Which solutionwill have pH closer to `1.0` ?

Options

A. `75 mL` of `M//5HC1 + 25 mL` of `M//5 NaOh`
B. `10mL` of `M//10 HC1 + 90 mL` of `M//10 NaOH`
C. `55mL` of `M//10 HC1` + `54mL` of `M//10 NaOH`
D. `100 mL` of `M//10 HC1 + 100 mL` of `M//10 NaOH`

Answer

A

Explanation

a.mmol of `HC1 = 75 xx (1)/(5) = 15`
mmol of `NaOH = 25 xx (1)/(5) = 5`
mmol of HC1 left `= 15 - 5 = 10`
Volume `= 75 + 25 = 100`
`[H^(o+)] = (10)/(100) = 0.1 = 10^(-1)M`
`pH = 1`
b. mmol of `HC1 = 10 xx (1)/(10) = 1`
mmol of `NaOH = 90 xx (1)/(10) = 9`
mmol of `NaOH` left `= 9 - 1 = 8`
Since base is left, `:. pH gt 7`
c. mmol of `HC1 = 55 xx (1)/(10) = 5.5`
mmol of `NaOH = 45 xx (1)/(10) = 4.5`
mmol of `HC1` left `= 5.5 - 4.5 = 1.0`
Volume `= 55 + 45 = 100`
`[H^(o+)] = (1)/(100) = 10^(-2)`
`pH = 2`
d. mmol of `HC1 = 100 xx (1)/(10) = 10`
mmol of `NaOH = 100 xx (1)/(10) = 10`
Both `S_(A)` and `S_(B)` are neutralised.
`:. pH = 7`.