PH

pH significance:

'environmental pH is the activity of its oxonium cations expressed on a negative logarithmic scale. It is thus defined as:

$$\mathrm{pH} = - \log_{10} a_{\mathrm{H}_3\mathrm{O}^{+}}$$

Since the activity is very dependent on concentration, $$a = \gamma_c \cdot c$$ and outside very concentrated solutions, it is possible to consider the activity coefficient \gamma_c< /math> equal to approximately one, i.e. $$a \approx c,$$ can be written:

$$\mathrm{pH} = -\log_{10}\ [\mathrm{H}_3\mathrm{O}^{+}],$$

where $$[\mathrm{H}_3\mathrm{O}^{+}]$$ is in mol · dm-3 and pH is then dimensionless.

In an aqueous environment, oxonium cations are de facto hydrated hydrogen cations, hydrons, i.e. particles identical to protons, so pH is often stated as

$$\mathrm{pH} = -\log_{10}\ [\mathrm{H}^{+}].$$

pH scale in aqueous environment
In almost all real situations, only the pH of the aqueous environment is considered. Water undergoes autoprotolysis according to the equilibrium reaction

$$\mathrm{H}_2\mathrm{O} + \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{H}_3\mathrm{O}^{+} + \mathrm{OH}^ {-}$$

with the equilibrium constant

$$K = \frac{[\mathrm{H}_3\mathrm{O}^{+}] \cdot [\mathrm{OH}^{-}]}{[\mathrm{H}_2\mathrm{ O}]^{2}}.$$

The concentration of water in usual systems can be considered practically constant, so it is advantageous to work with the ionic product of water $$K_w = K \cdot [\mathrm{H}_2\mathrm{O}]^{2}.$$ From the above equation, the relationship for it follows

$$ K_w = [\mathrm{H}_3\mathrm{O}^{+}] \cdot [\mathrm{OH}^{-}].$$

The ionic product of water $$K_w$$ is proportional to the equilibrium constant and therefore, like it, strongly depends on temperature. So the pH scale will be different at different temperatures. At 25 °C, laboratory temperature, Kw corresponds to 1.008 · 10-14, so the pH scale will have a center, the so-called neutral pH, almost exactly 7. This is because

$$-\log\ [\mathrm{H}_3\mathrm{O}^{+}] = -\log\ [\mathrm{OH}^{-}] = -\log \sqrt{K_w} = 7.$$

At other temperatures, the center of the scale is different (0 °C corresponds to 7.47; 10 °C 7.27; 20 °C 7.08; 30 °C 6.92; 40 °C 6.77; 50&nbsp ;°C 6.63; 100 °C 6.14). The pH can take on an infinite number of values, at 25 °C it can even be negative with the use of very strong acids, and under suitable conditions it can even exceed the value of 14.

Reason for introduction of pH
The concentration of oxonium ions takes on values in the range of many orders of magnitude, most commonly from $$10^{-1}$$ to $$10^{-14}$$. When specifying such numbers, it is advantageous to specify only the exponent, which is why a logarithmic scale was introduced, since $$\log 10^{-n} = -n \cdot \log 10 = -n$$ applies. At the same time, using logarithms converts multiplication to addition and division to subtraction (log (A · B) = log A + log B, which is a direct consequence of the fact that $$x^a \cdot x^b = x^{ a + b}$$). This fact was of general importance mainly at a time when computers and calculators were not commonly available and technical calculations were performed using a logarithmic ruler.

pH of medium strength acids and bases
Moderately strong acids and bases defy both assumptions from the previous models – complete dissociation cannot be assumed, but the amount of undissociated acid or base cannot be completely neglected either. If we use any of the previous procedures, which are in themselves idealized, i.e. burdened with a certain error, we will move even further away from the real situation, so it is necessary to realize that the error will be several times larger.

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