# Making a buffer with three components

- Page ID
- 434386

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Your job today is to make a buffered solution. We are not giving you the procedure, just the final concentrations in the solution. You will receive a "recipe card" such as the one below.

Solution B5 Make 50 mL of a buffer containing: · 50 mM trisodium citrate, · 20 mM HBr · 100 mM KCl |

Please work carefully and check your calculations. Other students (in this and other sections) will use this buffer next week for a colorimetric lab.

Research labs and industrial labs typically have a variety of solutions on hand to do their daily work. Often, these are made by one person and used by many. When hiring new people to work in the lab, one crucial question is whether they are able to make solutions that others can use with confidence.

This lab has two parts. In the first part, you are responsible for figuring out a recipe for your solution and for making it. In the second part, you team up to characterize your solutions, and to submit a solution you feel is closest to the specifications.

You have the following materials available:

- Pure sodium acetate trihydrate (NaCH
_{3}COO·3 H_{2}O, powder, molar mass is ~136g/mol) - Pure sodium phosphate, monobasic monohydrate (NaH
_{2}PO_{4}·H_{2}O, powder, molar mass is ~138 g/mol) - Solution of hydrochloric acid, HCl, concentration is 200 mM (or value on the bottle)
- Solution of sodium hydroxide, NaOH, concentration is 200 mM (or value on the bottle)
- Solution of sodium chloride, NaCl, concentration is 2.00 M
- Solution of sodium chloride, NaCl, concentration is 0.200 M

### Part one: individual tasks

Record your calculations and measurements in the data sheet.

**Formulate a recipe**to make your buffered solution. You will weigh out a certain mass of your buffer substance, add strong acid or base (this will adjust the pH), add sodium chloride and water. Choose which NaCl stock solution you will use to minimize volume errors.**Make the buffer**, using your recipe and checking off steps as you go. If there are any unexpected issues, take notes. Also, record the exact mass you used (it is fine if it is a couple of milligrams different from your recipe).**Calculate the estimated pH**of your solution after looking up the relevant pKa value.

**Part two: tasks done in pairs**

- Find the other individual(s) working on the same solution. Compare the recipes you used and the pH values you calculated. While the recipes might differ a bit, the calculated pH should be the same.
**Measure the pH**of your two solutions. You have measured pH values during lab last week. Use the same procedure, making sure the electrode is rinsed between uses. If you missed the lab, ask for a demonstration before you use the pH meter.**Measure the conductivity**of your two solutions: We are using an analog instrument that is a bit quirky. The following instructions will make more sense when you are at the instrument or after watching the video (QR code below).

For the conductivity measurement, make sure the probe and the provided 50 mL tube are rinsed with water before they come in contact with you solution. Transfer your solution into the 50 mL tube and insert the probe. For an accurate measurement, the probe has to be submerged past the line. Then, choose the appropriate measurement interval using the range dial while the sensitivity knob is turned all the way counterclockwise. Finally, increase the sensitivity, adjust the value dial to maximize the gap in the display, and read off the result on both dials. Don’t forget to retrieve your solution once you are done. There are two sample solutions provided along with the measurements if you need to troubleshoot.- Enter the data in the data table in your report, and discuss how different the measurements are for the different solutions. Are the differences within the range you expected? If not, what might have happened?
- Decide what you want to save for next week. You can either submit a mixture of your solutions (this would average out random errors) or decide to submit a single solution and dump the rest. If you discover that all solutions made had some “fatal flaw”, you can also make another solution together and submit that.
- Place your buffer in a 50 mL screw cap tube. Make a label, indicating the concentrations of all components, the data and your (first) names, and tape it on the tube. Then, put your solution in the provided Styrofoam rack in the hood.

### Hints for part 1

There are example calculations available on laminated sheets in the lab you may want to consult.

You have to do 3 calculations, one for each component you add. Your neighbor will do a different calculation, so don't copy their molar mass, their concentration, or their results. You are welcome to compare your calculations, but for the most part, answers should be different.

**Pure solid**

For the component that is a pure solid, you have to calculate the mass you need from the desired concentration and volume of the solution. This is a common calculation involving two steps ("how many moles do I need?", "how many grams do I need?"). It turns out you can combine these two steps into one using the formula: \[m = c \cdot V \cdot M \]

where m is the mass, c is the concentration, V is the volume and M is the molar mass. You can rationalize this formula by asking what happens to the required mass if you need a larger concentration, you need a larger volume, or you have a substance with a higher molar mass. In all of these cases, you would need a higher mass, so the formula makes sense. Make sure your units cancel and you end up with grams (or milligrams) for your units.

Example: To make 50 mL of a solution containing 50 mM trisodium citrate (M = 258.06 g/mol), the calculation is:

\[m = c \cdot V \cdot M = 0.050 \mathrm{mol/L} \cdot 0.050 \mathrm{L} \cdot 258.06 \mathrm{g/mol} = 0.6452 \mathrm{g} \]

Notice the change in units so that they cancel out, and the use of 4 digits behind the decimal point (matching what the balances read).

**Stock solutions**

For two substances, you have stock solutions. Diluting a stock solution is faster than weighing out a solid. For some solutions, it is more practical (hydrochloric acid is a mixture of HCl gas and water - you would have a hard time weighing out or otherwise measuring the amount of HCl). For those two components with available stock solutions, you have do two separate dilution law calculations. Make sure you keep these separate so you don't confuse the values you plug in or get out.

The dilution law is

\[c_1 V_1 = c_2 V_2\]

where c stands for concentration and V stands for volume. The subscript "1" is before dilution, and the subscript "2" is after dilution. For a visual, see the article on dilution on Wikipedia. When making a solution, we know the volume and concentration after dilution (c2 and V2), and the concentration of our stock solution (c1). What we need is the volumn of stock solution to add (V1). So we solve for V1:

\[V_1 = V_2 \cdot \frac{c_2}{c_1}\]

Let's see if that makes sense. If we want to make more of our solution or want to have a higher concentration, we have to add more (a bigger jug of lemonade or a stronger lemon flavor means we have to add more lemon juice). If we start with a more concentrated stock solution, we have to add less, which is why c1 is in the denominator.

Example: To make 50 mL of solution containing 100 mM KCl from a 500 mM KCl stock solution, the calculation is:

\[V_1 = V_2 \frac{c_2}{c_1} = 50 \mathrm{mL} \cdot \frac{100 \mathrm{mM}}{500 \mathrm{mM}} = 10 \mathrm{mL} \]

**Putting it all together**

In the end, you need a 50 mL solution. Don't prematurely fill up to 50 mL though. You have to make sure you added the three components before you fill to 50 mL. You can estimate the volume of water you need after finishing all three concentrations, but you don't know how much adding the solid will change the volume. You can use the water to rinse the containers you used to measure out the components, making sure that you don't lose any in the transfer.

### Hints for part 2

There are example calculations available on laminated sheets in the lab you may want to consult.

Depending on your recipe, you are either adding a weak base or a weak acid, not both. That is not a buffer, a buffer needs both.

Let's say your recipe has a weak base. In that case, you add HCl, but less of it (limiting reagent). The two react the following way:

\[\ce{Weak base + HCl -> Weak acid + Cl-}\]

Because the HCl is limiting, you turn some of your weak base into weak acid, but some weak base remains.

Let's say your recipe has a weak acid. In that case, you add NaOH, but less of it (limiting reagent). The two react the following way:

\[\ce{Weak acid + NaOH -> Weak base + H2O + Na+}\]

Because the NaOH is limiting, you turn some of your weak acid into weak base, but some weak acid remains.

In either case, you now have a buffer. Before you can predict the pH using the buffer equation, you have to calculate the concentrations of weak acid and base (and look up the pKa). For the calculation, you can use an ICE table, entering concentrations. Because the strong acid (or the strong base) is limiting, it should be zero after it reacts. This will allow you to figure out how much weak acid and weak base will be present after mixing. For example, if the concentration of HCl is half of that of the weak base, half of the weak base will turn into weak acid, and you have a 1:1 buffer. The pH of this buffer will be equal to the pKa. None of your recipes make 1:1 buffers (correct me if I'm wrong), so you expect a pH that is near but slightly different from the pKa. If your weak acid concentration is higher than your weak base concentration, your predicted pH should be more acidic than the 1:1 buffer; if the weak base concentration is higher, it should be more basic than the 1:1 buffer.