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Chapter 17: Problem 72

Calculate the \(\mathrm{pH}\) of the \(0.20 \mathrm{M} \mathrm{NH}_{3} / 0.20 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) buffer. What is the \(\mathrm{pH}\) of the buffer after the addition of \(10.0 \mathrm{~mL}\) of \(0.10 \mathrm{M} \mathrm{HCl}\) to \(65.0 \mathrm{~mL}\) of the buffer?

Short Answer

Expert verified
The initial pH of the \(NH_3 / NH_4Cl\) buffer system is 9.25, after the addition of \(10.0 \, mL\) of \(0.10 \, M\) \(HCl\) the pH of the system decreases due to the reaction. Using the provided calculations the final pH could be calculated.

Step by step solution

01

Calculate Initial pH

Firstly, use the Henderson-Hasselbalch equation to calculate the initial pH of the buffer using the formula \[pH = pKa + log\left( \frac{[NH_3]}{[NH_4^+]}\right)\]. Since the molarities of NH3 and NH4Cl are the same (0.20 M), their ratio is 1, therefore, the log part becomes 0. Using the provided pKa value of 9.25 for NH4+, the pH of the buffer initially is thus 9.25 + 0 = 9.25.
02

Calculate change in buffer species concentrations

After the addition of HCl, the HCl will react with NH3 and convert it to NH4+. Using the knowledge of stoichiometry and the volume and concentration of the added HCl (10.0 mL of 0.10 M, which will react to form 0.001 moles of NH4+), calculate the new concentrations of NH3 and NH4+. The initial volume of buffer is 65.0 mL. Therefore, when 10.0 mL of HCl is added the total volume of the solution is 75.0 mL and the new concentrations are: \[ [NH_3] = (0.20 * 65 - 0.001) / 75 ] = 0.17 M \] and \[ [NH_4^+] = (0.20 * 65 + 0.001) / 75 = 0.174M \].
03

Calculate final pH after HCl addition

Finally, substitute the found concentrations back into the Henderson-Hasselbalch equation to find the final pH of the buffer. Applying the equation with the new concentrations: \[ pH = 9.25 + log\left( \frac{0.17}{0.174}\right) \] which will give the new pH value.

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Most popular questions from this chapter

Give two examples of metal ions in each group (1 through 5) in the qualitative analysis scheme.

A diprotic acid, \(\mathrm{H}_{2} \mathrm{~A}\), has the following ionization constants: \(K_{\mathrm{a}_{1}}=1.1 \times 10^{-3}\) and \(K_{\mathrm{a}_{2}}=2.5 \times 10^{-6} .\) To make up a buffer solution of \(\mathrm{pH} 5.80\), which combination would you choose: \(\mathrm{NaHA} / \mathrm{H}_{2} \mathrm{~A}\) or \(\mathrm{Na}_{2} \mathrm{~A} / \mathrm{NaHA} ?\)

A sample of \(0.1276 \mathrm{~g}\) of an unknown monoprotic acid was dissolved in \(25.0 \mathrm{~mL}\) of water and titrated with \(0.0633 \mathrm{M} \mathrm{NaOH}\) solution. The volume of base required to reach the equivalence point was \(18.4 \mathrm{~mL}\). (a) Calculate the molar mass of the acid. (b) After \(10.0 \mathrm{~mL}\) of base had been added to the titration, the \(\mathrm{pH}\) was determined to be 5.87 . What is the \(K_{\mathrm{a}}\) of the unknown acid?

Amino acids are the building blocks of proteins. These compounds contain at least one amino group and one carboxyl group. Consider glycine, whose structure is shown in Figure 11.18 . Depending on the \(\mathrm{pH}\) of the solution, glycine can exist in one of three possible forms: Fully protonated: \(\mathrm{NH}_{3}-\mathrm{CH}_{2}-\mathrm{COOH}\) Dipolar ion: \(\mathrm{NH}_{3}-\mathrm{CH}_{2}-\mathrm{COO}^{-}\) Fully ionized: \(\mathrm{NH}_{2}-\mathrm{CH}_{2}-\mathrm{COO}^{-}\) Predict the predominant form of glycine at \(\mathrm{pH} 1.0,\) \(7.0,\) and \(12.0 .\) The \(\mathrm{p} K_{\mathrm{a}}\) of the carboxyl group is 2.3 and that of the ammonium group is 9.6.

One way to distinguish a buffer solution with an acid solution is by dilution. (a) Consider a buffer solution made of \(0.500 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) and \(0.500 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{COONa}\). Calculate its \(\mathrm{pH}\) and the \(\mathrm{pH}\) after it has been diluted 10 -fold. (b) Compare the result in (a) with the pHs of a \(0.500 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) solution before and after it has been diluted 10 -fold
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