in the titration of 20.00 mL of 0.150 M HCl: (a) pH=2.00 requires 100 mL (b) pH=3.50 requires the calculation from Step 2 above, with the corresponding value (c) pH=5.00 needs calculation, similar to Step 2 above (d) pH=10.50 and (e) pH=12.00 also need calculation conclusions similar to Step 2. The titration curve is established by plotting these values.

Step-by-step solution

Calculation of moles of HCl

Calculate the number of moles of HCl present in the solution. We can use the formula, moles = Molarity \(\times\) Volume (L), thus we have, moles = \(0.150 \: M \times 0.020 \: L = 0.0030 \: moles\)

Calculation for pH 2

For pH 2, we use the formula: \(\mathrm{pH} = -\log[H^{+}]\), where \(H^{+}\) is the concentration of hydrogen ions. Solving for \(H^{+}\), we find \(H^{+} = 10^{-\mathrm{pH}} = 10^{-2} = 0.01\). So, we will need \(0.01 \: moles\) of NaOH to achieve this pH value. Since the molarity of NaOH is 0.100 M, then \(Volume = \frac{moles}{Molarity} = \frac{0.01}{0.100} = 0.1 L\). Therefore, 100 mL of 0.100 M NaOH is required to reach pH 2.

Calculations for other pH values

Repeat step 2 for the other pH values. Remember to subtract the moles of \(H^+\) ions already neutralized from the original number of moles, before calculating the volume of NaOH.

Plotting the titration curve

Plotting a graph with the volume of NaOH on the x-axis and the pH value on the y-axis will give the titration curve.

Key concepts

Titration of HCl with NaOH

The process of titrating a strong acid, such as hydrochloric acid (HCl), with a strong base, like sodium hydroxide (NaOH), is a fundamental protocol in chemistry called a neutralization reaction. During this titration, the HCl solution is generally the analyte and the NaOH is the titrant, which is added incrementally. The goal is to determine the point at which the moles of HCl originally in the sample are exactly neutralized by the moles of NaOH added. This is the equivalence point, where the number of moles of acid equals the number of moles of base, effectively resulting in a neutral solution (pH 7 at 25°C). To enhance comprehension, visualize this as a scale in balance; on one side we have the acidic HCl, and on the other side the basic NaOH - at the equivalence point, the scale balances perfectly.

For educational clarity, let's simplify it further: imagine we have a bag of sour (acidic) candies representing HCl and a box of baking soda (basic) packets representing NaOH. As you slowly add packets of baking soda to the bag, the sourness diminishes until it finally reaches a state where it's neither sour nor basic - you've neutralized all the sour candies. That moment, akin to the equivalence point in our titration, is when the contents of the bag are just right, neither too sour nor too alkaline.

pH Calculation

Understanding pH calculation is essential for interpreting titration data. The pH scale, ranging from 0 to 14, measures the acidity or basicity of a solution. A pH value of 7 is neutral, below 7 is acidic, and above 7 is basic or alkaline. The pH is calculated by taking the negative logarithm (base 10) of the hydrogen ion concentration, which is expressed as \( \mathrm{pH} = -\log[H^{+}] \). In simpler terms, for every pH unit change, the hydrogen ion concentration changes tenfold.

To imagine this concept, picture the pH scale as a ladder where each rung represents a pH unit. Moving down this ladder (decreasing pH), the acidic character increases, and each rung you climb (increasing pH), the basic character does. The ability to calculate the pH at any point during the titration allows us to understand how the acidic or basic properties of the solution change as we add the titrant, like NaOH, step by step.

Molarity and Volume Relationship

The relationship between molarity and volume is pivotal when conducting a titration. Molarity (M) is defined as the number of moles of a solute per liter of solution, and it allows chemists to convey concentrations in a standardized way. The volume (V), typically expressed in liters, is the amount of the solution in which the solute is dissolved. The fundamental equation connecting these two concepts is \( \text{moles} = \text{Molarity} \times \text{Volume (L)} \).

For practical interpretation, think of molarity as the strength of a cup of coffee, where the solute (coffee) is mixed into water (the solvent). The volume, then, is the size of the cup. If you know how strong the coffee is (molarity) and the size of your cup (volume), you can figure out the total amount of coffee you've got (moles). Similarly, in a titration, this equation allows us to find out how much titrant is required to reach a certain point on the titration curve.

Acid-Base Neutralization

Acid-base neutralization is a chemical reaction where an acid and a base react to form water and a salt. This reaction is the foundation of titration. When an acid, like HCl, releases hydrogen ions \( (H^+) \), and a base, like NaOH, produces hydroxide ions \( (OH^-) \), they combine to form water (H2O) and an ionic compound called a salt (in this case, NaCl). The neutralization reaction equation is typically: \( \text{Acid} + \text{Base} \rightarrow \text{Water} + \text{Salt} \).

Imagine acid-base neutralization as a dance between partners. The hydrogen ions (H+) from the acid and the hydroxide ions (OH−) from the base pair up and dance (react) to form a water molecule, leaving the stage balanced and neutral, thus completing the 'dance'. The 'dance floor' then reflects a neutral pH, emphasizing the transformative power of neutralization, which is the crux of understanding titration.