Type the correct answer in the box. Round your answer to the nearest hundredth.
A solution has a hydronium concentration of [tex]$4.7 \times 10^{-11}$[/tex]. What is the pH of the solution?
The pH of the solution is $\square$
Answer (2)
We are given the hydronium concentration [ H 3 O + ] = 4.7 × 1 0 − 11 .
Apply the formula p H = − lo g 10 [ H 3 O + ] .
Calculate the logarithm: lo g 10 ( 4.7 × 1 0 − 11 ) ≈ − 10.3279 .
Round the result to the nearest hundredth: p H ≈ 10.33 .
Explanation
Understanding the Problem We are given the hydronium concentration of a solution, which is [ H 3 O + ] = 4.7 × 1 0 − 11 . We need to find the pH of the solution. The pH is a measure of the acidity or basicity of a solution.
Recalling the pH Formula The formula for calculating the pH of a solution is given by: p H = − lo g 10 [ H 3 O + ] where [ H 3 O + ] is the hydronium concentration.
Substituting the Given Value Now, we substitute the given hydronium concentration into the formula: p H = − lo g 10 ( 4.7 × 1 0 − 11 )
Calculating the pH Value We calculate the logarithm: lo g 10 ( 4.7 × 1 0 − 11 ) ≈ − 10.3279 So, p H = − ( − 10.3279 ) ≈ 10.3279
Rounding the Result Finally, we round the pH value to the nearest hundredth: p H ≈ 10.33
Final Answer The pH of the solution is approximately 10.33.
Examples
Understanding pH is crucial in many real-world applications. For instance, in agriculture, knowing the pH of the soil helps farmers determine the best crops to grow. Different plants thrive at different pH levels. Similarly, in medicine, maintaining the correct pH balance in our blood is vital for our health. The pH scale, and its calculation, is a fundamental concept in chemistry and biology.
The pH of the solution with a hydronium concentration of 4.7 × 1 0 − 11 is calculated using the formula p H = − lo g 10 [ H 3 O + ] . After substituting the concentration and performing the calculation, we find the pH to be approximately 10.33 . This indicates that the solution is basic since the pH is above 7.
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