Write the mathematical definition of \(\mathrm{pH}\), and explain what fundamental change there would be in the pH scale if you left the negative out.

pH is a measure of the acidity or basicity of a solution. It is defined as the negative logarithm (base 10) of the concentration of hydrogen ions (\(H^+\)) in the solution. Mathematically, the pH is given by the following equation: \[pH = -\log_{10} [H^+]\] Where \([H^+]\) represents the concentration of hydrogen ions in the solution, measured in moles per liter (M).

If we were to leave out the negative sign in the pH definition, the equation would be: \[pH' = \log_{10} [H^+]\] The omission of the negative sign would lead to fundamental changes in the pH scale, as detailed below: 1. Reverse interpretation of acidity and basicity: In the original pH scale, a lower pH value (less than 7) corresponds to higher acidity, whereas a higher pH value (greater than 7) corresponds to higher basicity. By removing the negative sign, the scale would be reversed; lower pH' values would indicate higher basicity, and higher pH' values would indicate higher acidity. 2. Shift in the neutral point: The neutral point in the original pH scale is at pH=7, representing a solution with equal concentrations of \(H^+\) and \(OH^-\) ions. In the modified pH' scale, the neutral point would shift to pH'=0, as the logarithm of unity is zero, i.e., \(log_{10}(1)=0\). 3. Loss of intuitive interpretation: The original pH scale ranges from 0 to 14, with each whole number step representing a tenfold change in hydrogen ion concentration. The loss of the negative sign would make it more difficult to intuitively interpret and understand the scale, as it would no longer represent how many times more acidic or basic a solution is relative to the neutral point. In conclusion, leaving the negative sign out of the pH definition would fundamentally change the pH scale, altering the interpretations of acidity and basicity, shifting the neutral point, and making the scale less intuitive.