Problem 29 - Chemistry: Principles and Reactions

Question

What is the \(\mathrm{pH}\) of a solution obtained by adding \(5.00 \mathrm{~g}\) of \(\mathrm{HI}\) to \(295 \mathrm{~mL}\) of a \(0.786 M\) solution of \(\mathrm{HNO}_{3} ?\) Assume that the HI addition does not change the volume of the resulting solution.

Step-by-Step Solution

Answer

Answer: The pH of the solution is approximately 0.04.

Step 1: Calculate the moles of HI and HNO3 in the solution.

First, we'll convert the mass of HI in grams to moles and find the moles of HNO3 in the given volume of the solution. The molar mass of HI is (1.01 g/mol for H) + (126.9 g/mol for I) = 127.91 g/mol. Moles of HI = (5.00 g) / (127.91 g/mol) = 0.0391 mol Moles of HNO3 = (0.786 mol/L) * (0.295 L) = 0.2319 mol

Step 2: Calculate the concentrations of HI and HNO3.

Since the volume of the solution does not change, we can use the moles calculated previously to find the concentrations of both acids in the resulting solution. Concentration of HI = (0.0391 mol) / (0.295 L) = 0.1325 M Concentration of HNO3 = (0.2319 mol) / (0.295 L) = 0.786 M

Step 3: Calculate the total concentration of H+ ions.

Both HI and HNO3 are strong acids, so the total concentration of H+ ions in the solution will be the sum of their individual concentrations. [H+] = (0.1325 M from HI) + (0.786 M from HNO3) = 0.9185 M

Step 4: Calculate the pH of the solution.

Now, we'll use the pH formula to calculate the pH of the solution: pH = -log10([H+]) pH = -log10(0.9185) ≈ 0.04 The pH of the solution obtained by adding 5.00 g of HI to 295 mL of a 0.786 M solution of HNO3 is approximately 0.04.

Key Concepts

Understanding Strong Acids

Strong acids are substances that completely dissociate into ions when they are dissolved in water. This characteristic is what makes them

Molarity and Its Role in pH Calculation

Molarity, denoted as M, is a way to express the concentration of a solution. It is defined as the number of moles of a solute per liter of solution. In pH calculations, molarity is used to determine the concentration of H⁺ ions in an acidic solution. The higher the molarity of an acid, the higher the H⁺ ion concentration, and therefore, the lower the pH value.

In the example from the textbook, molarity plays a central role. To find the pH of the resulting solution after combining HI and HNO₃, we first need to calculate the molarity of each acid separately. This is accomplished by dividing the number of moles of acid by the volume of the solution in liters. Even when two solutions are combined, as long as the total volume does not change significantly, we can assume that the resulting molarity is simply the sum of the molarities of the individual acids.

H+ Ion Concentration in pH Calculations

The concentration of H⁺ ions in a solution is the driving factor behind the calculation of pH. For strong acids like HI and HNO₃, every mole of acid will contribute one mole of H⁺ ions to the solution, due to complete dissociation. This allows for a straightforward calculation of the H⁺ ion concentration by summing up the molarities of all the strong acids present.

When a strong acid is diluted or mixed with another strong acid solution, the resulting H⁺ ion concentration is crucial for determining the pH. Our exercise illustrates this concept by combining the moles of H⁺ ions from both HI and HNO₃ to get the total concentration, which is then used directly in the pH formula.

The pH Formula

The pH of a solution is a measure of its acidity or alkalinity on a logarithmic scale. The pH formula is a convenient way to express H⁺ ion concentration as a single number:

10([H⁺])

Where [H⁺] represents the molarity of H⁺ ions in the solution. The pH scale typically ranges from 0 to 14, with lower values indicating more acidic and higher values more alkaline solutions. A pH of 7 is considered neutral.

In the exercise's final step, after obtaining the total H⁺ ion concentration, we use the pH formula to arrive at a numerical value which represents the acidity of the mixed acid solution. The calculation reveals that the solution is highly acidic, with a pH close to 0, reflecting the strong acidic nature of both HI and HNO₃.