For each [OH−], determine the pH and state whether the solution is acidic or basic.

(a) [OH−] = 1.8 × 10−5 M

(b) [OH−] = 8.9 × 10−12 M

(c) [OH−] = 3.1 × 10−2 M

(d) [OH−] = 1.96 × 10−9 M

Solution: Here, we are going to determine the pH of the given solutions.

Step1:

pH is the negative logarithm to base 10 of hydrogen ion concentration whereas pOH is the negative logarithm to base 10 of hydroxyl ion concentration, i.e.,

pOH = - log[OH- ] and pH = - log[H+ ]

And pH + pOH =14

We can distinguish acidic, neutral and basic aqueous solutions by the relative values of their pH

Acidic: pH < 7

Neutral: pH = 7

Basic: pH > 7

Step2:

- Given, [OH- ] = 1.8 x 10-5 M

Therefore pOH = - log[OH- ]

= - log (1.8 x 10-5)

= - log 1.8 - log 10-5

= -0.255 + 5

= 4.745

Therefore, pH = 14 - pOH

= 14 - 4.745

= 9.255

Thus, pH = 9.255

Since, pH > 7, therefore, the solution is basic.

b) Given, [OH- ] = 8.9 x 10-12 M

Therefore pOH = - log[OH- ]

= - log (8.9 x 10-12)

= - log 8.9 - log 10-12

= - 0.949 + 12

= 11.051

Therefore, pH = 14 - pOH

= 14 - 11.051

= 2.949

Thus, pH = 2.949

Since, pH < 7, therefore, the solution is acidic.

c) Given, [OH- ] = 3.1 x 10-2 M

Therefore pOH = - log[OH- ]

= - log (3.1 x 10-2)

= - log 3.1 - log 10-2

= - 0.491 + 2

= 1.509

Therefore, pH = 14 - pOH

= 14 - 1.509

= 12.491

Thus, pH = 12.491

Since, pH > 7, therefore, the solution is basic.

d) Given, [OH- ] = 1.96 x 10-9 M

Therefore pOH = - log[OH- ]

= - log (1.96 x 10-9)

= - log 1.96 - log 10-9

= -0.292 + 9

= 8.708

Therefore, pH = 14 - pOH

= 14 - 8.708

= 5.292

Thus, pH = 5.292

Since, pH < 7, therefore, the solution is acidic.

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