Scenario: You are testing two different household solutions with your cabbage indicator, using the color key to the right.
Cabbage pH Indicator Color Key
\begin{tabular}{l|l|l|l|l|}\0-2 & 3-4 & 5-6 & 7 & 8-9 \ \
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\end{tabular}
Using the results from the two previous questions:
Solution One: [tex]$1 \times 10^{-8} M$[/tex]
Solution Two: [tex]$1 \times 10^{-7} M$[/tex]
The hydrogen ion concentration of these two solutions differ from each other by a factor of
Answer (2)
Divide the hydrogen ion concentration of Solution Two by Solution One.
Perform the division: 1 × 1 0 − 8 1 × 1 0 − 7 = 10 .
The hydrogen ion concentration of the two solutions differs by a factor of 10 .
Explanation
Understanding the Problem We are given two solutions with different hydrogen ion concentrations. Solution One has a concentration of 1 × 1 0 − 8 M , and Solution Two has a concentration of 1 × 1 0 − 7 M . Our goal is to find the factor by which these concentrations differ. This means we need to determine how many times greater the concentration of Solution Two is compared to Solution One.
Setting up the Calculation To find the factor, we will divide the hydrogen ion concentration of Solution Two by the hydrogen ion concentration of Solution One. This will tell us how many times the concentration of Solution Two is greater than that of Solution One.
Factor = Concentration of Solution One Concentration of Solution Two
Substituting the given values:
Factor = 1 × 1 0 − 8 M 1 × 1 0 − 7 M
Calculating the Factor Now, let's calculate the factor:
Factor = 1 × 1 0 − 8 1 × 1 0 − 7 = 1 0 − 8 1 0 − 7 = 1 0 − 7 − ( − 8 ) = 1 0 − 7 + 8 = 1 0 1 = 10
So, the hydrogen ion concentration of Solution Two is 10 times greater than that of Solution One.
Final Answer The hydrogen ion concentration of Solution Two differs from Solution One by a factor of 10. This means that Solution Two is 10 times more concentrated in terms of hydrogen ions than Solution One.
Examples
Understanding the difference in hydrogen ion concentration is crucial in many real-world applications. For example, in environmental science, monitoring the pH levels of water bodies helps assess pollution levels. A tenfold difference in hydrogen ion concentration can indicate a significant change in acidity, affecting aquatic life and water quality. Similarly, in medicine, maintaining the correct pH balance in the body is vital for various biological processes, and even small changes can have significant health implications.
The hydrogen ion concentration of Solution Two is 10 times greater than that of Solution One. This is determined by dividing the concentrations of the two solutions. Thus, they differ by a factor of 10.
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