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

Answer:

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

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