Question

Both HCl and \(\mathrm{NaOH}\) are strong electrolytes. What is the \(\mathrm{pH}\) of the solution formed by adding \(40 \mathrm{ml}\) of \(0.10 \mathrm{M} \mathrm{NaOH}\) to 10 \(\mathrm{ml}\) of \(0.45 \mathrm{M} \mathrm{HCl} ?\)

Short answer

The pH of the solution formed by adding \(40 \mathrm{ml}\) of \(0.10 \mathrm{M} \mathrm{NaOH}\) to \(10 \mathrm{ml}\) of \(0.45 \mathrm{M} \mathrm{HCl}\) is approximately 2.

Step-by-step solution

Find the moles of HCl and NaOH

To find the moles of reactants, we will use the formula: moles = Molarity × Volume. Remember that the volume should be in liters. Moles of HCl = Molarity of HCl × Volume of HCl Moles of HCl = 0.45 M × 0.010 L = 0.0045 mol Moles of NaOH = Molarity of NaOH × Volume of NaOH Moles of NaOH = 0.10 M × 0.040 L = 0.0040 mol

Determine the amounts of HCl and NaOH after the reaction

As HCl and NaOH are strong electrolytes, they will completely react with each other to form water (H2O) and sodium chloride (NaCl). The limiting reactant will be NaOH since it has fewer moles. After the reaction, both HCl and NaOH will decrease, but there will still be some HCl left. Moles of HCl left = Moles of HCl - Moles of NaOH Moles of HCl left = 0.0045 mol - 0.0040 mol = 0.0005 mol

Calculate the concentration of H⁺ ions

Now that we know the moles of HCl left, we can calculate the concentration of H⁺ ions. To do this, we need to divide the moles of HCl left by the total volume of the solution. Remember that HCl dissociates completely into H⁺ and Cl⁻ ions. Total volume after mixing = Volume of HCl + Volume of NaOH Total volume after mixing = 0.010 L + 0.040 L = 0.050 L Concentration of H⁺ ions = Moles of HCl left / Total volume Concentration of H⁺ ions = 0.0005 mol / 0.050 L = 0.010 M

Calculate the pH of the solution

Finally, we can calculate the pH of the solution using the formula: pH = -log₁₀[H⁺]. Remember that pH is the negative logarithm of the H⁺ ion concentration. pH = -log₁₀(0.010) pH ≈ 2 The pH of the solution formed by adding \(40 \mathrm{ml}\) of \(0.10 \mathrm{M} \mathrm{NaOH}\) to \(10 \mathrm{ml}\) of \(0.45 \mathrm{M} \mathrm{HCl}\) is approximately 2.

Key concepts

pH calculation

Understanding pH is essential when dealing with acid-base reactions. pH is a scale used to determine the acidity or basicity of an aqueous solution. It ranges from 0 to 14, with lower values being more acidic and higher values more basic. A pH of 7 is neutral. The calculation of pH involves the concentration of hydrogen ions \(H^+\) in the solution.
To calculate pH, use the formula: \(-\log_{10}[H^+]\). This gives you a pH that tells you how acidic or basic the solution is. For instance, a pH of 2 indicates a very acidic solution.
In our exercise, after determining the residual \(HCl\) concentration post-reaction, we used its \(H^+\) ion concentration to ascertain the pH. The concentration was calculated by dividing the leftover moles by the total solution volume, and then plugging in the result into the pH formula to finally determine that the solution is quite acidic with a pH of 2.

Strong electrolytes

Strong electrolytes are substances that completely dissociate into ions when dissolved in water. This complete dissociation allows the solution to conduct electricity very well. Common strong electrolytes include strong acids, like \(HCl\), and strong bases, like \(NaOH\). In the context of the exercise, both hydrochloric acid \(HCl\) and sodium hydroxide \(NaOH\) are strong electrolytes.
When \(HCl\) is mixed with \(NaOH\), they react completely to form water and a salt (NaCl in this case). This reaction ensures that neither free \(NaOH\) nor \(HCl\) remains in solution except for any excess HCl, which affects the pH.
Understanding strong electrolytes helps us predict that the reaction goes to completion, resulting in a depletion of one reactant, in our case \(NaOH\), thus driving the calculation of leftover substances and the resulting pH of the solution.

Mole concept

The mole is a fundamental concept in chemistry, serving as the bridge between the atomic scale and the real-world scale of chemical reactions. A mole corresponds to Avogadro's number, \(6.022 \times 10^{23}\), entities, allowing chemists to precisely measure a substance's quantity.
In our exercise, we applied the mole concept to determine the amounts of \(HCl\) and \(NaOH\) in the reaction via their molar concentrations and volumes. This involved using the formula \(\text{moles} = \text{molarity} \times \text{volume}\).
By converting these amounts into moles, we could decide the limiting reactant, which turned out to be \(NaOH\) since it had the lesser number of moles. This informed the rest of the calculations, as we could then determine the concentration of excess hydrogen ions, necessary for calculating pH. Understanding the mole concept is crucial for grasping the amounts and progress of chemical reactions, providing insights into reaction stoichiometry and solution properties.