What is the \(\mathrm{pH}\) at \(25^{\circ} \mathrm{C}\) of water saturated with \(\mathrm{CO}_{2}\) at a partial pressure of 1.10 atm? The Henry's law constant for \(\mathrm{CO}_{2}\) at \(25^{\circ} \mathrm{C}\) is \(3.1 \times 10^{-2} \mathrm{mol} / \mathrm{L}\) -atm.

When we talk about the solubility of gases in liquids, Henry's law is a fundamental concept. This law states that at a constant temperature, the concentration of a dissolved gas in a liquid is directly proportional to the partial pressure of that gas above the liquid. The formula for Henry's law is expressed as:
\[C = k_H P\]
where \( C \) is the concentration of the dissolved gas, \( k_H \) is Henry's law constant specific to the gas, and \( P \) is the partial pressure of the gas.In our exercise, we use Henry's law to calculate the concentration of carbon dioxide (\(CO_2\)) dissolved in water at a given partial pressure. Understanding this step is crucial for further determining the behaviour of \(CO_2\) in the water, including its conversion to carbonic acid.

The equilibrium concentration is the amount of a substance present in a solution at equilibrium. Equilibrium is the state where the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of the reactants and products over time. In the context of dissolved \(CO_2\), once it reaches equilibrium with water, we have a constant concentration of carbonic acid formed from \(CO_2\).In our problem, we first calculate the initial concentration of \(CO_2\) using Henry's law. As the \(CO_2\) reacts with water to form carbonic acid (\(H_2CO_3\)), the concentrations of the reactants and products change until they reach an equilibrium. The concentrations at this point are essential to calculate the pH of the solution, as they dictate the number of hydrogen ions (\(H^+\)) in the solution.

The dissociation constant, represented by \(K_a\), is a measure of the strength of an acid in solution. It reflects the degree to which an acid dissociates into its ions - in our case, carbonic acid (\(H_2CO_3\)) dissociating into hydrogen ions (\(H^+\)) and bicarbonate ions (\(HCO_3^-\)). A low \(K_a\) value indicates a weak acid, which only partially dissociates in solution.When we approach the exercise, we use the known \(K_a\) value of carbonic acid to set up an ICE (Initial, Change, Equilibrium) table and determine the equilibrium concentrations of the ions. This step is important because the concentration of \(H^+\) directly determines the acidity or the pH of our solution. For a weak acid like carbonic acid, we often assume that the change in concentration due to dissociation (\(x\)) is small compared to the initial concentration, which simplifies our calculations.

Carbonic acid (\(H_2CO_3\)) is a weak acid formed when carbon dioxide (\(CO_2\)) dissolves in water. It plays a significant role in the body's buffering system and in environmental chemistry, contributing to the acidity of natural waters. In chemical equilibrium, carbonic acid can dissociate into hydrogen ions (\(H^+\)) and bicarbonate ions (\(HCO_3^-\)), which is a reversible reaction:

\[\(CO_2(g) + H_2O(l) \rightleftharpoons H_2CO_3(aq) \rightleftharpoons H^+(aq) + HCO_3^-(aq)\)\]

The extent of this reaction depends on the dissociation constant \(K_a\) and the starting concentration of dissolved \(CO_2\), which we calculate using Henry's law. As carbonic acid dissociates into ions, it impacts the pH of the solution, causing the water to become more acidic. Thus, understanding the properties of carbonic acid is key to predicting the pH of CO2-saturated water.