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Chapter 14: Problem 11

A buffer is prepared by dissolving \(0.0250 \mathrm{~mol}\) of sodium nitrite, \(\mathrm{NaNO}_{2}\), in \(250.0 \mathrm{~mL}\) of \(0.0410 \mathrm{M}\) nitrous acid, \(\mathrm{HNO}_{2}\). Assume no volume change after \(\mathrm{HNO}_{2}\) is dissolved. Calculate the \(\mathrm{pH}\) of this buffer.

Short Answer

Expert verified
Answer: The pH of the buffer solution is approximately 4.47.

Step by step solution

01

Calculate the concentration of HNO₂

We are given that the concentration of HNO₂ is 0.0410 M. Since the volume is 250.0 mL, we can find the moles of HNO₂ present in the solution: moles of HNO₂ = concentration × volume = 0.0410 M × 250.0 mL × (1 L / 1000 mL) = 0.01025 mol
02

Find the moles of NO₂⁻

The moles of NaNO₂ (the source of NO₂⁻) are given as 0.0250 mol. This is equal to the moles of NO₂⁻ produced in the buffer solution.
03

Calculate the new concentrations of NO₂⁻ and HNO₂

Since there is no change in volume after HNO₂ is dissolved, the new volume is still 250 mL. We can now calculate the new concentrations of both HNO₂ and NO₂⁻: [NO₂⁻] = moles of NO₂⁻ / volume = 0.0250 mol / (250.0 mL × (1 L / 1000 mL)) = 0.1 M [HNO₂] = moles of HNO₂ / volume = 0.01025 mol / (250.0 mL × (1 L / 1000 mL)) = 0.0410 M
04

Calculate the pKa of HNO₂

To find the pKa of HNO₂, we first need to find the Ka value. The Ka value for HNO₂ is 4.5 × 10⁻⁴. We can now calculate the pKa: pKa = -log(Ka) = -log(4.5 × 10⁻⁴) = 3.35
05

Use the Henderson-Hasselbalch equation to find the pH

We have all the necessary values to plug into the Henderson-Hasselbalch equation: pH = pKa + log([A⁻]/[HA]) = 3.35 + log(0.1/0.0410) = 3.35 + 1.12 ≈ 4.47 The pH of the buffer solution is approximately 4.47.

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Most popular questions from this chapter

There is a buffer system \(\left(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}-\mathrm{HPO}_{4}{ }^{2-}\right)\) in blood that helps keep the blood \(\mathrm{pH}\) at about \(7.40 .\left(\mathrm{K}_{\mathrm{a}} \mathrm{H}_{2} \mathrm{PO}_{4}^{-}=6.2 \times 10^{-8}\right)\). (a) Calculate the \(\left[\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\right] /\left[\mathrm{HPO}_{4}^{2-}\right]\) ratio at the normal \(\mathrm{pH}\) of blood. (b) What percentage of the \(\mathrm{HPO}_{4}{ }^{2-}\) ions are converted to \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) when the \(\mathrm{pH}\) goes down to \(6.80\) ? (c) What percentage of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) ions are converted to \(\mathrm{HPO}_{4}{ }^{2-}\) when the \(\mathrm{pH}\) goes up to \(7.80\) ?

A sodium hydrogen carbonate-sodium carbonate buffer is to be prepared with a \(\mathrm{pH}\) of \(9.40\). (a) What must the \(\left[\mathrm{HCO}_{3}^{-}\right] /\left[\mathrm{CO}_{3}^{2-}\right]\) ratio be? (b) How many moles of sodium hydrogen carbonate must be added to a liter of \(0.225 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}\) to give this \(\mathrm{pH}\) ? (c) How many grams of sodium carbonate must be added to \(475 \mathrm{~mL}\) of \(0.336 \mathrm{M} \mathrm{NaHCO}_{3}\) to give this \(\mathrm{pH}\) ? (Assume no volume change.) (d) What volume of \(0.200 \mathrm{M} \mathrm{NaHCO}_{3}\) must be added to \(735 \mathrm{~mL}\) of a \(0.139 \mathrm{M}\) solution of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) to give this \(\mathrm{pH}\) ? (Assume that volumes are additive.)

Explain why (a) the pH decreases when lactic acid is added to a sodium lactate solution. (b) the \(\mathrm{pH}\) of \(0.1 \mathrm{M} \mathrm{NH}_{3}\) is less than \(13.0\). (c) a buffer resists changes in pH caused by the addition of \(\mathrm{H}^{+}\) or \(\mathrm{OH}^{-} .\) (d) a solution with a low \(\mathrm{pH}\) is not necessarily a strong acid solution.

Which of the following would form a buffer if added to \(250.0 \mathrm{~mL}\) of \(0.150 \mathrm{M} \mathrm{SnF}_{2} ?\) (a) \(0.100 \mathrm{~mol}\) of \(\mathrm{HCl}\) (b) \(0.060 \mathrm{~mol}\) of \(\mathrm{HCl}\) (c) \(0.040 \mathrm{~mol}\) of \(\mathrm{HCl}\) (d) \(0.040 \mathrm{~mol}\) of \(\mathrm{NaOH}\) (e) \(0.040 \mathrm{~mol}\) of \(\mathrm{HF}\)

Indicate whether each of the following statements is true or false. If the statement is false, restate it to make it true. (a) The formate ion (CHO \(\left._{2}^{-}\right)\) concentration in \(0.10 \mathrm{M} \mathrm{HCHO}_{2}\) is the same as in \(0.10 \mathrm{M} \mathrm{NaCHO}_{2}\). (b) A buffer can be destroyed by adding too much strong acid. (c) A buffer can be made up by any combination of weak acid and weak base. (d) Because \(K_{\mathrm{a}}\) for \(\mathrm{HCO}_{3}^{-}\) is \(4.7 \times 10^{-11}, K_{\mathrm{b}}\) for \(\mathrm{HCO}_{3}^{-}\) is \(2.1 \times 10^{-4}\).
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