How to Draw a functional Equiligraph

What can i do today, with a nickel and a piece of string, to tell  me what I need to know? Figure 1. Horizontal pH axis, labled 0 at left and 14 at right. Provide space for 14 uniform spaces. Figure 6. diagonal lines represent the concentration of the acid and base forms . The acid form has a slope of -1 and the base form has a slope of +1 Figure 5. The horizontal line represents the total concentration. The point located on the pKa line Figure 4. Vertical line representing the acid dissociation constant, pKa. Figure 3. Lines representing dissociation of water as [H+] and [OH-] Figure 2. Vertical concentration axis Figure 11. The concentration of acetic acid solution that will produce a pH =3 is found to be about 0.16 (M) Figure 10. Figure 9. locate the desired pH and mark a point at (3. -3) Figure 8. Analysis showing the pH of a pure acid solution (Acetic acid and a solution made from a monobasic salt ( odium acetate), with a total concentration of 3.1x10-2 (M). Figure 7. The finished equiligraph for a molecule with pKa = 4.75 (e.g. acetic acid)

Step 1. Draw a horizontal line for the pH axis, as shown in figure 1. Provide enough space for 14 evenly spaced increments. Label from left to right as 0, 1, 2,...., 14

Step 2. Draw a vertical line for the pH axis, as shown in figure 2. Provide enough space for 14 evenly spaced increments.  Label these 0, -1, -2 ...,-14

Step 3. Draw diagonal lines as shown in figure 3. These represent the [H+] and [OH-] lines. The [H+] line has a slope of -1 and the [OH-] line has a slope of +1

Step 4. Draw a vertical line representing the acid dissociation constant, pKa, as shown in figure 4. The line crosses the horizontal pH axis at the value of the pKa.  In this case, pKa = 4.75.

Step 5. Add a horizontal line representing the total concentration of the chemical, as shown in figure 5. For this example CTotal = 3.1x10-2 (M), so the line intersects the vertical axis at log10(3.1x10-2) = -1.5. Break the line about 1 pH unit on either side of the vertical pKa line drawn in step 4.

Add a point on the pKa line one half of a log unit below the CTotal line. This is the mid-point and it represents the pH where the acid and base forms of the molecule have equal concentrations. For example [HB] = [B].

Note: The true mid-point is  log10(CTotal) - 0.3, however this difference is often the width of the line.

Step 6. Draw two diagonal lines, parallel to the [H+] and [OH-] lines. These diagonal lines intersect at the mid-point .These represent the concentration of the acid,HB, and base , B, forms of the molecule.

Step 7. Connect the CTotal lines drawn in step 5 to the [HB] and [B] lines drawn in step 6. The cure should be smooth, as shown in figure 7.

The equiligraph is now complete and you can proceed with your analysis!

Figure 8 shows two common analyses performed using the euqiligraph: finding the pH of pure acid and pure monobasic salt solutions of known concentration.

The pH of the pure acid is found by locating the intersection of the [H+] line and the [B] line. This intersection represents the pH where [H+] = [B].

Similarly, the pH of the monobasic salt solution is found by locating the intersection of the [OH-] line and the [HB] line. This intersection represents the pH where [OH-] = [HB].

Suppose we need to find the concentration of a pure acid solution that will have s specific pH. Let us choose pH= 3 for acetic acid.

We start by drawing an empty equiligraph, using steps 1 through 4, above.

Next follow steps 5A through A, shown below.

Step 5A. Locate the point representing the desired pH. It is at the intersection of pH = 3 and log10([H+]) = -3.

Figure 9 shows this point.

Step 6 A. Draw a diagonal line with slope = -1 passing through the point drawn in step 5A and ending at the vertical pKa line, as shown in figure 10. This line is the [B] line.

The intersection of [B] and pKa represents the point where [B] = [HB]

Step 7 A.  Mark a point one half log unit higher than the intersection of  the diagonal [B] line and the vertical  pKa line. This point represents the total concentration , CTotal = [HB] +[B].

Draw the two  horizontal CTotal line segments which passes through this point, and connect these horizontal lines with the [B] and [HB] lines. Figure 11 shows this process, which is similar to that show in steps 6 and 7 above.

Keywords:

For a monoprotic acid or base, the rules for drawing the composition lines on a log-log plot, with the X axis defined as pH are:

1. 1)When α0 or α1 are near unity, the line is horizontal and has a Y axis value = log(CTotal).

2. 2)When α0 is near unity,  α1 has a slope of +1.

3. 3)When α1 is near unity,  α0 has a slope of -1.

4. 4)When 0.05 < α0 < 0.95 , then the lines are smooth curves connecting the composition lines and the two lines intersect at  {pKa, log(CTotal ) - 0.3}

5. 5)The [H+] and [OH-] lines have slopes of -1 and + 1, respectively and they intersect at {7, -7}, where [H+] = [OH-].

Notes:

log10(0.5) = -0.30, so [HB] = [B] = 0.5 * CTotal  at Y = log(CTotal ) - 0.3.

log10(0.05) = 1.3  so:

α0 > 0.95 for pH <  pKa - 0.65

and

α1 > 0.95 for pH >  pKa + 0.65

Tutorials / Interpretation:

Worked examples:

Physics / Theory:

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Software / Apps:

Titration:    Apple AppStore

Equiligraph, buffer capacity and titration curve. Fizz:

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A calculator showing CaCO3 solubility as a function of atmospheric CO2 Solubility:

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Equiligraph showing solubility as function of pH

It is easy to sketch an equiligraph that is sufficient for most purposes. Graph paper works best,  however often an piece of scratch paper or a napkin will suffice.

all you really need is a pen or pencil. A square helps, but is not necessary.

When additional precision or accuracy is needed,  it is simple to create a spreadsheet. Here is a spreadsheet template in Excel format and in OpenOffice format.

A much simpler way is to use the iPhone and iPad app, which saves lots of time and trouble.