Question

The pain killer morphine is a weak base when added to water. The K b is 1.6  × 10 –6. What is the pOH of a 3.97  × 10 –3 M solution of morphine?

a.

4.10

b.

9.90

c.

5.80

d.

9.75

e.

none of these

Answer 1

Let us assume that B is morphine and it is weak base. So its reaction with water is as follows:-

B (aq) + H₂O (l) BH⁺ (aq) + OH^- (aq)

Make ICE table for this

	B	BH+	OH-
I	3.97*10-3	0	0
C	-x	+x	+x
E	3.97*103-x	x	x

Since K_b expression for above reaction will be

K_b = [BH⁺][OH^-]/[B]

Put all values in above expression

1.6*10^-6 = x*x/(3.97*10^-3-x)

Assume that x is small. Therefore

1.6*10^-6 = x²/3.97*10^-3

Multiply both side by 3.97*10^-3

x² = 1.6*10^-6*3.97*10^-3

x² = 6.352*10^-9

Take square root on both side

x = 7.96994*10^-5 M = [OH^-] = [BH⁺]

Since pOH for solution is calculated by formula

pOH = -log[OH^-]

pOH = -log(7.96994*10^-5)

pOH = 4.098 = 4.10

Hence pOH for 3.97*10^-3 M solution of morphine is 4.10. Hence option a is correct.

Since other options are not matched with calculated value. Hence option b,c,d and e are incorrect.