The pH of two solutions A and B are 2 and 4 respectively. What is the ratio of `H^(+)` ion concentration of the two solutions?

Explanation

To find the ratio of \( H^+ \) ion concentrations of the two solutions A and B, we can follow these steps:

### Step 1: Understand the relationship between pH and \( H^+ \) ion concentration
The pH of a solution is defined by the formula:
\[ \text{pH} = -\log[H^+] \]
where \([H^+]\) is the concentration of hydrogen ions in moles per liter.

### Step 2: Calculate the \( H^+ \) ion concentration for solution A
Given that the pH of solution A is 2, we can substitute this value into the pH formula:
\[ 2 = -\log[H^+_A] \]
To find \([H^+_A]\), we can rearrange the equation:
\[ [H^+_A] = 10^{-2} \, \text{M} \]

### Step 3: Calculate the \( H^+ \) ion concentration for solution B
Similarly, for solution B with a pH of 4, we substitute this value into the pH formula:
\[ 4 = -\log[H^+_B] \]
Rearranging gives us:
\[ [H^+_B] = 10^{-4} \, \text{M} \]

### Step 4: Find the ratio of \( H^+ \) ion concentrations of A and B
Now that we have both concentrations, we can find the ratio:
\[ \text{Ratio} = \frac{[H^+_A]}{[H^+_B]} = \frac{10^{-2}}{10^{-4}} \]
This simplifies to:
\[ \text{Ratio} = 10^{(-2) - (-4)} = 10^{2} = 100 \]

### Final Answer
The ratio of \( H^+ \) ion concentration of solutions A and B is:
\[ \text{Ratio} = 100 \]

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