An aqueous solution has hydrogen ion concentration = 1.0 × 10^-10 mol per litre. Determine the pH of the solution. I need full explanation and full process
Answers
By the end of this section, you will be able to:
Explain the characterization of aqueous solutions as acidic, basic, or neutral
Express hydronium and hydroxide ion concentrations on the pH and pOH scales
Perform calculations relating pH and pOH
As discussed earlier, hydronium and hydroxide ions are present both in pure water and in all aqueous solutions, and their concentrations are inversely proportional as determined by the ion product of water (Kw). The concentrations of these ions in a solution are often critical determinants of the solution’s properties and the chemical behaviors of its other solutes, and specific vocabulary has been developed to describe these concentrations in relative terms. A solution is neutral if it contains equal concentrations of hydronium and hydroxide ions; acidic if it contains a greater concentration of hydronium ions than hydroxide ions; and basic if it contains a lesser concentration of hydronium ions than hydroxide ions.
A common means of expressing quantities, the values of which may span many orders of magnitude, is to use a logarithmic scale. One such scale that is very popular for chemical concentrations and equilibrium constants is based on the p-function, defined as shown where “X” is the quantity of interest and “log” is the base-10 logarithm:
pX
=
−
log\;X
The pH of a solution is therefore defined as shown here, where [H3O+] is the molar concentration of hydronium ion in the solution:
pH
=
−
log[H
3
O
+
]
Rearranging this equation to isolate the hydronium ion molarity yields the equivalent expression:
[
H
3
O
+
]
=
10
−
pH
Likewise, the hydroxide ion molarity may be expressed as a p-function, or pOH:
pOH
=
−
log[OH
−
]
or
[
OH
−
]
=
10
−
pOH
Finally, the relation between these two ion concentration expressed as p-functions is easily derived from the Kw expression:
K
w
=
[
H
3
O
+
]
[
OH
−
]
−
log
K
w
=
−
log([H
3
O
+
]
[
OH
−
]
)
=
−
log[H
3
O
+
]
+
−
log[OH
−
]
p
K
w
=
pH
+
pOH
At 25 °C, the value of Kw is 1.0 × 10−14, and so:
14.00
=
pH
+
pOH
As was shown in Example 1 in Chapter 14.1 Brønsted-Lowry Acids and Bases, the hydronium ion molarity in pure water (or any neutral solution) is 1.0 × 10−7M at 25 °C. The pH and pOH of a neutral solution at this temperature are therefore:
pH
=
−
log[H
3
O
+
]
=
−
log
(
1.0
×
10
−
7
)
=
7.00
pOH
=
−
log[OH
−
]
=
−
log
(
1.0
×
10
−
7
)
=
7.00
And so, at this temperature, acidic solutions are those with hydronium ion molarities greater than 1.0 × 10−7M and hydroxide ion molarities less than 1.0 × 10−7M (corresponding to pH values less than 7.00 and pOH values greater than 7.00). Basic solutions are those with hydronium ion molarities less than 1.0 × 10−7M and hydroxide ion molarities greater than 1.0 × 10−7M (corresponding to pH values greater than 7.00 and pOH values less than 7.00).
Since the autoionization constant Kw is temperature dependent, these correlations between pH values and the acidic/neutral/basic adjectives will be different at temperatures other than 25 °C. For example, the “Check Your Learning” exercise accompanying Example 1 in Chapter 14.1 Brønsted-Lowry Acids and Bases showed the hydronium molarity of pure water at 80 °C is 4.9 × 10−7M, which corresponds to pH and pOH values of:
pH
=
−
log[H
3
O
+
]
=
−
log
(
4.9
×
10
−
7
)
=
6.31
pOH
=
−
log[OH
−
]
=
−
log
(
4.9
×
10
−
7
)
=
6.31