The concentration of hydrogen ions, [H+], in a solution can be calculated from the pH value using the following formula:
[tex]\[ [H^+] = 10^{-\text{pH}} \][/tex]
Given:
[tex]\[ \text{pH} = 4.5 \][/tex]
Using the formula, we can find the hydrogen ion concentration:
[tex]\[ [H^+] = 10^{-4.5} \][/tex]
To calculate this, we take the negative power of 10 to the pH value:
[tex]\[ [H^+] = \frac{1}{10^{4.5}} \][/tex]
Since [tex]\( 10^{4.5} \)[/tex] is the same as [tex]\( \sqrt{10^9} \)[/tex] or [tex]\( 10^{9/2} \)[/tex], we can also write it as:
[tex]\[ [H^+] = \frac{1}{\sqrt{10^9}} \][/tex]
Now, because [tex]\( 10^9 = 1,000,000,000 \)[/tex], its square root is [tex]\( 31,622.7766 \)[/tex] (approximately).
Thus:
[tex]\[ [H^+] = \frac{1}{31,622.7766} \][/tex]
[tex]\[ [H^+] \approx 3.162 \times 10^{-5} \][/tex]
Therefore, the concentration of H+ ions in the solution is approximately [tex]\( 3.16 \times 10^{-5} \)[/tex] M. From the answer choices, the correct one is:
[tex]\[ [H^+] = 3.16 \times 10^{-5} \][/tex]
