Respuesta :
Answer:
The concentration of [tex]H^{+}[/tex] is 1.48 × [tex]10^{-9}[/tex] M
The absolute uncertainty of [tex][{H^{+}][/tex] is ±0.12 × [tex]10^{-9}[/tex] M
The concentration of [tex]H^{+}[/tex] is written as 1.48(±0.12) × [tex]10^{-9}[/tex] M
Explanation:
The pH of a solution is given by the formula below
pH = [tex]-log_{10}[{H^{+}][/tex]
∴ [tex][H^{+}] = 10^{-pH}[/tex]
where [tex][{H^{+}][/tex] is the [tex]H^{+}[/tex] concentration
From the question,
pH = 8.83±0.04
That is,
pH =8.83 and the uncertainty is ±0.04
First, we will determine [tex][{H^{+}][/tex] from
[tex][H^{+}] = 10^{-pH}[/tex]
[tex][{H^{+}] = 10^{-8.83}[/tex]
[tex][{H^{+}] = 1.4791[/tex] × [tex]10^{-9}[/tex] M
[tex][{H^{+}] = 1.48[/tex] × [tex]10^{-9}[/tex] M
The concentration of [tex]H^{+}[/tex] is 1.48 × [tex]10^{-9}[/tex] M
The uncertainty of [tex][{H^{+}][/tex] ( [tex]U_{[H^{+}] }[/tex] ) from the equation [tex][H^{+}] = 10^{-pH}[/tex] is
[tex]U_{[H^{+}] } = 2.303 \\[/tex] × [tex]{[H^{+}] }[/tex] × [tex]U_{pH }[/tex]
Where [tex]U_{[H^{+}] }[/tex] is the uncertainty of [tex][{H^{+}][/tex]
[tex]U_{pH }[/tex] is the uncertainty of the pH
Hence,
[tex]U_{[H^{+}] }[/tex] = 2.303 × 1.4791 × [tex]10^{-9}[/tex] × 0.04
[tex]U_{[H^{+}] }[/tex] = 1.36 × [tex]10^{-10}[/tex] M
[tex]U_{[H^{+}] }[/tex] = 0.12 × [tex]10^{-9}[/tex] M
Hence, the absolute uncertainty of [tex][{H^{+}][/tex] is ±0.12 × [tex]10^{-9}[/tex] M
