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Calculating pH is fundamental in understanding acid-base equilibrium. pH is a measure of the acidity or basicity of a solution. It is defined as the negative logarithm of the hydrogen ion concentration: \( \text{pH} = -\log [\text{H}^+] \). This means that if you know the concentration of hydrogen ions in a solution, you can find its pH by using a calculator to compute the logarithm.
For instance, in this exercise, the concentration was calculated to be \(1.7 \times 10^{-2}\) M. By plugging this value into the formula, we get an initial pH of approximately 1.77. Understanding how to manipulate this formula is crucial when adjusting the pH of solutions, such as adding HCl to decrease pH.

• Low pH values (< 7) indicate acidic solutions.
• pH of exactly 7 signifies a neutral solution.
• High pH values (> 7) indicate basic solutions.

When the pH decreases by 1 unit, the hydrogen ion concentration increases tenfold. This is critical to grasp when predicting how much acid is needed to achieve desired changes in pH.

The equilibrium constant, especially the acid dissociation constant \(K_a\), is key to understanding how acids ionize in solution. The \(K_a\) value measures the strength of an acid in solution. It tells us how well an acid can donate protons to a base. Formic acid has a \(K_a\) of \(3.0 \times 10^{-4}\), indicating it's a weak acid because it ionizes partially in water.
To find the hydrogen ion concentration, we use the formula: \[\text{HCOOH} \rightleftharpoons \text{H}^+ + \text{HCOO}^-\]\( K_a = \frac{[\text{H}^+][\text{HCOO}^-]}{[\text{HCOOH}]}\)
This equilibrium equation helps set up the relationship between the concentrations of reactants and products at equilibrium. By solving this equation, we find the concentration of \([\text{H}^+]\) at equilibrium. It’s important to apply simplifying assumptions, like \([\text{HCOOH}]\) remaining mostly unchanged, when the acid is weak and the equilibrium concentration is small compared to the initial concentration.
This concept is pivotal when predicting how a system responds to changes, such as adding more acid to shift the equilibrium.

Hydrogen ion concentration \([\text{H}^+]\) is a direct measure of a solution's acidity. The greater this concentration, the more acidic the solution. In the given exercise, changes in \([\text{H}^+]\) are essential to understand how much HCl gas is needed to achieve the desired pH.
Initially, the concentration was found to be \(1.7 \times 10^{-2}\) M. With a target pH drop of 1 unit, the \([\text{H}^+]\) needs to increase to approximately \(1.7 \times 10^{-1}\) M. The difference, \(1.53 \times 10^{-1}\) M, indicates how much more hydrogen ion concentration is needed.
This increase can be achieved through the addition of HCl, which dissociates completely in solution, directly contributing to the \([\text{H}^+]\). Hence, the volume of gas needed is calculated based on this change.
Ensuring clarity around these concentration changes is crucial for effective pH regulation, allowing calculations to directly inform how chemical additions will impact a system.