Question

How would you prepare \(1600 \mathrm{mL}\) of a \(\mathrm{pH}=1.50\) solution using concentrated (12 \(M\) ) HCl?

Short answer

To prepare \(1600 \mathrm{mL}\) of a \(\mathrm{pH} = 1.50\) solution using concentrated (12 M) HCl, first calculate the desired hydrogen ion concentration (\([H^{+}]\)) using the given pH value as \([H^{+}] \approx 0.031623 \mathrm{M}\). Next, use the dilution formula \(V_1 = \frac{M_2V_2}{M_1}\) to find the required volume of concentrated HCl, which is approximately \(42.16 \mathrm{mL}\). Finally, measure \(42.16 \mathrm{mL}\) of concentrated HCl, pour it into a container, and slowly add deionized or distilled water to reach a total volume of \(1600 \mathrm{mL}\). Mix well and check the pH to ensure the desired value is achieved. Use appropriate personal protective equipment while handling concentrated HCl.

Step-by-step solution

Convert pH to molarity

Recall that the relationship between pH and the hydrogen ion concentration \([H^{+}]\) is given by the formula: \[pH = -\log_{10} [H^{+}]\] We need to calculate the hydrogen ion concentration \([H^{+}]\) for the \(\mathrm{pH}=1.50\) solution. Solve for \([H^{+}]\) using the given pH value: \[[H^{+}] = 10^{-pH}\]

Calculate the hydrogen ion concentration

Using the formula from Step 1, plug the given pH value of \(1.50\): \[[H^{+}] = 10^{-1.50} \approx 0.031623\] So the desired hydrogen ion concentration is \(0.031623 \mathrm{M}\).

Use the dilution formula to determine the required volume of concentrated HCl

We will use the dilution formula to determine the volume of concentrated (12 M) HCl needed to prepare \(1600 \mathrm{mL}\) of the desired solution. The dilution formula is: \[M_1V_1 = M_2V_2\] Where, - \(M_1\) is the initial molarity of the concentrated solution, which is \(12 \mathrm{M}\), - \(V_1\) is the initial volume of the concentrated solution, - \(M_2\) is the final molarity of the diluted solution, which is the calculated \([H^{+}] \approx 0.031623 \mathrm{M}\), and - \(V_2\) is the final volume of the diluted solution, which is \(1600 \mathrm{mL}\). We need to find \(V_1\), so rearrange the formula to solve for \(V_1\): \[V_1 = \frac{M_2V_2}{M_1}\]

Calculate the required volume of concentrated HCl

Plug the values into the formula from Step 3: \[V_1 = \frac{(0.031623 \mathrm{M})(1600 \mathrm{mL})}{12 \mathrm{M}} \approx 42.16 \mathrm{mL}\] So, approximately \(42.16 \mathrm{mL}\) of the concentrated (12 M) HCl is needed to prepare \(1600 \mathrm{mL}\) of the desired \(\mathrm{pH} = 1.50\) solution.

Prepare the required solution

To prepare \(1600 \mathrm{mL}\) of the desired \(\mathrm{pH} = 1.50\) solution using concentrated (12 M) HCl: 1. Measure approximately \(42.16 \mathrm{mL}\) of concentrated HCl using a graduated cylinder or pipette. 2. Pour the measured HCl into a volumetric flask or container. 3. Slowly add deionized or distilled water to the container to bring the total volume to \(1600 \mathrm{mL}\). Be sure to mix well. 4. Check the pH of the solution using a pH meter or pH indicator paper to ensure the desired pH value is achieved. Note: Concentrated HCl is highly corrosive and irritant; use appropriate personal protective equipment (gloves, goggles, etc.) while handling.

Key concepts

pH calculation

Calculating pH is fundamental when working with acid-base solutions, as it provides insights into the acidity or basicity of a solution. The formula connecting pH and hydrogen ion concentration \([H^+]\) is: \[pH = -\log_{10} [H^+]\]. This equation allows us to determine how acidic a solution is.
For instance, a solution with a lower pH has a higher concentration of hydrogen ions and is more acidic. For our specific problem, where the pH is given as 1.50, we can compute the hydrogen ion concentration using the inverse operation. Thus, \([H^+]\) is calculated as \([H^+] = 10^{-1.50}\), yielding a concentration of approximately \0.031623 \, M\.
Understanding this calculation helps in preparing solutions with precise pH values, which is vital in many chemical processes.

Dilution formula

The dilution formula is crucial when you need to obtain a less concentrated solution from a more concentrated one. The formula is expressed as \[M_1V_1 = M_2V_2\]. Here:

• \(M_1\) is the molarity of the concentrated solution.
• \(V_1\) is the volume of the concentrated solution required.
• \(M_2\) is the molarity of the desired diluted solution.
• \(V_2\) is the total volume of the diluted solution you want to prepare.

In our task, we're using this formula to determine how much of the concentrated \(12 \, M\) hydrochloric acid (HCl) is needed to make \(1600 \, mL\) of a solution with a pH of 1.50, which corresponds to a molarity of about \(0.031623 \, M\).
By rearranging the dilution formula to solve for \(V_1\), we find \[V_1 = \frac{M_2V_2}{M_1} \approx \frac{(0.031623 \, M)(1600 \, mL)}{12 \, M} \]. Calculating gives us \(42.16 \, mL\). This means you need \(42.16 \, mL\) of the concentrated acid to prepare the desired solution.

Molarity

Molarity, also referred to as concentration, is a measure of the number of moles of solute per liter of solution. It is denoted as \(M\) and serves as an essential concept when preparing a solution of a specific concentration.
For example, if a solution is \(12 \, M\), it means there are \(12\) moles of solute per liter of solution. Understanding molarity allows chemists to dictate the exact concentration of an acidic or basic solution. This is important in adjusting the solution to meet specific reaction needs.
In our sample preparation, knowing that the initial concentration of HCl is \(12 \, M\) enabled us to use the dilution formula to attain the desired hydrogen ion concentration that corresponds with the target pH of 1.50.
Grasping the concept of molarity ensures accuracy and safety when creating solutions, especially when dealing with strong acids like HCl.

Hydrochloric Acid

Hydrochloric acid, or HCl, is a strong mineral acid with significant industrial and laboratory uses. Its concentrated form, which is \(12 \, M\), is highly corrosive and should be handled with care. It is an important chemical reagent in research and manufacturing processes.
When preparing a solution with hydrochloric acid, understanding its concentration is key. Concentrated HCl releases a large number of hydrogen ions, leading to low pH solutions. Thus, its use must be carefully controlled through formulas like dilution to ensure the desired concentration is achieved.

• Storage: Keep in a well-ventilated area and avoid direct sunlight.
• Handling: Use personal protective equipment (gloves, goggles) and work in a fume hood if possible.
• Disposal: Follow all local regulations for acid disposal.

Adhering to safety protocols makes working with hydrochloric acid safer, enabling precise solution preparation and minimizing risks.