Question

Following five solutions of \(\mathrm{KOH}\) were prepared as: first, \(0.1\) mole in \(1 \mathrm{~L} ;\) second. \(0.2\) mole in \(2 \mathrm{~L}\); third, \(0.3\) mole in \(3 \mathrm{~L}\); fourth, \(0.4\) mole in \(4 \mathrm{~L} ;\) fifth, \(0.5\) mole in \(5 \mathrm{~L}\). The \(\mathrm{pH}\) of resultant solution, when all these solutions are mixed, is (a) 2 (b) 1 (c) 13 (d) 7

Short answer

The pH of the resultant solution is 13.

Step-by-step solution

Calculate total moles of KOH

Calculate the total moles of KOH by summing the moles of each solution. Since each solution is prepared by dissolving n moles of KOH in n liters of water, the total moles of KOH would be the sum of the moles from all five solutions: \(0.1 + 0.2 + 0.3 + 0.4 + 0.5 = 1.5\) moles.

Calculate total volume of the solution

The total volume is the sum of the volumes of individual solutions. Since each solution has a volume equal to the number of liters corresponding to the number of moles, the total volume will be: \(1 + 2 + 3 + 4 + 5 = 15\) liters.

Calculate the concentration of the resultant solution

The concentration (\( C \) in moles per liter) of the resultant KOH solution is calculated by dividing the total moles of solute by the total volume of the solution: \( C = \frac{1.5 \text{ moles}}{15 \text{ liters}} = 0.1 \text{ M}\).

Find the \(\text{pOH}\) of the solution

Since KOH is a strong base, it dissociates completely in water. The \(\text{pOH}\) can be found using the formula: \(\text{pOH} = -\log[OH^-]\), where \([OH^-]\) is the concentration of hydroxide ions which equals the concentration of KOH. Thus, \(\text{pOH} = -\log[0.1] = 1\).

Calculate the pH of the solution

The pH is related to the \(\text{pOH}\) by the relation \(14 = \text{pH} + \text{pOH}\). Therefore, the \(\text{pH}\) of the solution is: \(\text{pH} = 14 - \text{pOH} = 14 - 1 = 13\).

Key concepts

Chemical Concentration

Understanding chemical concentration is essential for conducting experiments and analyzing results in chemistry. Concentration refers to the amount of a substance (solute) dissolved in a certain volume of solvent, typically expressed in moles per liter (M), which is also known as molarity.

The calculation of concentration involves determining the amount of substance within a given volume. As seen in our exercise with KOH solutions, the moles of KOH were added together, and the total volume of the solutions was calculated. By performing a simple division of moles by volume, the molarity of the solution was found. For the mixed solutions, despite the varying volumes, the concentration was consistent because the amount of solute and solvent increased proportionally.

In lab settings, accurate concentration measurements are crucial because they can significantly affect the reaction's outcome. Inadequacies in calculating concentrations can lead to ineffective or hazardous results, especially when dealing with strong acids or bases.

pOH and pH Relationship

Understanding the relationship between pOH and pH is an invaluable part of chemistry, particularly when working with acid-base reactions. The pH scale measures how acidic or basic a solution is, ranging from 0 to 14, with lower values being acidic, higher values being basic, and 7 being neutral.

The pH and pOH of a solution are interconnected. The pOH represents the concentration of hydroxide ions (\(OH^-\)). The pH instead focuses on the concentration of hydrogen ions (\(H^+\)). For any aqueous solution at 25°C, their sum is always constant, equal to 14 (which is derived from the product of the dissociation constants of water).

In our exercise, we used the formula \(pOH = -\log[OH^-]\) to determine the pOH from the KOH concentration. Since \(pOH + pH = 14\), we can rearrange this to find \(pH = 14 - pOH\) once we have either the pOH or pH value. This crucial relationship allows us to convert back and forth between the two values effortlessly, which is indispensable in acid-base chemistry.

Dissociation of Strong Base

The dissociation of strong bases such as KOH is another key aspect of understanding chemical reactions. In aqueous solutions, strong bases dissociate completely into their ions. This means that each molecule of a strong base will produce one hydroxide ion (\(OH^-\)) and one metal cation (such as \(K^+\) in the case of KOH).

Complete dissociation is important to recognize because it simplifies the calculation of the concentration of hydroxide ions. As demonstrated in the exercise, the concentration of KOH is equivalent to the concentration of hydroxide ions, as one mole of KOH yields one mole of \(OH^-\).

This property of strong bases contrasts with weak bases, which only partially dissociate in solution. The complete dissociation maximizes the pH effect of the strong base, making such solutions highly basic. Hence, the pH calculation becomes straightforward by directly relating it to the molarity of the original base before dissociation.