Question

If one liter of water at pH 7 is mixed with one liter of water at pH 6, the resulting pH of the mixture is ____________

Hint:

When mixing solutions with different pH values, remember that the resulting pH depends on the concentration of hydrogen ions in each solution.

Answer 1

Step 1: Understanding pH. 
The pH scale is logarithmic and measures the concentration of hydrogen ions \([H^+]\). The formula for pH is: \[ {pH} = -\log[H^+] \] Thus, a solution with pH 7 has a hydrogen ion concentration of \([H^+] = 10^{-7}\) mol/L, and a solution with pH 6 has \([H^+] = 10^{-6}\) mol/L. 
Step 2: Mixing the two solutions. 
When two solutions are mixed, the resulting concentration of \([H^+]\) is the average of the two concentrations, as the volumes are equal. The combined concentration of hydrogen ions is: \[ [H^+]_{{mix}} = \frac{(10^{-7} + 10^{-6})}{2} = \frac{1.1 \times 10^{-6}}{2} = 5.5 \times 10^{-7} \] Step 3: Calculating the resulting pH. 
Now, we calculate the pH of the resulting solution: \[ {pH}_{{mix}} = -\log(5.5 \times 10^{-7}) = 6.26 \] Therefore, the resulting pH of the mixture is approximately \(6.26\).