The concentration of hydronium ions $(H_3 O ^{\prime})$ in a solution of
(a) Calculate the concentration of hydroxide ions (OHF) in the solution of hydrofluoric acid (HF) at $25^{\circ} C$.
(b) Write down the expression for the equilibrium constant for reaction (i).
Calculate the concentration of un-ionised hydrofluoric in the solution at $25^{\circ} C$.
for the hydrolysis of $NH _4 NO _3$ in water as represented by chemical equations below:
Answer (2)
Calculate the hydroxide ion concentration using the ion product of water: [ O H − ] = [ H 3 O + ] K w = 4.0 1.0 × 1 0 − 14 = 2.5 × 1 0 − 15 M .
Write the equilibrium constant expression for the dissociation of HF: K a = [ H F ] [ H 3 O + ] [ F − ] .
Calculate the initial concentration of HF using the K a value and equilibrium concentrations: [ H F ] 0 = K a [ H 3 O + ] [ F − ] + [ H 3 O + ] = 6.8 × 1 0 − 4 ( 4.0 ) ( 4.0 ) + 4.0 ≈ 23533.41 M .
Determine the concentration of unionized HF at equilibrium: [ H F ] = [ H F ] 0 − [ H 3 O + ] = 23533.41 − 4.0 = 23529.41 M . The final answer is the concentration of hydroxide ions, the equilibrium expression, and the concentration of unionized hydrofluoric acid: 2.5 × 1 0 − 15 M , K a = [ H F ] [ H 3 O + ] [ F − ] , 23529.41 M
Explanation
Problem Analysis and Given Data The problem is about finding the concentration of hydroxide ions in a hydrofluoric acid solution, writing the equilibrium constant expression for the dissociation of hydrofluoric acid, and calculating the concentration of unionized hydrofluoric acid. We are given that the concentration of hydronium ions ( H 3 O + ) is 4.0 M. We will use the ion product of water to find the hydroxide ion concentration, the equilibrium expression to represent the acid dissociation constant, and an ICE table approach to find the concentration of unionized HF.
Calculating Hydroxide Ion Concentration (a) To calculate the concentration of hydroxide ions ( O H − ), we use the ion product of water, K w , which is 1.0 × 1 0 − 14 at 2 5 ∘ C . The relationship is given by: K w = [ H 3 O + ] [ O H − ] We are given [ H 3 O + ] = 4.0 M. Therefore, [ O H − ] = [ H 3 O + ] K w = 4.0 1.0 × 1 0 − 14 = 2.5 × 1 0 − 15 M So, the concentration of hydroxide ions is 2.5 × 1 0 − 15 M.
Writing the Equilibrium Constant Expression (b) The equilibrium reaction for the dissociation of hydrofluoric acid (HF) in water is: H F ( a q ) + H 2 O ( l ) ⇌ H 3 O + ( a q ) + F − ( a q ) The expression for the equilibrium constant, K a , is given by: K a = [ H F ] [ H 3 O + ] [ F − ] This is the equilibrium constant expression for the reaction.
Calculating Unionized Hydrofluoric Acid Concentration (c) To calculate the concentration of unionized hydrofluoric acid, we need to use the K a value for HF, which is 6.8 × 1 0 − 4 . We know that at equilibrium, [ H 3 O + ] = [ F − ] = 4.0 M. We can set up an ICE table to find the initial concentration of HF, [ H F ] 0 , and then calculate the concentration of unionized HF at equilibrium.
K a = [ H F ] [ H 3 O + ] [ F − ] = [ H F ] 0 − 4.0 ( 4.0 ) ( 4.0 ) = 6.8 × 1 0 − 4
Solving for [ H F ] 0 :
[ H F ] 0 − 4.0 = 6.8 × 1 0 − 4 ( 4.0 ) ( 4.0 ) = 6.8 × 1 0 − 4 16 ≈ 23529.41 [ H F ] 0 = 23529.41 + 4.0 = 23533.41 M
Now, the concentration of unionized HF at equilibrium is: [ H F ] = [ H F ] 0 − [ H 3 O + ] = 23533.41 − 4.0 = 23529.41 M Therefore, the concentration of unionized hydrofluoric acid in the solution is approximately 23529.41 M.
Final Answer (a) The concentration of hydroxide ions ( O H − ) in the solution is 2.5 × 1 0 − 15 M. (b) The expression for the equilibrium constant K a is [ H F ] [ H 3 O + ] [ F − ] .
(c) The concentration of unionized hydrofluoric acid in the solution is approximately 23529.41 M.
Examples
Understanding acid-base equilibria is crucial in many real-world applications, such as in environmental monitoring, where the pH of water sources needs to be carefully controlled to protect aquatic life. In chemical manufacturing, precise control of pH is essential for optimizing reaction yields and minimizing unwanted side reactions. In medicine, maintaining the correct pH balance in the body is vital for proper enzyme function and overall health. For example, the concentration of hydroxide ions and un-ionized acids in a solution can affect the rate of a chemical reaction or the solubility of a compound, which are important considerations in drug development and formulation.
The concentration of hydroxide ions is 2.5 × 1 0 − 15 M . The equilibrium constant for hydrofluoric acid dissociation is K a = [ H F ] [ H 3 O + ] [ F − ] . The concentration of un-ionized hydrofluoric acid is approximately 23525.41 M .
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