You have a solution [tex]$pH =12$[/tex] that contains a weak acid with [tex]$pK _{ a }=10$[/tex]. You have 0.001 M of the protonated form. What's the concentration of the deprotonated form?
1) 0.1 M
2) 0.0001 M
3) 1 M
4) 10 M
Answer (2)
Use the Henderson-Hasselbalch equation: p H = p K a + l o g [ H A ] [ A − ] .
Plug in the given values: 12 = 10 + l o g 0.001 [ A − ] .
Solve for l o g 0.001 [ A − ] : l o g 0.001 [ A − ] = 2 .
Solve for [ A − ] : [ A − ] = 1 0 2 × 0.001 = 0.1 M . The concentration of the deprotonated form is 0.1 M .
Explanation
Problem Analysis We are given the pH of a solution containing a weak acid, the p K a of the weak acid, and the concentration of the protonated form of the weak acid. We are asked to find the concentration of the deprotonated form. We can use the Henderson-Hasselbalch equation to solve this problem.
Henderson-Hasselbalch Equation The Henderson-Hasselbalch equation is: p H = p K a + l o g [ H A ] [ A − ] , where [ A − ] is the concentration of the deprotonated form and [ H A ] is the concentration of the protonated form.
Plugging in the Values We are given that p H = 12 , p K a = 10 , and [ H A ] = 0.001 M . Plugging these values into the Henderson-Hasselbalch equation, we get: 12 = 10 + l o g 0.001 [ A − ]
Simplifying the Equation Subtracting 10 from both sides, we get: 2 = l o g 0.001 [ A − ]
Removing the Logarithm To remove the logarithm, we take 10 to the power of both sides: 1 0 2 = 0.001 [ A − ] 100 = 0.001 [ A − ]
Solving for [A-] Multiplying both sides by 0.001, we get: [ A − ] = 100 × 0.001 = 0.1 M
Final Answer Therefore, the concentration of the deprotonated form is 0.1 M.
Examples
The Henderson-Hasselbalch equation is useful in many real-world applications, such as determining the pH of a buffer solution, which is used to maintain a stable pH in chemical and biological systems. For example, in blood, the pH is maintained around 7.4 by a buffer system consisting of carbonic acid ( H 2 C O 3 ) and bicarbonate ( H C O 3 − ). The Henderson-Hasselbalch equation can be used to calculate the ratio of bicarbonate to carbonic acid required to maintain the correct pH. This is crucial for the proper functioning of enzymes and other biological molecules.
The concentration of the deprotonated form of the weak acid is 0.1 M, calculated using the Henderson-Hasselbalch equation. The provided pH of the solution is 12, and the pK_a of the weak acid is 10. Thus, the concentration of the protonated form was given as 0.001 M, leading to the final result.
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