Question

The pH of a solution is 8.83±0.048.83±0.04 . What is the concentration of H+H+ in the solution and its absolute uncertainty?

Answer 1

The concentration of
`H^(+)` is 1.48 ×
`10^(-9)` M

The absolute uncertainty of
`[{H^(+)]` is ±0.12 ×
`10^(-9)` M

The concentration of
`H^(+)` is written as 1.48(±0.12) ×
`10^(-9)` M

Step-by-step explanation:

The pH of a solution is given by the formula below

pH =
`-log_(10)[{H^(+)]`

∴
`[H^(+)] = 10^(-pH)`

where
`[{H^(+)]` is the
`H^(+)` concentration

From the question,

pH = 8.83±0.04

That is,

pH =8.83 and the uncertainty is ±0.04

First, we will determine
`[{H^(+)]` from

`[H^(+)] = 10^(-pH)`

`[{H^(+)] = 10^(-8.83)`

`[{H^(+)] = 1.4791` ×
`10^(-9)` M

`[{H^(+)] = 1.48` ×
`10^(-9)` M

The concentration of
`H^(+)` is 1.48 ×
`10^(-9)` M

The uncertainty of
`[{H^(+)]` (
`U_([H^(+)] )` ) from the equation
`[H^(+)] = 10^(-pH)` is

`U_([H^(+)] ) = 2.303 \\` ×
`{[H^(+)] }` ×
`U_(pH )`

Where
`U_([H^(+)] )` is the uncertainty of
`[{H^(+)]`

`U_(pH )` is the uncertainty of the pH

Hence,

`U_([H^(+)] )` = 2.303 × 1.4791 ×
`10^(-9)` × 0.04

`U_([H^(+)] )` = 1.36 ×
`10^(-10)` M

`U_([H^(+)] )` = 0.12 ×
`10^(-9)` M

Hence, the absolute uncertainty of
`[{H^(+)]` is ±0.12 ×
`10^(-9)` M