Problem 11
Question
The hydrogen ion concentration of a solution is \(0.000439\). What is the \(\mathrm{pH}\) ? a. \(3.36\) b. \(4.39 \times 10^{-5}\) c. \(4.39\) d. \(8.03\)
Step-by-Step Solution
Verified Answer
The pH is 3.36. (Option a)
1Step 1 - Understand the Definition of pH
The \bm{pH} of a solution is defined as the negative logarithm (base 10) of the hydrogen ion concentration \([H^+ ]\). Mathematically, this is represented as: \[\text{pH} = -\text{log}_{10} [H^+ ]\]
2Step 2 - Identify the Hydrogen Ion Concentration
From the problem, the hydrogen ion concentration \([H^+ ]\) of the solution is given as \0.000439\.
3Step 3 - Apply the pH Formula
Substitute the given hydrogen ion concentration into the pH formula: \[\text{pH} = -\text{log}_{10} (0.000439)\]
4Step 4 - Calculate the Logarithm
Using a calculator to find the logarithm of \0.000439\ to the base 10, \[\text{log}_{10} (0.000439) = -3.3579\]
5Step 5 - Compute the Negative of the Logarithm
Compute the negative of the logarithm to find the pH: \[\text{pH} = -(-3.3579) = 3.3579\]
6Step 6 - Round the Result
Round the result to two decimal places to match the answer choices: \[\text{pH} = 3.36\]
7Step 7 - Select the Correct Answer
From the given choices, the correct answer is: \(a. \ 3.36\)
Key Concepts
hydrogen ion concentrationlogarithm base 10negative logarithm
hydrogen ion concentration
The hydrogen ion concentration \([H^+ ]\) measures how many hydrogen ions are present in a solution.
It's a central concept in acid-base chemistry.
Higher concentrations of hydrogen ions mean the solution is more acidic.
For example, a concentration of \([H^+ ]\ = 0.000439\) tells us there are about 0.000439 moles of hydrogen ions per liter of solution.
This value is important because we use it to calculate the pH of the solution.
Always ensure you have the correct hydrogen ion concentration before attempting any pH calculations.
It's a central concept in acid-base chemistry.
Higher concentrations of hydrogen ions mean the solution is more acidic.
For example, a concentration of \([H^+ ]\ = 0.000439\) tells us there are about 0.000439 moles of hydrogen ions per liter of solution.
This value is important because we use it to calculate the pH of the solution.
Always ensure you have the correct hydrogen ion concentration before attempting any pH calculations.
logarithm base 10
Logarithms are a way of simplifying very large or very small numbers.
A base 10 logarithm (denoted \( \text{log}_{10} \)) answers the question: 'To what power must 10 be raised, to produce a given number?'.
For example, \(\text{log}_{10} (1000) = 3\) because \ (10^3 = 1000) \.
In pH calculations, we use the logarithm base 10 to transform the hydrogen ion concentration into a more manageable number.
For instance, \(\text{log}_{10} (0.000439) = -3.3579 \).
This simplification allows us to better understand and compare the acidity of solutions.
A base 10 logarithm (denoted \( \text{log}_{10} \)) answers the question: 'To what power must 10 be raised, to produce a given number?'.
For example, \(\text{log}_{10} (1000) = 3\) because \ (10^3 = 1000) \.
In pH calculations, we use the logarithm base 10 to transform the hydrogen ion concentration into a more manageable number.
For instance, \(\text{log}_{10} (0.000439) = -3.3579 \).
This simplification allows us to better understand and compare the acidity of solutions.
negative logarithm
The pH formula is defined using the negative logarithm.
Specifically, pH is \(- \text{log}_{10} [H^+ ]\).
This means after finding the logarithm of the hydrogen ion concentration, we take its negative.
For instance, if \(\text{log}_{10} (0.000439) = -3.3579 \), then pH will be \-(-3.3579) = 3.3579\.
The negative sign is essential because it ensures that pH values are positive and easier to interpret.
In summary, calculating pH is about using logarithms to simplify the value and the negative sign to ensure positivity.
Specifically, pH is \(- \text{log}_{10} [H^+ ]\).
This means after finding the logarithm of the hydrogen ion concentration, we take its negative.
For instance, if \(\text{log}_{10} (0.000439) = -3.3579 \), then pH will be \-(-3.3579) = 3.3579\.
The negative sign is essential because it ensures that pH values are positive and easier to interpret.
In summary, calculating pH is about using logarithms to simplify the value and the negative sign to ensure positivity.
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