Problem 112 - Chemistry An Atoms First Approach

Question

Consider a solution formed by mixing \(50.0 \mathrm{mL}\) of \(0.100 \mathrm{M}\) \(\mathrm{H}_{2} \mathrm{SO}_{4}, 30.0 \mathrm{mL}\) of \(0.100 \mathrm{M} \mathrm{HOCl}, 25.0 \mathrm{mL}\) of \(0.200 \mathrm{M} \mathrm{NaOH}\), \(25.0 \mathrm{mL}\) of \(0.100 M \mathrm{Ba}(\mathrm{OH})_{2},\) and \(10.0 \mathrm{mL}\) of \(0.150 \mathrm{M} \mathrm{KOH}\) Calculate the pH of this solution.

Step-by-Step Solution

Answer

The pH of the solution is calculated by first finding the moles of each individual species in their respective solutions. Then the net moles of \(H^+\) and \(OH^-\) ions are calculated leading to the determination that the solution will be acidic since the moles of \(OH^-\) ions are less than the moles of \(H^+\) ions. After calculating the total volume of the mixture, we find the net concentration of \(H^+\) ions, which turns out to be 0.09286 M. Finally, using the formula pH = -log[H+], the pH of the solution is found to be approximately 1.032.

Step 1: Calculate moles of each species

First, let's calculate the moles of each species in their individual solutions.formula is Moles = Molarity × Volume (in L): 1. \(H_2SO_4\) moles: \( 0.100\,\text{M} \times 0.050\,\text{L} = 0.005\,\text{moles} \) Since there are 2 moles of H+ ions in 1 mole of \(H_2SO_4\): moles of H+ ions from \(H_2SO_4\): \( 0.005\,\text{moles} \times 2 = 0.010\,\text{moles} \) 2. \(HOCl\) moles: \( 0.100\,\text{M} \times 0.030\,\text{L} = 0.003\,\text{moles} \) 3. \(NaOH\) moles: \( 0.200\,\text{M} \times 0.025\,\text{L} = 0.005\,\text{moles} \) 4. \(Ba(OH)_2\) moles: \( 0.100\,\text{M} \times 0.025\,\text{L} = 0.0025\,\text{moles} \) Since there are 2 moles of OH- ions in 1 mole of \(Ba(OH)_2\): moles of OH- ions from \(Ba(OH)_2\): \( 0.0025\,\text{moles} \times 2 = 0.005\,\text{moles} \) 5. \(KOH\) moles: \( 0.150\,\text{M} \times 0.010\,\text{L} = 0.0015\,\text{moles} \)

Step 2: Calculate net moles of H+ and OH- ions

Now, let's calculate the net moles of H+ and OH- ions in the mixture: Net moles of H+ ions: \(0.010\,\text{moles} + 0.003\,\text{moles} = 0.013\,\text{moles}\) Net moles of OH- ions: \(0.005\,\text{moles} + 0.005\,\text{moles} + 0.0015\,\text{moles} = 0.0115\,\text{moles}\) Since the moles of OH- ions are less than the moles of H+ ions, we will have an acidic solution.

Step 3: Calculate total volume and H+ concentration

Next, let's calculate the total volume of the mixture: \(0.050\,\text{L} + 0.030\,\text{L } + 0.025\,\text{L} + 0.025\,\text{L} + 0.010\,\text{L} = 0.140\,\text{L}\) Now we can calculate the net concentration of H+ ions, which is: Net H+ moles \(÷\) Total Volume = Net H+ concentration \(0.013\,\text{moles} ÷ 0.140\,\text{L} = 0.09286\,\text{M}\) (rounded to 5 decimal places)

Step 4: Calculate the pH of the solution

Finally, to calculate the pH of the solution, use the formula pH = -log[H+]: pH =\(-\log{(0.09286)}\approx 1.032\) (rounded to 3 decimal places) So, the pH of this solution is approximately 1.032.

Key Concepts

Molarity

Molarity is a key concept in chemistry, especially when dealing with solutions. It refers to the concentration of a solute in a solution. More specifically, it is the number of moles of a substance dissolved in one liter of solution. This is expressed with the unit \( ext{M (molar)}\). Understanding molarity is essential for calculating how much of a substance is present in the solution.

For example, in the problem we have, the molarity of each component in the solution (such as \(H_2SO_4\) and \(NaOH\)) was used to calculate the number of moles. The formula \([ ext{Moles} = ext{Molarity} \times ext{Volume in L}]\) helps us determine how these components will interact during a chemical reaction.

Acid-Base Reaction

Acid-base reactions are fundamental chemical reactions where an acid reacts with a base. This leads to the formation of water and a salt. In the context of this exercise, the goal is to determine the pH of the solution formed when mixing various acidic and basic solutions.

Acids, such as \(H_2SO_4\), donate \( ext{H}^+\) ions, while bases like \(NaOH\) donate \( ext{OH}^-\) ions. When mixed, these ions combine to form water, impacting the pH level of the solution. In our specific example, the solution is slightly acidic, as indicated by the net positive concentration of \( ext{H}^+\) ions.

Solution Concentration

Solution concentration tells us how much solute is present in a given volume of solution. It is an integral part of understanding how solutions behave and how they interact in chemical reactions. The concentration is often expressed using molarity, which provides a clear picture of the solution's strength or weakness.

In our exercise, various solutions with specific concentrations were combined. Calculating each solute's contribution helps predict the final mixture's behavior. Through this process, we can assess which ions dominate, influencing whether the solution is acidic or basic.

Chemistry Problem-Solving

Problem-solving in chemistry can be approached systematically by breaking the problem into clear steps. Understanding and calculating each component's molarity and then combining these to evaluate the net effect is crucial.

For example, the step-by-step solution involves:

• Calculating the moles of each component using their molarity and volume.
• Determining the net moles of \( ext{H}^+\) and \( ext{OH}^-\) ions.
• Using these values to evaluate the solution's overall pH.

Each of these steps builds on the previous, providing a comprehensive answer to the problem and enhancing your problem-solving skills in chemistry.