To determine how many times greater the hydrogen ion concentration in solution A is compared to solution B, we need to understand the relationship between pH and hydrogen ion concentration.
The pH of a solution is calculated as:
[tex]\[ \text{pH} = -\log_{10} [\text{H}^+] \][/tex]
where [tex]\([\text{H}^+]\)[/tex] represents the hydrogen ion concentration. Therefore, we can find the hydrogen ion concentration from the pH by rearranging the formula:
[tex]\[ [\text{H}^+] = 10^{-\text{pH}} \][/tex]
Given:
- Solution A has a pH of 2
- Solution B has a pH of 6
First, we calculate the hydrogen ion concentration for each solution.
For solution A:
[tex]\[ [\text{H}^+]_A = 10^{-2} = 1 \times 10^{-2} \][/tex]
For solution B:
[tex]\[ [\text{H}^+]_B = 10^{-6} = 1 \times 10^{-6} \][/tex]
Next, we determine the ratio of hydrogen ion concentrations between solution A and solution B:
[tex]\[ \text{Ratio} = \frac{[\text{H}^+]_A}{[\text{H}^+]_B} = \frac{1 \times 10^{-2}}{1 \times 10^{-6}} \][/tex]
[tex]\[ \text{Ratio} = 10^{-2} \div 10^{-6} = 10^{(-2) - (-6)} = 10^{-2 + 6} = 10^{4} \][/tex]
So, the hydrogen ion concentration in solution A is 10,000 times greater than that in solution B.
Thus, the answer is:
[tex]\[ \boxed{10000} \][/tex]
