Answer to Question #268099 in Math for John

Question

The pH of a solution is defined by the equation pH = –log H^+

where the concentration of hydronium ions, H+ , in a solution is measured in moles per litre.

Determine algebraically the pH of a solution that is 50 times less acidic than vinegar, which has a pH of 2.5

Answer 1

$$[H^+]=10^{-pH}$$

For a $pH=2.5$ we get $[H^+]=10^{-2.5}$

$$50=\dfrac{10^{-2.5}}{10^{-x}}$$

$$\log_{10}50=-2.5-(-x)$$

$$x=2.5+\log_{10}50$$

$$x=4.5-\log_{10}2$$

$$x\approx4.19897$$

The pH of a solution is $4.19897.$