Problem 45 - Chemistry: The Central Science

Question

Calculate the pH of each of the following strong acid solutions: (a) \(8.5 \times 10^{-3} \mathrm{M} \mathrm{HBr}\), (b) \(1.52 \mathrm{~g}\) of \(\mathrm{HNO}_{3}\) in \(575 \mathrm{~mL}\) of solution, \((\mathrm{c}) 5.00 \mathrm{~mL}\) of \(0.250 \mathrm{M} \mathrm{HClO}_{4}\) diluted to \(50.0 \mathrm{~mL}\), (d) a solution formed by mixing \(10.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{HBr}\) with \(20.0 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{HCl}\).

Step-by-Step Solution

Answer

The pH values of the strong acid solutions are as follows: (a) 2.07, (b) 1.10, (c) 1.40, and (d) 1.17.

Step 1: Find the concentration of H+ ions

HBr is a strong acid, which means it will ionize 100% in the solution. The concentration of H+ ions will be equal to the concentration of HBr. In this case, the concentration of H+ ions is \(8.5 \times 10^{-3} \mathrm{M}\).

Step 2: Calculate the pH

Now, we'll use the pH formula to find the pH of this solution: \(pH = -\log[H^+]\) \(pH = -\log(8.5 \times 10^{-3})\) The pH of solution (a) is approximately 2.07. ## Solution (b): 1.52 g of HNO3 in 575 mL of solution ##

Step 1: Find the concentration of H+ ions

First, we need to convert the mass of HNO3 to moles. We know that the molar mass of HNO3 is approximately 63 g/mol. Therefore, the moles of HNO3 are: Moles of HNO3 = mass of HNO3 / molar mass of HNO3 = \(\frac{1.52}{63}\) Now, to find the concentration of HNO3 in the solution, we need to divide the moles of HNO3 by the volume of the solution in liters: Concentration of HNO3 = moles of HNO3 / volume of the solution in L = \(\frac{\frac{1.52}{63}}{0.575}\) Since HNO3 is a strong acid, the concentration of H+ ions is equal to the concentration of HNO3.

Step 2: Calculate the pH

Now, we'll use the pH formula to find the pH of this solution: \(pH = -\log[H^+]\) \(pH = -\log\left(\frac{\frac{1.52}{63}}{0.575}\right)\) The pH of solution (b) is approximately 1.10. ## Solution (c): 5.00 mL of 0.250 M HClO4 diluted to 50.0 mL ##

Step 1: Find the concentration of H+ ions

Diluting a solution does not change the moles of solute present. Therefore, let's first calculate the moles of HClO4: Moles of HClO4 = original_volume x original_concentration = 5.00 mL x 0.250 M (Don't forget to convert the volume from mL to L: 5.00 mL = 0.00500 L) Moles of HClO4 = 0.00500 L x 0.250 M = 0.00125 mol Now, we will find the new concentration, considering the diluted solution: New concentration = moles of HClO4 / diluted volume = \(\frac{0.00125}{0.0500}\) Since HClO4 is a strong acid, the concentration of H+ ions is equal to the concentration of HClO4.

Step 2: Calculate the pH

Now, we'll use the pH formula to find the pH of this solution: \(pH = -\log[H^+]\) \(pH = -\log\left(\frac{0.00125}{0.0500}\right)\) The pH of solution (c) is approximately 1.40. ## Solution (d): A solution formed by mixing 10.0 mL of 0.100 M HBr with 20.0 mL of 0.200 M HCl ##

Step 1: Find the moles of H+ ions

First, we'll find the moles of H+ ions from each acid separately. Moles of H+ from HBr = original_volume x concentration = 10.0 mL x 0.100 M (Don't forget to convert the volume from mL to L: 10.0 mL = 0.0100 L) Moles of H+ from HBr = 0.0100 x 0.100 = 0.00100 mol Moles of H+ from HCl = original_volume x concentration = 20.0 mL x 0.200 M (Don't forget to convert the volume from mL to L: 20.0 mL = 0.0200 L) Moles of H+ from HCl = 0.0200 x 0.200 = 0.00400 mol Now, let's find the total moles of H+ ions Total moles of H+ ions = moles of H+ from HBr + moles of H+ from HCl = 0.00100 + 0.00400 = 0.00500 mol

Step 2: Find the concentration of H+ ions

The total volume of the mixed solution is 10.0 mL + 20.0 mL = 30.0 mL (0.0300 L). Therefore, the concentration of H+ ions is: \[H^+]=\frac{0.00500 \text{ mol}}{0.0300 \text L} \]

Step 3: Calculate the pH

Now, we'll use the pH formula to find the pH of this solution: \(pH = -\log[H^+]\) \(pH = -\log\left(\frac{0.00500}{0.0300}\right)\) The pH of solution (d) is approximately 1.17.

Key Concepts

pH Calculation

Understanding the calculation of pH is crucial for those studying chemistry, especially when dealing with acidic or basic solutions. The pH scale is a measure of the acidity or alkalinity of an aqueous solution. It ranges from 0 to 14, with 7 being neutral pH, values less than 7 indicating acidity, and values greater than 7 indicating alkalinity.

Understanding pH is essential in many chemical processes including reaction kinetics and enzyme activity in biology. To calculate the pH, we use the formula: \[\begin{equation}\text{pH} = -\log[H^+]\end{equation}\]where \( [H^+] \) is the concentration of hydrogen ions in moles per liter (M). The \( \log \) here refers to the base 10 logarithm. Calculating pH involves only two steps: identifying the concentration of hydrogen ions and then applying the formula. It's a straightforward process with strong acids, as they fully dissociate in water.

Strong Acid Ionization

Strong acids are unique because they ionize completely in solution. This means that the acid molecules dissociate fully, releasing all of their hydrogen ions into the solution. Due to this complete ionization, the concentration of hydrogen ions \( [H^+] \) is equal to the original concentration of the strong acid. When calculating the pH of a strong acid solution, one can assume that there is a direct one-to-one relationship between the concentration of the original acid and the resulting hydrogen ions.

For instance, if we have a 1 M solution of hydrochloric acid (HCl), we can say with certainty that the concentration of \( [H^+] \) is also 1 M. This property simplifies the calculation of pH for strong acids, as we don't need to take into account any equilibrium constants or degrees of ionization, which would be the case for weak acids.

Acid Concentration

In the context of pH calculations, acid concentration refers to the molarity (M) of an acid in a given solution. Molarity is defined as the number of moles of a solute per liter of solution. It is a key factor when determining the pH of a solution, as the pH is dependent on the concentration of hydrogen ions released by the acid into the solution.

When working with different formats of data, such as the mass of an acid or the volume of a diluted solution, it's essential to convert these values into molarity. For instance, to find the molarity from mass, you must divide the given mass of the acid by its molar mass, and then divide by the volume of the solution in liters. If dilution is involved, you must adjust the concentration to account for the change in volume while remembering that the moles of acid remain constant. High precision in measuring these concentrations is imperative, as small changes can lead to significant variations in pH.