Rainwater is slightly acidic due to dissolved \(\mathrm{CO}_{2}\). Use the following data to calculate the \(\mathrm{pH}\) of unpolluted rainwater at \(25^{\circ} \mathrm{C}\) : vol \(\%\) in air of \(\mathrm{CO}_{2}=0.040\) vol \(\%\); solubility of \(\mathrm{CO}_{2}\) in pure water at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}=88 \mathrm{~mL} \mathrm{CO}_{2} / 100 . \mathrm{mL} \mathrm{H}_{2} \mathrm{O} ; K_{\mathrm{a} 1}\) of \(\mathrm{H}_{2} \mathrm{CO}_{3}=4.5 \times 10^{-7}\)

The acid dissociation constant, often represented as \(K_a\), is a crucial concept in chemistry. It measures the strength of an acid in solution. Specifically, for carbonic acid \( (\text{H}_2\text{CO}_3)\), the \(K_{a1}\) value tells us how readily it donates protons (H^+) to form bicarbonate ions (HCO_3^-). A smaller \(K_a\) value indicates a weaker acid, meaning it doesn't dissociate much in water. For example, carbonic acid has a \(K_{a1}\) of \(4.5 \times 10^{-7}\), which implies it is a weak acid and only slightly dissociates to give hydrogen ions and bicarbonate ions.
Understanding \(K_a\) helps in determining the pH of a solution, providing insight into how acidic or basic the solution is.

Carbonic acid is formed when carbon dioxide (CO_2) dissolves in water (H_2O). The equation is: \(\text{CO}_2 + \text{H}_2\text{O} \rightleftharpoons \text{H}_2\text{CO}_3\). This weak acid plays a significant role in the carbon cycle and influences the pH of natural waters.
In the given problem, rainwater's pH is affected by dissolved carbon dioxide, forming carbonic acid. Since carbonic acid dissociates slightly, it releases hydrogen ions into the water, making it slightly acidic.
To calculate pH, the concentration of carbonic acid is determined first, which is then used with the acid dissociation constant.

Partial pressure is the pressure exerted by a single gas in a mixture of gases. It is proportional to the concentration of that gas in the mixture. For example, in the problem, we are given that the volume percentage of CO_2 in air is 0.040%, which converts to a partial pressure of 0.0004 atm.
This partial pressure helps determine how much CO_2 will dissolve in water to form carbonic acid. Using Henry's law, we can relate the solubility of CO_2 to its partial pressure, which helps us calculate the concentration of dissolved CO_2.

Solubility is the ability of a substance to dissolve in a solvent. In this problem, it refers to how much CO_2 gas can dissolve in water. Given that the solubility of CO_2 in water at 25°C and 1 atm is 88 mL CO_2 per 100 mL H_2O, we can determine the concentration of dissolved CO_2 under different conditions.
Using the partial pressure of CO_2 (0.0004 atm), we adjust the solubility accordingly to find the actual concentration of CO_2 in water. This concentration is essential for calculating the subsequent formation of carbonic acid and its effect on pH.

Weak acids only partially dissociate in water, releasing fewer hydrogen ions compared to strong acids. As a result, they have higher pH values and lower acid dissociation constants (K_a). Carbonic acid (H_2CO_3) is an example of a weak acid, with a \(K_{a1}\) of 4.5 × 10^(-7).
Understanding the behavior of weak acids is crucial for pH calculations. In this context, the weak dissociation of carbonic acid means that even a small concentration of H_2CO_3 will still result in a slightly acidic solution, which we observe in unpolluted rainwater.
The properties of weak acids help us predict and calculate the resulting pH of solutions they are part of, using their dissociation constants and concentrations.