Question

In a particular fresh water sample, the concentrations of cations and anions are (in \(\mu \mathrm{mol} \mathrm{L}^{-1}\) ): \(\begin{array}{lrlr}\mathrm{Na}^{+} & 33 & \mathrm{Cl} & 120 \\\ \mathrm{~K}^{+} & 4 & \mathrm{NO}_{3}^{-} & 13 \\ \mathrm{Mg}^{2+} & 31 & \mathrm{HCO}_{3}^{-} & 270 \\ \mathrm{Ca}^{2+} & 160 & \mathrm{CO}_{3}^{2} & 0.67 \\ & & \mathrm{SO}_{4}^{2-} & 11\end{array}\) Compare the concentration of total positive and negative charge in the solution. Assume that the difference is due to hydronium or hydroxyl ion, and calculate the \(\mathrm{pH}\).

Short answer

pH = 8.87

Step-by-step solution

Calculate Total Positive Charge

First, calculate the total positive charge contributed by the cations in the solution.- For Na\(^+\), the concentration is 33 \(\mu \mathrm{mol} \mathrm{L}^{-1}\) and the charge is +1.- For K\(^+\), the concentration is 4 \(\mu \mathrm{mol} \mathrm{L}^{-1}\) and the charge is +1.- For Mg\(^{2+}\), the concentration is 31 \(\mu \mathrm{mol} \mathrm{L}^{-1}\) and the charge is +2.- For Ca\(^{2+}\), the concentration is 160 \(\mu \mathrm{mol} \mathrm{L}^{-1}\) and the charge is +2.Calculate the total positive charge:\[\text{Total Positive Charge} = (33 \times 1) + (4 \times 1) + (31 \times 2) + (160 \times 2)\]\[= 33 + 4 + 62 + 320 = 419 \; \mu \mathrm{eq} \mathrm{L}^{-1}\]

Calculate Total Negative Charge

Next, calculate the total negative charge contributed by the anions in the solution.- For Cl\(^-\), the concentration is 120 \(\mu \mathrm{mol} \mathrm{L}^{-1}\) and the charge is -1.- For NO\(_3^-\), the concentration is 13 \(\mu \mathrm{mol} \mathrm{L}^{-1}\) and the charge is -1.- For HCO\(_3^-\), the concentration is 270 \(\mu \mathrm{mol} \mathrm{L}^{-1}\) and the charge is -1.- For CO\(_3^{2-}\), the concentration is 0.67 \(\mu \mathrm{mol} \mathrm{L}^{-1}\) and the charge is -2.- For SO\(_4^{2-}\), the concentration is 11 \(\mu \mathrm{mol} \mathrm{L}^{-1}\) and the charge is -2.Calculate the total negative charge:\[\text{Total Negative Charge} = (120 \times 1) + (13 \times 1) + (270 \times 1) + (0.67 \times 2) + (11 \times 2)\]\[= 120 + 13 + 270 + 1.34 + 22 = 426.34 \; \mu \mathrm{eq} \mathrm{L}^{-1}\]

Calculate Charge Difference

The charge difference is the difference between the total positive charge and the total negative charge:\[\text{Charge Difference} = 426.34 \; \mu \mathrm{eq} \mathrm{L}^{-1} - 419 \; \mu \mathrm{eq} \mathrm{L}^{-1} = 7.34 \; \mu \mathrm{eq} \mathrm{L}^{-1}\]This difference is assumed to be due to either hydronium ions \([\text{H}^+]\) or hydroxyl ions \([\text{OH}^-]\).

Calculate pH of the Solution

Since the anions exceed the cations, the solution is slightly basic. This indicates the presence of excess hydroxyl ions \([\text{OH}^-]\).The concentration of \([\text{OH}^-]\) is equivalent to the charge difference:\[[\text{OH}^-] = 7.34 \; \mu \mathrm{mol} \mathrm{L}^{-1} \times 10^{-6} \; \mathrm{mol} \mathrm{L}^{-1}\]The relation between \([\text{OH}^-]\) concentration and \(\text{pH}\) is given by:\[\text{pOH} = -\log([\text{OH}^-])\]Calculate the \(\text{pOH}\):\[\text{pOH} = -\log(7.34 \times 10^{-6}) \approx 5.13\]The relation between \(\text{pH}\) and \(\text{pOH}\) is:\[\text{pH} = 14 - \text{pOH} = 14 - 5.13 = 8.87\]

Final Step: Conclusion

The pH of the solution indicates it is slightly basic due to the excess OH\(^-\) ions.

Key concepts

Ion Concentration

Understanding ion concentration is crucial for analyzing chemical equilibrium in solutions. Ions are charged particles that arise from dissolved substances. They can carry either a positive or negative charge, known as cations and anions, respectively. To find ion concentration, we measure the amount of ions present in a volume of the solution, usually in \( \mu \mathrm{mol} \mathrm{L}^{-1} \), which helps in understanding the nature of the solution.In our exercise, we measure concentrations for both cations like Na\(^+\), K\(^+\), Mg\(^{2+}\), and Ca\(^{2+}\) and anions such as Cl\(^-\), NO\(_3^-\), HCO\(_3^-\), CO\(_3^{2-}\), and SO\(_4^{2-}\). Knowing these concentrations allows us to calculate the total positive and negative charges in the solution.

Charge Balance

Charge balance is an essential concept when studying water chemistry. It accounts for the equality of total charges from cations and anions in a solution.In a chemically stable solution, the sum of positive charges (cations) should equal the sum of negative charges (anions). However, small differences can occur due to hydronium \( [\text{H}^+] \) or hydroxyl ions \( [\text{OH}^-] \), which can influence the solution's pH.To calculate the charge balance, we sum the charges contributed by each ion present in the solution. In practice, adding all the products of ion concentration and their respective charges provides a clear view of the overall charge balance. Our exercise identifies minor charge differences, indicating a basic solution with excess hydroxyl ions.

pH Calculation

Calculating the pH of a solution is an important step in understanding its acidity or basicity. The pH is a measure of the hydrogen ion concentration, with lower values being acidic, higher values basic, and a pH of 7 being neutral.In the given solution, we calculated a charge difference of 7.34 \( \mu \mathrm{eq} \mathrm{L}^{-1} \), suggesting a slight excess of negative charge from OH\(^-\) ions. We used this concentration to find the pOH first:\[\text{pOH} = -\log(7.34 \times 10^{-6})\]Finally, with the relation \( \text{pH} + \text{pOH} = 14 \), we can deduce a pH of 8.87, indicating the solution is slightly basic due to the presence of excess hydroxyl ions.

Water Chemistry

Water chemistry involves understanding how different ions and molecules interact in aquatic environments. Chemical equilibrium is particularly important in natural water bodies where a complex array of ions exist. In water chemistry, the interplay between different ions dictates the chemical behavior of the solution. Factors such as pH, temperature, and the concentration of various ions play key roles in determining the solution's overall properties. By analyzing a water sample's ion concentrations and charge balance, we gain insights into potential environmental impacts or the usability of the water. Moreover, understanding how ions behave allows us to predict changes in water chemistry under different conditions, crucial for fields such as environmental science and chemical engineering.