pH scale
The pH scale is a logarithmic measure of the concentration of hydrogen ions ($ [H^+] $) in an aqueous solution.
It is defined mathematically as:
$$ \text{pH} = -\log_{10} [H^+] $$
Here:
If the $ [H^+] $ of a solution is $ 1.0 \times 10^{-3} \, \text{mol dm}^{-3} $ at 298 K, its pH is: $$ \text{pH} = -\log_{10} [H^+] = -\log_{10} (1.0 \times 10^{-3}) = 3.00 $$
This indicates the solution is acidic.
If you know the pH, you can reverse the process to calculate the $ [H^+] $ concentration using the equation:
$$ [H^+] = 10^{-\text{pH}} $$
If the pH of a solution is $ 5.0 $ at 298 K, the $ [H^+] $ is:
$$ [H^+] = 10^{-\text{pH}} = 10^{-5} = 1.0 \times 10^{-5} \, \text{mol dm}^{-3} $$
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