Problem 13
Question
A solution contains \(4.25 \mathrm{~g}\) ammonia per \(250.0 \mathrm{~m}\) lof solution. Electrical conductivity measurement at \(25^{\circ} \mathrm{C}\) show that \(0.40 \%\) of the ammonia has reacted with water. The pH of the solution is \((\log 2=0.3)\) (a) \(11.6\) (b) \(2.4\) (c) \(12.6\) (d) \(10.6\)
Step-by-Step Solution
Verified Answer
The pH of the solution is 11.6.
1Step 1: Calculate the amount of ammonia that reacted
Calculate the mass of ammonia that has reacted with water, which is 0.4% of the total ammonia present in the solution. The total mass of ammonia is 4.25 g. The mass of reacted ammonia is given by 0.004 * 4.25 g.
2Step 2: Determine the concentration of NH4+ ions
The reacted ammonia forms ammonium ions NH4+. The mass of NH4+ ions is the same as the mass of reacted ammonia. To find the concentration in moles per liter, divide the mass of NH4+ ions by the molar mass of ammonia (NH3), which is approximately 17 g/mol, and then divide by the volume of the solution in liters.
3Step 3: Calculate the concentration of OH- ions
Ammonia is a weak base, and the reaction of ammonia with water produces hydroxide ions (OH-). Since a small amount (0.40%) of ammonia reacts with water, it can be assumed that the concentration of OH- produced is equal to the concentration of NH4+ ions.
4Step 4: Use the pOH to find the pH
Use the pOH formula, which is pOH = -log[OH-], to calculate the pOH of the solution. Then, use the relation pH + pOH = 14 (at 25 degrees Celsius) to find the pH of the solution.
5Step 5: Compare pH with given options
After calculating the pH, compare the result with the given options (a) 11.6, (b) 2.4, (c) 12.6, (d) 10.6 to find the correct answer.
Key Concepts
Ammonia in Aqueous SolutionElectrical Conductivity MeasurementWeak Base EquilibriapH and pOH Relationship
Ammonia in Aqueous Solution
When ammonia (\r(\(NH_3\))) is dissolved in water, it creates an aqueous solution that exhibits basic properties. This occurs due to the reaction where ammonia, a weak base, accepts protons from water molecules forming hydroxide ions (\r(\(OH^-\))) and ammonium ions (\r(\(NH_4^+\))). An important aspect of this process is that ammonia in water is only partially dissociated because of its weak basicity.
\rUnderstanding this behavior is essential when calculating the pH of such solutions, as we must account for only the small fraction of ammonia that actually reacts with water. In our exercise, 0.40% of the 4.25 g of ammonia has reacted, which demonstrates how sparingly ammonia dissociates in water. This small percentage of reacted ammonia is significant in calculating equilibrium concentrations necessary for determining pH values.
\rUnderstanding this behavior is essential when calculating the pH of such solutions, as we must account for only the small fraction of ammonia that actually reacts with water. In our exercise, 0.40% of the 4.25 g of ammonia has reacted, which demonstrates how sparingly ammonia dissociates in water. This small percentage of reacted ammonia is significant in calculating equilibrium concentrations necessary for determining pH values.
Electrical Conductivity Measurement
Electrical conductivity measurements provide information about the ionic content of a solution. Since ions are the charge carriers in aqueous solutions, the presence of free ions, such as \r(\(NH_4^+\)) and \r(\(OH^-\)), will allow electricity to flow through the solution.
\rIn weak base equilibria, such as with ammonia solutions, the degree of ionization is often low. Consequently, these solutions will have lower conductivity than strong electrolytes (fully dissociated). The given exercise mentions that only 0.40% of the ammonia has reacted with water, indicating low ion production and correspondingly low conductivity. Being able to link the extent of ammonia's reaction with water to conductivity provides a valuable insight into the concentration of ions in solution, which is a critical step in pH calculation.
\rIn weak base equilibria, such as with ammonia solutions, the degree of ionization is often low. Consequently, these solutions will have lower conductivity than strong electrolytes (fully dissociated). The given exercise mentions that only 0.40% of the ammonia has reacted with water, indicating low ion production and correspondingly low conductivity. Being able to link the extent of ammonia's reaction with water to conductivity provides a valuable insight into the concentration of ions in solution, which is a critical step in pH calculation.
Weak Base Equilibria
Understanding weak base equilibria is crucial for comprehending why all of the ammonia does not react with water. Unlike strong bases that fully dissociate in water, weak bases such as ammonia (\r(\(NH_3\))) reach a state of dynamic equilibrium with the water, producing \r(\(NH_4^+\)) and \r(\(OH^-\)) ions in a reversible reaction.
\rTo analyze this process, we apply the equilibrium constant for the base, known as Kb, which gives us the ratio of the concentration of the products over reactants at equilibrium. The small amount of ionization also implies that the initial concentration of ammonia can be considered virtually unchanged for the equilibrium calculations, simplifying the process and allowing for the assumption that [OH-] equals the concentration of \r(\(NH_4^+\)).
\rTo analyze this process, we apply the equilibrium constant for the base, known as Kb, which gives us the ratio of the concentration of the products over reactants at equilibrium. The small amount of ionization also implies that the initial concentration of ammonia can be considered virtually unchanged for the equilibrium calculations, simplifying the process and allowing for the assumption that [OH-] equals the concentration of \r(\(NH_4^+\)).
pH and pOH Relationship
The pH and pOH of a solution are important concepts in acid-base chemistry. pH is the negative logarithm of hydrogen ion concentration, while pOH is the negative logarithm of hydroxide ion concentration. For any aqueous solution at 25 degrees Celsius, the sum of the pH and pOH values is always 14.
\rThis relationship is a convenient tool for converting between pH and pOH, which is especially helpful when dealing with weak bases like ammonia. In the problem at hand, by determining the pOH through the known concentration of \r(\(OH^-\)), we can easily calculate the pH of the solution, leading to the identification of the correct pH value among the provided options.
\rThis relationship is a convenient tool for converting between pH and pOH, which is especially helpful when dealing with weak bases like ammonia. In the problem at hand, by determining the pOH through the known concentration of \r(\(OH^-\)), we can easily calculate the pH of the solution, leading to the identification of the correct pH value among the provided options.
Other exercises in this chapter
Problem 10
The number of hydronium ions in \(1 \mathrm{ml}\) of an aqueous solution of \(\mathrm{pH} 12.0\) at \(25^{\circ} \mathrm{C}\) is (a) \(0.01\) (b) \(10^{-12}\) (
View solution Problem 11
The \(\mathrm{pH}\) of \(4.0 \times 10^{-4} \mathrm{M}-\mathrm{HNO}_{3}\) solution is \((\log 2=0.3)\) (a) \(4.6\) (b) \(3.4\) (c) \(3.6\) (d) \(4.0\)
View solution Problem 15
What mass of NaOH should be dissolved in sufficient water to get \(20 \mathrm{~m}^{3}\) of an aqueous solution of \(\mathrm{pH}, 7.3\), at \(25^{\circ} \mathrm{
View solution Problem 17
At \(25^{\circ} \mathrm{C}\), the dissociation constants of acid HA and base BOH in aqueous solution is same. The \(\mathrm{pH}\) of \(0.01 \mathrm{M}\) solutio
View solution