Question

Calculate the pH of the solution that results from mixing \(25.0 \mathrm{mL}\) of \(0.14 \mathrm{M}\) formic acid and \(50.0 \mathrm{mL}\) of \(0.070 \mathrm{M}\) sodium hydroxide.

Short answer

The pH of the solution is 9.28.

Step-by-step solution

Determine the moles of formic acid

To find the moles of formic acid \( ext{HCOOH}\), use the equation \(n = M imes V\), where \(M\) is molarity and \(V\) is volume in liters. For the formic acid: \(n = 0.14 \, \mathrm{M} \times 0.025 \, \mathrm{L} = 0.0035 \, \mathrm{moles}\).

Determine the moles of sodium hydroxide

Using the same formula \(n = M \times V\), calculate the moles of sodium hydroxide \(\text{NaOH}\) present: \(n = 0.070 \, \mathrm{M} \times 0.050 \, \mathrm{L} = 0.0035 \, \mathrm{moles}\).

Identify reaction completion

Formic acid and sodium hydroxide react in a 1:1 ratio. Since the moles of both are equal \(0.0035 \, \mathrm{moles}\), all of each reactant is consumed, forming formate \(\text{HCOO}^-\) and water.

Calculate concentration of formate ion

After the reaction, the solution has a total volume of \(25.0 \, \mathrm{mL} + 50.0 \, \mathrm{mL} = 75.0 \, \mathrm{mL} = 0.075 \, \mathrm{L}\). The concentration of \([\text{HCOO}^-]\) is \(c = \frac{\text{0.0035 moles}}{0.075 \, \mathrm{L}} = 0.0467 \, \mathrm{M}\).

Calculate the pH of the resulting solution

Formate is a base (conjugate base of formic acid), and its presence suggests we have a slightly basic solution. Use the equation \(pH = 14 - pOH\). First, find \(pOH\) using \(\text{K}_w = \text{K}_a \times \text{K}_b\), where \(\text{K}_a = 1.8 \times 10^{-4}\) for formic acid:\[\text{K}_b = \frac{\text{K}_w}{\text{K}_a} = \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-4}} \approx 5.56 \times 10^{-11}\] The equation \(pOH = -\log\left(\sqrt{\text{K}_b \times 0.0467}\right)\) yields \(pOH = 4.72\). Therefore, \(pH = 14 - 4.72 = 9.28\).

Key concepts

Formic Acid

Formic acid, known chemically as HCOOH, is the simplest carboxylic acid. It naturally occurs in some ant species and has a pungent, acrid smell. In chemistry, it is considered a weak acid, meaning it does not completely dissociate in water. This partial dissociation is quantified by its acid dissociation constant, known as the \(K_a\). For formic acid, the \(K_a\) is \(1.8 \times 10^{-4}\). This value tells us that in an aqueous solution, only a small fraction of formic acid molecules will release protons to form hydrogen ions (H⁺) and formate ions (HCOO⁻).
Understanding how formic acid behaves in a solution is crucial for calculating the pH, especially when it reacts with bases like sodium hydroxide. In such reactions, the formic acid will donate its protons to the hydroxide ions. This acid-base reaction results in the formation of water and formate ions, shifting the balance of the solution.

Sodium Hydroxide

Sodium hydroxide (NaOH), commonly known as lye or caustic soda, is a strong base. In contrast to weak acids like formic acid, strong bases fully dissociate in water. So, each NaOH molecule separates into sodium ions (Na⁺) and hydroxide ions (OH⁻).
The strong basic nature and full dissociation property of sodium hydroxide make it an excellent choice for reacting with acids in neutralization reactions. In our example, NaOH neutralizes formic acid by reacting with its available hydrogen ions. This reaction forms water and formate ions. It's this neutralization that allows us to further explore the resulting pH of the solution.

Acid-Base Reaction

An acid-base reaction is a chemical reaction that occurs between an acid and a base. These reactions are fundamental in chemistry, as they help us understand how substances interact and alter each other's properties. In our exercise, the acid-base reaction occurs between formic acid and sodium hydroxide.
Since both components react in a 1:1 molar ratio, all moles of formic acid and sodium hydroxide are consumed. This perfect stoichiometry results in the complete conversion of reactants into products, namely water and formate ions. Understanding this stoichiometric relationship is essential for predicting the final state of the solution and its pH.

Molarity

Molarity is a measure of concentration, denoted by M, representing the number of moles of a solute per liter of solution. It provides a way to express how much of a substance is present in a solution, which is crucial for calculating chemical reactions and understanding their dynamics.
In this exercise, we determined the molarity of formic acid and sodium hydroxide to find out how many moles of each were present in their respective solutions. We used the formula \(n = M \times V\), where \(n\) is the number of moles, \(M\) is molarity, and \(V\) is volume in liters. By knowing the molarity of the remaining formate ions after the reaction, we could ultimately determine the basicity of the solution.

Chemical Equilibrium

Chemical equilibrium refers to a state where the chemical reaction has proceeded to a point that the concentrations of reactants and products remain constant over time. In the case of the formic acid and sodium hydroxide reaction, the equilibrium concept helps us understand why the pH remains stable over time.
After neutralization, the reaction shifts to produce formate ions. The reaction's equilibrium is essentially between the formate ions acting as a base in water, restoring the balance between the formic acid and hydroxide ions. This dynamic balance is crucial for determining the resultant pH of the solution; in this example, it leads to a basic solution with a pH calculated to be 9.28.