A student combined equal amounts of two solutions. One solution had a pH of 2 and the other had a pH of 12. Which would most likely be the resulting pH?
A. 1
B. 3
C. 11
Answer (1)
Convert the pH values to hydrogen ion concentrations: [ H + ] 1 = 1 0 − 2 and [ H + ] 2 = 1 0 − 12 .
Calculate the average hydrogen ion concentration: [ H + ] a vg = 2 1 0 − 2 + 1 0 − 12 ≈ 0.005 .
Calculate the resulting pH: p H = − l o g 10 ( 0.005 ) ≈ 2.30 .
The resulting pH is approximately 3 .
Explanation
Problem Analysis We are given two solutions with pH values of 2 and 12, respectively, and we are mixing equal amounts of each. We need to determine the resulting pH of the mixture.
Converting pH to [H+] First, we need to convert the pH values to hydrogen ion concentrations ([H+]). Recall that pH = -log10([H+]), so [H+] = 10^(-pH).
[H+] of Acidic Solution For the solution with pH = 2, the hydrogen ion concentration is: [ H + ] 1 = 1 0 − 2 M = 0.01 M
[H+] of Basic Solution For the solution with pH = 12, the hydrogen ion concentration is: [ H + ] 2 = 1 0 − 12 M
Calculating Average [H+] Since we are mixing equal amounts of the two solutions, we can find the average hydrogen ion concentration by adding the two concentrations and dividing by 2: [ H + ] a vg = 2 [ H + ] 1 + [ H + ] 2 = 2 1 0 − 2 + 1 0 − 12 = 2 0.01 + 0.000000000001 ≈ 2 0.01 = 0.005 M
Calculating Resulting pH Now, we can calculate the resulting pH using the formula pH = -log10([H+]): p H = − l o g 10 ([ H + ] a vg ) = − l o g 10 ( 0.005 ) ≈ 2.30
Final Answer Therefore, the resulting pH is approximately 2.30. The closest answer choice is 3.
Examples
Understanding pH is crucial in many real-world applications. For example, in agriculture, knowing the pH of the soil helps farmers determine the best crops to grow. If the soil is too acidic or alkaline, they can adjust it to the optimal range for the desired plants. Similarly, in water treatment, maintaining the correct pH is essential for effective disinfection and preventing corrosion of pipes. In medicine, the pH of blood and other bodily fluids must be carefully regulated to ensure proper physiological function. Mixing solutions with different pH values, as in this problem, is a common task in chemistry labs and industrial processes, where precise control of pH is often necessary.
