Select the correct answer.
What is the hydronium $(H_3O^+)$ concentration of a solution with a pH of 3.60?
A. $2.5 \times 10^{-4} M$
B. $3.0 \times 10^{-4} M$
C. $4.0 \times 10^{-11} M$
D. $4.5 \times 10^{-11} M
Answer (2)
The hydronium ion concentration for a solution with a pH of 3.60 is calculated using the formula [ H 3 O + ] = 1 0 − p H . Plugging in the value gives approximately 2.5 × 1 0 − 4 M , which corresponds to option A. Therefore, the answer is A: 2.5 × 1 0 − 4 M .
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Use the formula [ H 3 O + ] = 1 0 − p H .
Substitute the given pH value: [ H 3 O + ] = 1 0 − 3.60 .
Calculate the hydronium ion concentration: [ H 3 O + ] ≈ 2.5 × 1 0 − 4 M .
The correct answer is 2.5 × 1 0 − 4 M , which corresponds to option A. 2.5 × 1 0 − 4 M
Explanation
Understanding the Problem We are given the pH of a solution and asked to find the hydronium ion concentration, denoted as [ H 3 O + ] . The pH is related to the hydronium ion concentration by the formula: p H = − lo g 10 [ H 3 O + ]
Finding the Formula for Hydronium Ion Concentration To find the hydronium ion concentration, we need to rearrange the formula to solve for [ H 3 O + ] : [ H 3 O + ] = 1 0 − p H
Substituting the Given pH Value We are given that the pH of the solution is 3.60. Substituting this value into the formula, we get: [ H 3 O + ] = 1 0 − 3.60
Calculating the Hydronium Ion Concentration Calculating 1 0 − 3.60 , we find: [ H 3 O + ] ≈ 0.00025118864315095795 This can be written in scientific notation as approximately 2.5 × 1 0 − 4 .
Selecting the Correct Answer Comparing this result with the given options, we see that option A, 2.5 × 1 0 − 4 M , is the closest to our calculated value.
Examples
Understanding pH and hydronium ion concentration is crucial in many real-world applications. For instance, in agriculture, the pH of the soil affects nutrient availability for plants. In medicine, maintaining the correct pH balance in the blood is vital for bodily functions. In environmental science, monitoring the pH of water sources helps assess pollution levels and protect aquatic life. Knowing how to calculate hydronium ion concentration from pH allows us to quantify acidity and make informed decisions in these diverse fields.
