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Soil pH is one of the most important chemical properties that affect nutrient interactions in soils and plants. It is, however, one of the most misunderstood measurements, particularly when comparing one pH value to another.
A question that is often asked is, “How many times more acid is one pH than another?” This question is not straightforward to answer, because pH expresses acid concentration on a negative logarithm scale, rather than on a linear one where such comparisons would make sense.
The pH scale goes from 0 to 14. The 0 end of the scale is more acid. The 14 end is basic, and a pH of 7 is neutral, dividing acidic from basic, so we know that, for instance, a pH of 5.8 is more acid than a pH of 6.6. But how many more times acid is it?
To answer this question, we must first recognize that pH is a transformed measure of the concentration of acid. To find out “how many times more acid” one pH value is than another, we have to do some mathematical manipulations to get out of the negative log scale and back to a linear scale where such comparisons make sense.
Table 1 was developed from these mathematical manipulations and is provided to allow you to quickly determine how many times more acid a lower pH value is than a higher one. To use the table, take the higher pH value and subtract the lower one. Look up the difference in the table, under the heading “pH difference.” Then look at the corresponding number in the column to the right labeled “Times more acid.” Using our example, we want to compare pH 5.8 and 6.6. We take the higher value and subtract the lower one: 6.6 – 5.8 = 0.8. When we look up 0.8 in the table, we get 6.3. So the lower pH of 5.8 is 6.3 times more acid than the higher pH of 6.6. Using this table, you can easily determine how two pH values compare to one another throughout the pH scale.
Table 1. How many times more acid a lower pH is than a higher pH, where:
pH difference = higher pH – lower pH
times more acid = how many times more acid the lower pH is than the higher pH
Note: differences 0.1 to 9.9 are rounded to 2 significant figures. Differences 10.0 to 14.0 are rounded to 3 significant figures.
pH difference | times more acid | pH difference | times more acid | pH difference | times more acid |
0.1 | 1.0 | 5.1 | 130,000 | 10.1 | 12,600,000,000 |
0.2 | 1.6 | 5.2 | 160,000 | 10.2 | 15,800,000,000 |
0.3 | 2.0 | 5.3 | 200,000 | 10.3 | 20,000,000,000 |
0.4 | 2.5 | 5.4 | 250,000 | 10.4 | 25,100,000,000 |
0.5 | 3.2 | 5.5 | 320,000 | 10.5 | 31,600,000,000 |
0.6 | 4.0 | 5.6 | 400,000 | 10.6 | 39,800,000,000 |
0.7 | 5.0 | 5.7 | 500,000 | 10.7 | 50,100,000,000 |
0.8 | 6.3 | 5.8 | 630,000 | 10.8 | 63,100,000,000 |
0.9 | 7.9 | 5.9 | 790,000 | 10.9 | 79,400,000,000 |
1.0 | 10 | 6.0 | 1,000,000 | 11.0 | 100,000,000,000 |
1.1 | 13 | 6.1 | 1,300,000 | 11.1 | 126,000,000,000 |
1.2 | 16 | 6.2 | 1,600,000 | 11.2 | 158,000,000,000 |
1.3 | 20 | 6.3 | 2,000,000 | 11.3 | 200,000,000,000 |
1.4 | 25 | 6.4 | 2,500,000 | 11.4 | 251,000,000,000 |
1.5 | 32 | 6.5 | 3,200,000 | 11.5 | 316,000,000,000 |
1.6 | 40 | 6.6 | 4,000,000 | 11.6 | 398,000,000,000 |
1.7 | 50 | 6.7 | 5,000,000 | 11.7 | 501,000,000,000 |
1.8 | 63 | 6.8 | 6,300,000 | 11.8 | 631,000,000,000 |
1.9 | 79 | 6.9 | 7,900,000 | 11.9 | 794,000,000,000 |
2.0 | 100 | 7.0 | 10,000,000 | 12.0 | 1,000,000,000,000 |
2.1 | 130 | 7.1 | 13,000,000 | 12.1 | 1,260,000,000,000 |
2.2 | 160 | 7.2 | 16,000,000 | 12.2 | 1,580,000,000,000 |
2.3 | 200 | 7.3 | 20,000,000 | 12.3 | 2,000,000,000,000 |
2.4 | 250 | 7.4 | 25,000,000 | 12.4 | 2,510,000,000,000 |
2.5 | 320 | 7.5 | 32,000,000 | 12.5 | 3,160,000,000,000 |
2.6 | 400 | 7.6 | 40,000,000 | 12.6 | 3,980,000,000,000 |
2.7 | 500 | 7.7 | 50,000,000 | 12.7 | 5,010,000,000,000 |
2.8 | 630 | 7.8 | 63,000,000 | 12.8 | 6,310,000,000,000 |
2.9 | 790 | 7.9 | 79,000,000 | 12.9 | 7,940,000,000,000 |
3.0 | 1,000 | 8.0 | 100,000,000 | 13.0 | 10,000,000,000,000 |
3.1 | 1,300 | 8.1 | 130,000,000 | 13.1 | 12,600,000,000,000 |
3.2 | 1,600 | 8.2 | 160,000,000 | 13.2 | 15,800,000,000,000 |
3.3 | 2,000 | 8.3 | 200,000,000 | 13.3 | 20,000,000,000,000 |
3.4 | 2,500 | 8.4 | 250,000,000 | 13.4 | 25,100,000,000,000 |
3.5 | 3,200 | 8.5 | 320,000,000 | 13.5 | 31,600,000,000,000 |
3.6 | 4,000 | 8.6 | 400,000,000 | 13.6 | 39,800,000,000,000 |
3.7 | 5,000 | 8.7 | 500,000,000 | 13.7 | 50,100,000,000,000 |
3.8 | 6,300 | 8.8 | 630,000,000 | 13.8 | 63,100,000,000,000 |
3.9 | 7,900 | 8.9 | 790,000,000 | 13.9 | 79,400,000,000,000 |
4.0 | 10,000 | 9.0 | 1,000,000,000 | 14.0 | 100,000,000,000,000 |
4.1 | 13,000 | 9.1 | 1,300,000,000 |  | |
4.2 | 16,000 | 9.2 | 1,600,000,000 | | |
4.3 | 20,000 | 9.3 | 2,000,000,000 | | |
4.4 | 25,000 | 9.4 | 2,500,000,000 | | |
4.5 | 32,000 | 9.5 | 3,200,000,000 | | |
4.6 | 40,000 | 9.6 | 4,000,000,000 | | |
4.7 | 50,000 | 9.7 | 5,000,000,000 | | |
4.8 | 63,000 | 9.8 | 6,300,000,000 | | |
4.9 | 79,000 | 9.9 | 7,900,000,000 | | |
5.0 | 100,000 | 10.0 | 10,000,000,000 | | |
The Mathematics behind the Table
We start with the definition of pH:
where [H+] is the concentration of acid (moles per liter, or molar), which is a shorthand notation of the concentration of the hydronium ion [H3O+]; log10 is the logarithm function in base 10; and ion concentration is assumed to be equal to ion activity (the activity coefficient is equal to 1, not shown in the equation).
We then multiply both sides by -1, which changes the signs:
 .
Next, both sides are raised to the power of 10:
 .
Since raising an expression to the power of 10 is the inverse function of the logarithm, the expression on the right side of the equation simplifies to:
 . [1]
This expression (Equation 1) shows how the actual molar concentration of acid is related to the pH. Table 2 shows this relationship for various integer values of pH and demonstrates that as the pH gets lower, the concentration of acid increases, meaning that a lower pH has a higher concentration of acid.
Table 2. The relationship between pH and molar acid concentration.
pH | [H+] |
| (molar) |
| 0 | 1 |
| 1 | 0.1 |
| 2 | 0.01 |
| 3 | 0.001 |
| 4 | 0.0001 |
| 5 | 0.00001 |
| 6 | 0.000001 |
| 7 | 0.0000001 |
| 8 | 0.00000001 |
| 9 | 0.000000001 |
| 10 | 0.0000000001 |
| 11 | 0.00000000001 |
| 12 | 0.000000000001 |
| 13 | 0.0000000000001 |
| 14 | 0.00000000000001 |
To find how many more times acid a lower pH is than a higher one, two variables are defined:
pHL = Lower, more acid pH
pHU = Upper, less acid pH
Using Equation 1, we have the following equalities:
 [2]
 [3]
To find out how many more times acid the lower pH is, we calculate the ratio of the more acid concentration to the less acid one:
Next, we use Equations 2 and 3 to convert the above expression into the following one:
Using the properties of exponents, the above expression can be rewritten as:
 ,
or in final form:
 . [4]
So Equation 4 shows that to determine how many times more acid a lower pH is than an upper one, we simply subtract the lower pH from the upper pH and raise that difference to the power of ten. Going back to the original example of comparing pH 5.8 to pH 6.6, we subtract the lower pH from the upper one: 6.6 – 5.8 = 0.8. Next, we raise 10 to this power: 100.8 = 6.3. So we see that pH 5.8 is 6.3 times more acid than pH 6.6. All of the values in Table 1 were determined using the formula in Equation 4.
References
Fritz, J.S. 1973. Acid-base titrations in nonaqueous solvents. Allyn and Bacon, Inc., Boston, MA.
Skoog, D.A., D.M. West, and F.J. Holler. 1992. Analytical chemistry. 6th ed. Saunders College Publishing, New York, NY.
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