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Chapter 13: Problem 61

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

Short Answer

Expert verified
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

01

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

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 \(0.031623 \mathrm{M}\).
03

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 \(V_1\): \[V_1 = \frac{M_2V_2}{M_1}\]
04

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.
05

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.

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Most popular questions from this chapter

A typical aspirin tablet contains 325 mg acetylsalicylic acid \(\left(\mathrm{HC}_{9} \mathrm{H}_{7} \mathrm{O}_{4}\right) .\) Calculate the \(\mathrm{pH}\) of a solution that is prepared by dissolving two aspirin tablets in enough water to make one cup \((237 \mathrm{mL})\) of solution. Assume the aspirin tablets are pure acetylsalicylic acid, \(K_{\mathrm{a}}=3.3 \times 10^{-4}\)

Calculate \(\left[\mathrm{OH}^{-}\right],\left[\mathrm{H}^{+}\right],\) and the \(\mathrm{pH}\) of \(0.40 M\) solutions of each of the following amines (the \(K_{\mathrm{b}}\) values are found in Table 13-3). a. aniline b. methylamine

Consider a \(0.67-M\) solution of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\left(K_{\mathrm{b}}=5.6 \times 10^{-4}\right)\) a. Which of the following are major species in the solution? i. \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) ii. \(\mathrm{H}^{+}\) iii. OH \(^{-}\) iv. \(\mathrm{H}_{2} \mathrm{O}\) v. \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}^{+}\) b. Calculate the \(p\) H of this solution.

What are the major species present in the following mixtures of bases? a. \(0.050 M \mathrm{NaOH}\) and \(0.050 \mathrm{M} \mathrm{LiOH}\) b. \(0.0010 M \mathrm{Ca}(\mathrm{OH})_{2}\) and \(0.020 \mathrm{M} \mathrm{RbOH}\) What is \(\left[\mathrm{OH}^{-}\right]\) and the \(\mathrm{pH}\) of each of these solutions?

Arrange the following 0.10 \(M\) solutions in order of most acidic to most basic. \(\begin{array}{llll} & \text { KOH, } & \text { KNO }_{3}, & \text { KCN, } & \text { NH_Cl, } & \text { HCl }\end{array}\)
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