Problem 41
Question
Determine the \(\mathrm{pH}\) of a solution with the given hydrogen-ion concentration \(\left[\mathrm{H}^{+}\right]\). $$ 10^{-6} $$
Step-by-Step Solution
Verified Answer
The pH of the solution is 6.
1Step 1: Understanding pH Calculation
The pH of a solution is calculated using the formula: \( \text{pH} = -\log_{10} \left[ \text{H}^+ \right] \). This formula means we need to find the base-10 logarithm of the hydrogen ion concentration, and then take the negative of that value.
2Step 2: Identifying the Hydrogen Ion Concentration
We are given the hydrogen ion concentration as \( \left[ \text{H}^+ \right] = 10^{-6} \). This represents the value we will use in our pH calculation.
3Step 3: Applying the Logarithmic Formula
Using the hydrogen ion concentration \( 10^{-6} \), substitute it into the pH formula: \( \text{pH} = -\log_{10} (10^{-6}) \). When you take the logarithm of \( 10^{-6} \), you obtain \(-6\).
4Step 4: Calculating the pH Value
Since \(-\log_{10} (10^{-6}) = -(-6) \), the pH is \(6\). This means the pH of the solution is 6.
Key Concepts
Understanding Hydrogen Ion ConcentrationExploring the Logarithmic Function in pH CalculationBasics of Acid-Base Chemistry
Understanding Hydrogen Ion Concentration
In chemistry, hydrogen ion concentration is a crucial factor in determining the acidity or basicity of a solution. When we talk about hydrogen ion concentration, we are referring to the number of hydrogen ions (
) present in a solution. These ions are denoted as
[H^+]
.
- A higher [H^+] indicates a more acidic solution. - A lower [H^+] means the solution is more basic.
In our example, [H^+] = 10^{-6}. This value signifies that there are 0.000001 moles of hydrogen ions per liter of solution.
Keeping track of these ions is important because they directly affect the pH of the solution. A change in the [H^+] concentration has a logarithmic impact on the pH value, which helps us quickly assess how acidic or basic the solution is.
- A higher [H^+] indicates a more acidic solution. - A lower [H^+] means the solution is more basic.
In our example, [H^+] = 10^{-6}. This value signifies that there are 0.000001 moles of hydrogen ions per liter of solution.
Keeping track of these ions is important because they directly affect the pH of the solution. A change in the [H^+] concentration has a logarithmic impact on the pH value, which helps us quickly assess how acidic or basic the solution is.
Exploring the Logarithmic Function in pH Calculation
The logarithmic function is essential in pH calculation. The pH scale itself is logarithmic. This means that each unit change in pH represents a tenfold change in hydrogen ion concentration.
The formula used to calculate the pH is:\[\text{pH} = -\log_{10} \left[ \text{H}^+ \right]\]- The "log" here stands for logarithm, specifically base-10 (common logarithm).- When you see \(-\log_{10} (10^{-6})\), you are essentially finding a power of ten that equals 10^{-6}.
Using the properties of logarithms, \(\log_{10}(10^{-6}) = -6\).So you take the negative of that to find the pH: \(-(-6) = 6\).
Employing this logarithmic relationship allows us to easily express very large or small numbers, like [H^+], in a manageable pH format.
The formula used to calculate the pH is:\[\text{pH} = -\log_{10} \left[ \text{H}^+ \right]\]- The "log" here stands for logarithm, specifically base-10 (common logarithm).- When you see \(-\log_{10} (10^{-6})\), you are essentially finding a power of ten that equals 10^{-6}.
Using the properties of logarithms, \(\log_{10}(10^{-6}) = -6\).So you take the negative of that to find the pH: \(-(-6) = 6\).
Employing this logarithmic relationship allows us to easily express very large or small numbers, like [H^+], in a manageable pH format.
Basics of Acid-Base Chemistry
Acid-base chemistry is a fundamental part of chemistry that focuses on the behavior of acids and bases in solutions. An acid, like hydrochloric acid (HCl), donates hydrogen ions
([H^+])
in a solution, while a base, like sodium hydroxide (NaOH), can accept them. The pH scale, ranging from 0 to 14, is used to classify solutions as acidic or basic, based on their
[H^+]
level.
- A pH less than 7 signals an acidic solution. - A pH greater than 7 indicates a basic solution. - A pH of 7 means the solution is neutral, like pure water.
In our exercise, we calculated a pH of 6, slightly acidic. Understanding this scale helps in various applications, like pharmaceuticals and environmental science, where managing acidity or alkalinity is crucial.
- A pH less than 7 signals an acidic solution. - A pH greater than 7 indicates a basic solution. - A pH of 7 means the solution is neutral, like pure water.
In our exercise, we calculated a pH of 6, slightly acidic. Understanding this scale helps in various applications, like pharmaceuticals and environmental science, where managing acidity or alkalinity is crucial.
Other exercises in this chapter
Problem 41
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