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

Short Answer

Expert verified
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

01

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: \[H+ = 10^{-1.50}\]
02

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: \[HCl_{final} = H+ = 10^{-1.50}\]
03

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: \[moles_{HCl} = HCl_{final} \times volume_{L} = 10^{-1.50} \times 1.6\]
04

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.
05

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.

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