To determine the pH of a solution given its hydrogen ion concentration, you can use the formula:
[tex]\[ \text{pH} = -\log_{10} [H^+] \][/tex]
where [tex]\([H^+]\)[/tex] represents the concentration of hydrogen ions in the solution.
Given the hydrogen ion concentration of the solution is [tex]\(2 \times 10^{-9}\)[/tex]:
[tex]\[ [H^+] = 2 \times 10^{-9} \text{ moles per liter} \][/tex]
Now, let's calculate the pH:
1. Substitute the given hydrogen ion concentration into the pH formula:
[tex]\[ \text{pH} = -\log_{10} (2 \times 10^{-9}) \][/tex]
2. Use the properties of logarithms to separate the multiplication inside the logarithm:
[tex]\[ \text{pH} = -(\log_{10} 2 + \log_{10} 10^{-9}) \][/tex]
3. Evaluate the two logarithmic components:
[tex]\[ \log_{10} 10^{-9} = -9 \][/tex]
[tex]\[ \log_{10} 2 \approx 0.3010 \][/tex] (This is a standard logarithm value)
4. Substitute these values back into the equation:
[tex]\[ \text{pH} = - (\log_{10} 2 - 9) \][/tex]
[tex]\[ \text{pH} = - (0.3010 - 9) \][/tex]
[tex]\[ \text{pH} = -0.3010 + 9 \][/tex]
[tex]\[ \text{pH} = 8.699 \][/tex]
Thus, the calculated pH of the solution is approximately [tex]\(8.699\)[/tex].
When compared to the given choices:
1. 1.0
2. 2.9
3. 8.7
4. 9.3
The closest value to 8.699 is 8.7.
Therefore, the approximate pH of the solution is [tex]\(8.7\)[/tex].
