Problem 36 - Chemistry The Science in Context

Question

Calculate the \(\mathrm{pH}\) and \(\mathrm{pOH}\) of the following solutions: a. \(0.0450 M\) NaOH b. \(0.160 M \mathrm{Ca}(\mathrm{OH})_{2}\) c. a 1: 1 mixture of \(0.0125 M \mathrm{HCl}\) and \(0.0125 M \mathrm{Ca}(\mathrm{OH})_{2}\) d. a 2: 3 mixture of \(0.0125 M \mathrm{HNO}_{3}\) and \(0.0125 \mathrm{MKOH}\)

Step-by-Step Solution

Answer

a. 0.0450 M NaOH solution b. 0.160 M Ca(OH)2 solution c. 1:1 mixture of 0.0125 M HCl and 0.0125 M Ca(OH)2 solution d. 2:3 mixture of 0.0125 M HNO3 and 0.0125 M KOH solution Answer: a. pH ≈ 12.65, pOH ≈ 1.35 b. pH ≈ 13.51, pOH ≈ 0.49 c. pH = 7, pOH = 7 d. pH ≈ 13.30, pOH ≈ 0.70

Step 1: a. Calculating pH and pOH of 0.0450 M NaOH solution

NaOH is a strong base that dissociates completely in water. When it dissociates, it produces OH- ions. Since the concentration of the NaOH solution is 0.0450 M, the concentration of OH- ions will also be 0.0450 M. Now we can use the formula pOH = -log[OH-] to find the pOH: pOH = -log(0.0450) ≈ 1.35 Since pH + pOH = 14, we can find the pH: pH = 14 - pOH = 14 - 1.35 ≈ 12.65

Step 2: b. Calculating pH and pOH of 0.160 M Ca(OH)2 solution

Ca(OH)2 is a strong base that dissociates completely in water, producing 2 moles of OH- ions for every 1 mole of Ca(OH)2. So, the concentration of OH- ions will be 2 * 0.160 M = 0.320 M. Now we can use the formula pOH = -log[OH-]: pOH = -log(0.320) ≈ 0.49 And pH = 14 - pOH = 14 - 0.49 ≈ 13.51

Step 3: c. Calculating pH and pOH of a 1:1 mixture of 0.0125 M HCl and 0.0125 M Ca(OH)2 solution

Since both HCl and Ca(OH)2 are strong acids and bases, they will react with each other to produce water and salt. The balanced equation for the reaction is: 2 HCl + Ca(OH)2 → 2 H2O + CaCl2 As the ratio is 1:1, 0.0125 M HCl will react completely with 0.0125 M Ca(OH)2. There will be no excess acid or base in the solution, and hence, the pH will be neutral and equal to 7. pOH will also be equal to 7.

Step 4: d. Calculating pH and pOH of a 2:3 mixture of 0.0125 M HNO3 and 0.0125 M KOH solution

Given the ratio 2:3, let's calculate the moles of HNO3 and KOH in the mixture: Moles of HNO3 = 2 * 0.0125 = 0.025 mol Moles of KOH = 3 * 0.0125 = 0.0375 mol The balanced reaction equation is: HNO3 + KOH → H2O + KNO3 0.025 mol HNO3 will react with 0.025 mol KOH, leaving an excess of 0.0125 mol KOH in the solution. To find the concentration of OH- ions, we can divide the remaining moles of KOH by the total volume of the mixture, which is 5 * 0.0125 L = 0.0625 L. Concentration of OH- ions = 0.0125 mol / 0.0625 L = 0.20 M Now we can calculate the pOH and pH: pOH = -log(0.20) ≈ 0.70 pH = 14 - pOH = 14 - 0.70 ≈ 13.30

Key Concepts

pH scale

The pH scale is an essential concept in chemistry that measures the acidity or basicity of a solution. It is a logarithmic scale ranging from 0 to 14, with 7 being neutral, values below 7 indicating acidity, and values above 7 indicating basicity. The pH of a solution is calculated using the formula \(\text{pH} = -\log[H^+]\), where \(H^+\) represents the concentration of hydrogen ions in moles per liter.

The scale is inverse to the concentration of hydrogen ions; a low pH means high \(H^+\) concentration (acidic), while a high pH means low \(H^+\) concentration (basic).

For example, lemon juice, with a typical pH of around 2, is acidic, whereas household ammonia, with a pH of about 11, is basic. It's important to note that each whole pH value below or above 7 is tenfold more acidic or basic respectively than the next whole value. Water, at a pH of 7, is considered neutral because the concentration of \(H^+\) and \(OH^-\) ions are equal. Understanding the pH scale helps in predicting the properties of a substance and its reactions in different environments.

acid-base neutralization

Acid-base neutralization is a chemical reaction where an acid and a base react to form water and a salt. This is an example of a double displacement reaction, typically represented by the general equation: \(\text{acid} + \text{base} \rightarrow \text{water} + \text{salt}\).

These reactions occur when the \(H^+\) ions from the acid combine with the \(OH^-\) ions from the base to produce water, while the remaining ions form a salt. The resulting pH of such a reaction is typically neutral, around 7, if equal amounts of acid and base are used. However, if one reactant is in excess, the solution's pH could remain acidic or basic after the reaction.

An everyday example of neutralization is the use of baking soda, a basic substance, to neutralize stomach acid when experiencing heartburn. In a classroom setting, when a student mixes hydrochloric acid (HCl) with sodium hydroxide (NaOH) in equal molar amounts, they witness the neutralization process as the solution reaches a neutral pH.

strong acids and bases

Strong acids and bases are substances that completely dissociate into their ions in water, leading to high conductivity and the ability to neutralize each other when mixed in proper proportions.

For strong acids, common examples include hydrochloric acid (HCl), sulfuric acid (H2SO4), and nitric acid (HNO3). These acids produce a high concentration of \(H^+\) ions when dissolved in water.

Similarly, strong bases such as sodium hydroxide (NaOH) and calcium hydroxide \(Ca(OH)_2\) completely dissociate to release \(OH^-\) ions. The strength of an acid or base is an important factor in calculating the pH and pOH of a solution because it dictates how much the substance will impact the hydrogen or hydroxide ion concentration. Knowing whether an acid or base is strong allows for accurate predictions of the outcome of an acid-base reaction and the resulting pH of the solution.

When a strong acid and a strong base mix, they neutralize each other, potentially resulting in a neutral solution, as demonstrated in the provided exercise with the mixture of HCl and \(Ca(OH)_2\). In contrast, if the reaction involves a mixture with a higher proportion of a strong base, such as the example of HNO3 and KOH, the resulting solution will be basic.