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Chapter 17: Problem 47

In the titration of \(20.00 \mathrm{mL}\) of \(0.175 \mathrm{M} \mathrm{NaOH},\) calculate the number of milliliters of \(0.200 \mathrm{M} \mathrm{HCl}\) that must be added to reach a pH of (a) \(12.55,\) (b) \(10.80,\) (c) 4.25

Short Answer

Expert verified
The volumes of 0.200 M HCl solution required to reach the pH values of 12.55, 10.80, and 4.25 are respectively calculated in steps 2 through 4. The calculations need to be repeated separately for each of the given pH values.

Step by step solution

01

Understanding the reagent relationship

The reaction that occurs during the titration of NaOH with HCl is a neutralization reaction, which produces water and sodium chloride. This reaction can be represented as \( \mathrm{NaOH} + \mathrm{HCl} \rightarrow \mathrm{H_2 O} + \mathrm{NaCl} \). From this reaction, it can be observed that NaOH and HCl react in a 1:1 ratio. Hence, the concentration and volume of NaOH can be used to calculate the moles of NaOH.
02

Calculating the moles of NaOH

The moles of NaOH can be calculated using the formula: moles = concentration * volume. The volume of NaOH provided is 20.00 mL, which needs to be converted to liters; hence, the volume is 0.02 L. Multiplying the volume (0.02 L) and the concentration (0.175 M), we get 0.0035 moles of NaOH.
03

Calculating the moles of HCl for respective pH values

The pH at which the volume required is to be calculated is given, so we can use the pH formula to find the concentration of HCl at that pH. The formula for the pH is \( \mathrm{pH} = -\log (\mathrm{[H+]}) \). So we can rearrange this to get the hydrogen ion concentration [H+] = \(10^{-pH}\). Calculate [H+] for each of the given pH values.
04

Calculating the volume of HCl required

After the [H+] concentration is known, subtract the concentration of HCl required before the equivalence point from the remaining moles of OH- ions left after the equivalence point. Then, divide these moles by the concentration of the HCl solution to find the volume. Convert the volume to mL by multiplying by 1000.
05

Repeat calculations for given pH levels

Repeat steps 3 and 4 to calculate the volume of HCl required to reach each of the other two given pH levels.

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Most popular questions from this chapter

Is a solution that is \(0.10 \mathrm{M} \mathrm{Na}_{2} \mathrm{S}(\mathrm{aq})\) likely to be acidic, basic, or pH neutral? Explain.

The Henderson-Hasselbalch equation can be written as \(\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}-\log \left(\frac{1}{\alpha}-1\right)\) where \(\alpha=\frac{\left[\mathrm{A}^{-}\right]}{\left[\mathrm{A}^{-}\right]+[\mathrm{HA}]}\) Thus, the degree of ionization \((\alpha)\) of an acid can be determined if both the \(\mathrm{pH}\) of the solution and the \(\mathrm{p} K_{\mathrm{a}}\) of the acid are known. (a) Use this equation to plot the pH versus the degree of ionization for the second ionization constant of phosphoric acid \(\left(K_{\mathrm{a}}=6.3 \times 10^{-8}\right)\) (b) If \(\mathrm{pH}=\mathrm{p} K_{\mathrm{a}}\) what is the degree of ionization? (c) If the solution had a pH of 6.0 what would the value of \(\alpha\) be?

What concentration of ammonia, \(\left[\mathrm{NH}_{3}\right],\) should be present in a solution with \(\left[\mathrm{NH}_{4}^{+}\right]=0.732 \mathrm{M}\) to produce a buffer solution with \(\mathrm{pH}=9.12 ?\) For \(\mathrm{NH}_{3}\) \(K_{\mathrm{h}}=1.8 \times 10^{-5}\)

The most acidic of the following \(0.10 \mathrm{M}\) salt solutions is (a) \(\mathrm{Na}_{2} \mathrm{S} ;\) (b) \(\mathrm{NaHSO}_{4} ;\) (c) \(\mathrm{NaHCO}_{3} ;\) (d) \(\mathrm{Na}_{2} \mathrm{HPO}_{4}\)

The \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}-\mathrm{HPO}_{4}^{2-}\) combination plays a role in maintaining the pH of blood. (a) Write equations to show how a solution containing these ions functions as a buffer. (b) Verify that this buffer is most effective at \(\mathrm{pH} 7.2\) (c) Calculate the \(\mathrm{pH}\) of a buffer solution in which \(\left[\mathrm{H}_{2} \mathrm{PO}_{4}\right]=0.050 \mathrm{M}\) and \(\left[\mathrm{HPO}_{4}^{2-}\right]=0.150 \mathrm{M} .[\)Hint: Focus on the second step of the phosphoric acid ionization.]
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