Question

Hydroponics is a method for growing plants in water with added nutrients and oxygen. No soil is used. A deviation from the optimal pH range of $5.5-6.5$ can prevent a hydroponic plant from obtaining the necessary minerals and oxygen it needs to grow. To help maintain a pH of 5.5-6.5, growers use a citrate salt buffer system. Citric acid, $\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7},$ is a triprotic acid that has three carboxylic acid groups (Figure a $\nabla )$ . Use the information provided in the figures and equations to answer the following questions: $\begin{array}{l}{\text { a. Write a chemical equation that shows how citric acid reacts }} \\ {\text { with a hydroxide ion. }} \\ {\text { b. Which two of the citrate salts listed in Table a would you use }} \\ {\text { to make a buffer with a pH range of } 5.5-6.5 ? \text { Explain. }}\end{array}$ $ \begin{array}{l}{\text { c. Show how your buffer system (from part b) reacts with in- }} \\ {\text { coming acid }\left(\mathrm{H}_{3} \mathrm{O}^{+}\right) \text { and incoming base }\left(\mathrm{OH}^{-}\right)}\end{array}$ $\begin{array}{l}{\text { d. Figure bl- represents a titration curve for citric acid }} \\ {\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right) \text { with a strong base. On the graph, indicate the }} \\ {\text { buffer region involving the salts you chose in part b. }}\end{array}$ $\begin{array}{l}{\text { e. To prepare a buffer with } \mathrm{pH}=6.0, \text { what is the proper ratio of }} \\ {\text { the concentrations of the two citrate salts (from part b)? If }} \\ {\text { the buffer must neutralize at least } 0.010 \mathrm{M} \text { added acid, what }} \\ {\text { should the minimum concentration be for each of the two }} \\ {\text { buffer components? }}\end{array}$

Name: Problem 160, Chapter 17: Chemistry A Molecular Approach
Uploaded: 2019-07-11T22:53:08-08:00
Duration: 8 min 8 s
Channel: Lena Jake

   Hydroponics is a method for growing plants in water with added nutrients and oxygen. No soil is used. A deviation from the optimal pH range of $5.5-6.5$ can prevent a hydroponic plant from obtaining the necessary minerals and oxygen it needs to grow. To help maintain a pH of 5.5-6.5, growers use a citrate salt buffer system. Citric acid, $\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7},$ is a triprotic acid that has three carboxylic acid groups (Figure a $\nabla )$ . Use the information provided in the figures and equations to answer the following questions: $\begin{array}{l}{\text { a. Write a chemical equation that shows how citric acid reacts }} \\ {\text { with a hydroxide ion. }} \\ {\text { b. Which two of the citrate salts listed in Table a would you use }} \\ {\text { to make a buffer with a pH range of } 5.5-6.5 ? \text { Explain. }}\end{array}$ $
\begin{array}{l}{\text { c. Show how your buffer system (from part b) reacts with in- }} \\ {\text { coming acid }\left(\mathrm{H}_{3} \mathrm{O}^{+}\right) \text { and incoming base }\left(\mathrm{OH}^{-}\right)}\end{array}$ $\begin{array}{l}{\text { d. Figure bl- represents a titration curve for citric acid }} \\ {\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right) \text { with a strong base. On the graph, indicate the }} \\ {\text { buffer region involving the salts you chose in part b. }}\end{array}$ $\begin{array}{l}{\text { e. To prepare a buffer with } \mathrm{pH}=6.0, \text { what is the proper ratio of }} \\ {\text { the concentrations of the two citrate salts (from part b)? If }} \\ {\text { the buffer must neutralize at least } 0.010 \mathrm{M} \text { added acid, what }} \\ {\text { should the minimum concentration be for each of the two }} \\ {\text { buffer components? }}\end{array}$

Chemistry A Molecular Approach

Nivaldo J. Tro 4th Edition

Chapter 17, Problem 160

Instant Answer

Solved by Expert Lena Jake

07/11/2019

Step 1

Citric acid is a triprotic acid, meaning it can donate three protons (H+ ions). When it reacts with a hydroxide ion (OH-), it donates one of its protons to form water (H2O) and a citrate ion. The equation is as follows: \[ \mathrm{H}_{3} \mathrm{C}_{6} Show more…

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Hydroponics is a method for growing plants in water with added nutrients and oxygen. No soil is used. A deviation from the optimal pH range of $5.5-6.5$ can prevent a hydroponic plant from obtaining the necessary minerals and oxygen it needs to grow. To help maintain a pH of 5.5-6.5, growers use a citrate salt buffer system. Citric acid, $\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7},$ is a triprotic acid that has three carboxylic acid groups (Figure a $\nabla )$ . Use the information provided in the figures and equations to answer the following questions: $\begin{array}{l}{\text { a. Write a chemical equation that shows how citric acid reacts }} \\ {\text { with a hydroxide ion. }} \\ {\text { b. Which two of the citrate salts listed in Table a would you use }} \\ {\text { to make a buffer with a pH range of } 5.5-6.5 ? \text { Explain. }}\end{array}$ $ \begin{array}{l}{\text { c. Show how your buffer system (from part b) reacts with in- }} \\ {\text { coming acid }\left(\mathrm{H}_{3} \mathrm{O}^{+}\right) \text { and incoming base }\left(\mathrm{OH}^{-}\right)}\end{array}$ $\begin{array}{l}{\text { d. Figure bl- represents a titration curve for citric acid }} \\ {\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right) \text { with a strong base. On the graph, indicate the }} \\ {\text { buffer region involving the salts you chose in part b. }}\end{array}$ $\begin{array}{l}{\text { e. To prepare a buffer with } \mathrm{pH}=6.0, \text { what is the proper ratio of }} \\ {\text { the concentrations of the two citrate salts (from part b)? If }} \\ {\text { the buffer must neutralize at least } 0.010 \mathrm{M} \text { added acid, what }} \\ {\text { should the minimum concentration be for each of the two }} \\ {\text { buffer components? }}\end{array}$

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Key Concepts

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation provides a quantitative way to relate the pH of a buffer solution to the pKa of the acid and the ratio of the concentrations of the conjugate base to the acid. This equation is fundamental for calculating the proper ratio of the buffer components needed to achieve a target pH and is particularly useful when preparing buffers for precise biological or chemical applications.

Buffer Systems

A buffer system is a solution that resists changes in pH upon the addition of small amounts of acid or base. It typically consists of a weak acid and its conjugate base or a weak base and its conjugate acid. This equilibrium maintains the pH within a narrow range, which is critical in many chemical and biological processes, including those in hydroponics where plants require a fairly constant pH for optimal nutrient uptake.

Polyprotic Acids

Polyprotic acids are acids that can donate more than one proton (hydrogen ion) per molecule. They undergo multiple dissociation steps, each with its own dissociation constant, and are important in creating buffer systems because each dissociation produces a conjugate base that can participate in neutralization reactions. Understanding the behavior of polyprotic acids is crucial for designing buffers that operate effectively over a desired pH range.

Acid-Base Neutralization Reactions

Acid-base neutralization reactions involve the reaction between acids and bases to form water and a salt. In the context of pH regulation, these reactions are central to buffer functionality, as the buffer must be able to react with added acid or base to prevent significant deviations in pH. The principles of these reactions ensure that excess H+ or OH– ions are neutralized, thereby maintaining chemical equilibrium.

Titration Curves

Titration curves graphically represent the change in pH as a titrant is added to a solution. They are essential for understanding the behavior of acids and bases during titration, especially in identifying buffering regions where the pH changes more gradually. In buffer systems involving polyprotic acids, these curves help pinpoint the regions corresponding to the effective buffering capacity, indicating when the mixture most effectively resists pH changes.

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Transcript

00:01 Okay, so in this video we're going to be answering question 160 from chapter 17, which tells us hydroponics is a method for growing plants and water with added nutrients and oxygen.

00:11 No soil is used.

00:12 A deviation from the optimal ph range of 5 .5 to 6 .5 can prevent a hydroponic plant from obtaining the necessary minerals in oxygen it needs to grow.

00:21 To help maintain a ph of 5 .5 to 6 .5, growers use a citrate salt buffer system.

00:27 Citric acid, which i'm going to denote is h3a, is a triprotic acid that has three carboxylic acid groups.

00:35 Use the information provided in the figures and the equations to answer the following question.

00:40 So the first question we're asked is to write a chemical equation that shows how citric acid reacts with a hydroxide ion.

00:46 And for simplicity, i do this using the h3a symbol for citric acid rather than the full chemical formula.

00:54 But pretty much our hydroxide ion takes one proton from our tripodic acid to form the conjugate base in water.

01:03 So h3a plus oh minus forms h2a minus plus h2o.

01:10 In b, we're asked which of the two citrate salts listed in table a would you use to make a buffer with a ph range of 5 .5 to 6 .5.

01:19 Explain.

01:19 So in table a, we're given kh2a, k2ha, and k3a, except instead of a, they use the the full formula for citrate.

01:28 But essentially we're given the first, second, and third conjugate basis for citric acid, h2a minus, h2, and a minus three.

01:37 So after we've removed one proton, two protons, and three protons.

01:42 And the other information we're given, oh, and since we're asked what, which ones we would use to make a buffer with a ph range of 5 .5 to 6 .5, what's going to, make that what qualities are we looking for in our buffer the ph of a buffer according to the henderson -hosselbach equation is the p -k -a plus log of our concentration of base divided by our concentration of acid so the best buffer solution is one where the p -ka is nearest to the desired ph range so we want to look at the p -k -a of each of the acids in these buffer and the possible buffer solutions and we can do that we're given that information we're given k -a -we're given k -a -we're given k -a -we.

02:25 1, ka2, and ka3 for citric acid.

02:29 So for ka1, we're removing the first proton from citric acid.

02:34 So we're going from h3a to h2a minus.

02:37 So the pca1 is 3 .13.

02:41 And ka2, for ka2, we're removing another proton from h2a minus to form ha minus 2.

02:47 And the pka2, which is just negative log of the ka2, is 4 .77.

02:54 For ka3, we're removing the last proton from h .a.

02:58 Minus to form a minus 3.

03:00 H .a.

03:01 Minus 2, sorry, to form a minus 3.

03:04 And the p .a .3, which is negative log of ka3, is 6 .40.

03:09 So 6 .40 falls within our desired ph range of 5 .5 to 6 .5.