Question

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

Short answer

To prepare a 1600 mL solution with a pH of 1.50 using concentrated 12 M HCl, first calculate the hydrogen ion concentration (H+) using the formula \(H+ = 10^{-1.50}\). Then, calculate the moles of HCl needed for the desired solution using the formula \(moles_{HCl} = HCl_{final} \times volume_{L} = 10^{-1.50} \times 1.6\). Next, calculate the volume of concentrated HCl needed using the formula \(volume_{HCl} = \frac{10^{-1.50} \times 1.6}{12}\) and convert the volume to mL. Finally, measure the calculated volume of concentrated HCl, slowly add it to a beaker containing approximately 1500 mL of deionized water, stir the mixture carefully, and add more deionized water if necessary to reach the final volume of 1600 mL.

Step-by-step solution

Calculate the hydrogen ion concentration of the desired solution

We can calculate the hydrogen ion concentration (H+) of the solution from the given pH using the formula: \[pH = -\log[H+]\] We need to find the value of (H+), given that pH = 1.50. To find the H+ concentration in the resultant solution, we use the equation: \[H+ = 10^{-pH}\] Plugging the given pH value (1.50) into the equation, we get: \[H+ = 10^{-1.50}\]

Calculate the final concentration of HCl in the desired solution

Since HCl is a strong acid and dissociates completely in water, its concentration is equal to the hydrogen ion concentration (H+). Therefore, the final concentration of HCl in the desired solution is: \[HCl_{final} = H+ = 10^{-1.50}\]

Calculate the amount of HCl in moles needed for the desired volume

Using the relationship between the concentration and volume, we can find the amount of HCl in moles needed for the desired 1600 mL solution. The formula is: \[moles = concentration \times volume\] Convert the volume from mL to L: \[ volume_{L} = \frac{1600 \mathrm{mL}}{1000} = 1.6 \mathrm{L} \] Now, we can find the moles of HCl needed for the desired solution: \[moles_{HCl} = HCl_{final} \times volume_{L} = 10^{-1.50} \times 1.6\]

Calculate the volume of concentrated HCl needed

We have the moles of HCl required and the concentration of the concentrated HCl (12 M). We can now determine the volume of concentrated HCl needed using the formula: \[volume = \frac{moles}{concentration}\] Plug in the values we obtained: \[volume_{HCl} = \frac{10^{-1.50} \times 1.6}{12}\] Make sure to convert the volume to mL by multiplying by 1000.

Prepare the solution

Now that we have the volume of concentrated HCl required, we can prepare the pH = 1.50 solution using the following steps: 1. Put on appropriate safety equipment (gloves, goggles, and a lab coat). 2. Measure the calculated volume of concentrated HCl using a graduated cylinder. 3. Slowly add the concentrated HCl to a beaker containing approximately 1500 mL of deionized water. 4. Stir the mixture carefully to ensure uniform distribution. 5. Add more deionized water if necessary to reach the final volume of 1600 mL.

Key concepts

pH calculation

Calculating pH is an essential concept in chemistry. It tells us how acidic or basic a solution is on a scale from 0 to 14. A pH less than 7 is acidic, while a pH greater than 7 is basic, and a pH of 7 is neutral. The pH of a solution is calculated using the formula:
\[ \text{pH} = -\log[\text{H}^+] \]
This equation helps determine the concentration of hydrogen ions \( [H^+] \) in the solution. In our problem, we know the pH is 1.50.

• By substituting pH = 1.50 into the formula, we can calculate the hydrogen ion concentration as follows:

\[ \text{H}^+ = 10^{-1.50} \]
This step is crucial in preparing solutions with a specific pH, as it tells us how many hydrogen ions are in each liter of solution.

acid-base titration

Acid-base titration is a method used to find the concentration of an acid or base in a solution. During titration, a solution of known concentration (titrant) is added to a solution of unknown concentration until the reaction reaches its endpoint.
This technique involves a few key components:

• Titrant: The solution with a known concentration.
• Analyte: The solution with an unknown concentration.
• Indicator: A chemical that changes color at the endpoint.

For strong acids like HCl, we need to consider that they dissociate completely in water.
Therefore, the concentration of the acid is equal to the concentration of hydrogen ions.
This complete dissociation allows for straightforward calculation when determining pH or during titration analysis.

molarity

Molarity is a measure of the concentration of a solution, defined in terms of the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L) or simply "M".
To find the molarity of a solution, use the formula:

• \( \, \text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} \)

In the example problem, we are given the concentration of concentrated HCl as 12 M, meaning there are 12 moles of HCl in every liter of solution.
Knowing the molarity allows us to calculate the number of moles needed when preparing a specified volume of solution. Understanding molarity is crucial for accurately conducting laboratory experiments and in the preparation of solutions.

dilution calculation

Dilution is the process of reducing the concentration of a solute in solution, typically by adding more solvent. The key to understanding dilution is that it involves a change in volume, not the number of moles of solute.
The dilution formula \( C_1V_1 = C_2V_2 \) is commonly used, where:

• \( C_1 \) is the concentration of the stock solution.
• \( V_1 \) is the volume of the stock solution.
• \( C_2 \) is the concentration of the diluted solution.
• \( V_2 \) is the volume of the diluted solution.

For our exercise, we determine \( V_1 \) by using the moles needed and the provided molarity of the concentrated solution:
\[ \text{volume}_{HCl} = \frac{10^{-1.50} \times 1.6}{12} \]
This tells us how much concentrated solution is needed to achieve the desired final concentration in 1600 mL of solution. Understanding dilution calculations helps in ensuring the correct preparation and safety of chemical solutions.