Given the equation:
[tex]pH=-log\mleft(H^+\mright)[/tex]
You know that a lab technician finds that a sample of fluid has this pH:
[tex]pH=4.5[/tex]
Then, in order to find the hydrogen ion concentration of the fluid, you need to follow these steps:
1. Substitute the pH given in the exercise into the equation:
[tex]4.5=-log(H^+)[/tex]
Multiply both sides by -1:
[tex]-4.5=\log (H^+)[/tex]
2. Solve for:
[tex]H^+[/tex]
Remember that, by definition:
[tex]\log _b\mleft(c\mright)=a\Rightarrow b^a=c[/tex]
In this case, you can identify that:
[tex]\begin{gathered} a=-4.5 \\ b=10 \\ c=H^+ \end{gathered}[/tex]
Hence, substituting values and simplifying, you get:
[tex]\begin{gathered} b^a=c \\ 10^{-4.5}=H^+ \\ H^+=0.00003162278\text{ }\frac{moles}{liter} \end{gathered}[/tex]
Therefore, the answer is:
[tex]H^+=0.00003162278\text{ }\frac{moles}{liter}[/tex]
