Chemists use a number denoted by pH to describe quantitatively the acidity or basicity of solutions. By definition, pH = −log[H+], where [H+] is the hydrogen ion concentration in moles per liter.
Many solutions have a pH between 1 and 14. Find the range
I assume you mean range of hydrogen ion concentration (assuming there exist hydrogen ions in solution).
Low end: 1*10^-14 moles per liter
High end: 1*10^-1 (ie, 0.1) moles per liter
To find the range of pH, we need to determine the lowest possible value and the highest possible value.
The lowest possible value for pH occurs when the hydrogen ion concentration ([H+]) is at its highest. According to the definition pH = -log[H+], when [H+] is highest, the logarithm value becomes smallest. This occurs when [H+] is 1 mole per liter.
Using this value in the pH equation, we have:
pH = -log(1) = 0.
Therefore, the lowest possible value of pH is 0.
The highest possible value for pH occurs when the hydrogen ion concentration ([H+]) is at its lowest. According to the definition pH = -log[H+], when [H+] is lowest, the logarithm value becomes largest. This occurs when [H+] is 10^(-14) moles per liter.
Using this value in the pH equation, we have:
pH = -log(10^(-14)) = -(-14) = 14.
Therefore, the highest possible value of pH is 14.
Hence, the range of pH is from 0 to 14.