Pregunta
How many times more acidic is solution A with a pH of 2.2 than solution B with a pH of 9.2 ?
Ask by Fowler Harrington. in the United States
Mar 12,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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Solution A is \(10^7\) times more acidic than solution B.
Solución
Let the concentration of hydrogen ions be represented by \([H^+]\). The pH of a solution is defined as
\[
\text{pH} = -\log [H^+]
\]
For solution A with \(\text{pH} = 2.2\):
\[
[H^+]_A = 10^{-2.2}
\]
For solution B with \(\text{pH} = 9.2\):
\[
[H^+]_B = 10^{-9.2}
\]
To find how many times more acidic solution A is than solution B, we compute the ratio of their hydrogen ion concentrations:
\[
\frac{[H^+]_A}{[H^+]_B} = \frac{10^{-2.2}}{10^{-9.2}} = 10^{-2.2 - (-9.2)} = 10^{7.0}
\]
Therefore, solution A is
\[
10^7
\]
times more acidic than solution B.
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Extra Insights
To determine how many times more acidic solution A is compared to solution B, we can use the pH scale, which is logarithmic. A pH change of 1 unit represents a tenfold change in acidity. Solution A has a pH of 2.2, and solution B has a pH of 9.2. The difference between these pH values is 9.2 - 2.2 = 7.0. Therefore, solution A is 10^7 times more acidic than solution B. That's a whopping 10 million times more acidic! So, if you ever need to dial up the acidity for some culinary explosion or chemical reaction, you know exactly the power of that pH!
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