Question

Amphetamine (c9h13n is a weak base with a pkb of 4.2. calculate the ph of a solution containing an amphetamine concentration of 205 mg/l.

Answer 1

The answer to the question is;

The pH of a solution containing an amphetamine (with pKb of 4.2) concentration of 205 mg/l is 10.4.

Step-by-step explanation:

To solve the question we note that the

The mass of amphetamine = 205 mg/l

The molar mass of amphetamine = 135.2062 g/mol

Number of moles of amphetamine = (205 mg)/(135.2062 g/mol) = 1.5×10⁻³ moles

That is the initial concentration of amphetamine = 1.5×10⁻³ M

We have
`pK_b = -log K_b` therefore
`K_b` =
`10^(-pK_b) = 10^(-4.2)` = 6.3×10⁻⁵

Then
`K_b=([C_9H_(14)N][OH^-])/([C_9H_(13)N])` = 6.3×10⁻⁵

Which gives 6.3×10⁻⁵ =
`(x^(2) )/(0.001516-x)`

Solving, we get
`(0.001516-x)*6.3*10^(-5) = x^(2)`

`(0.001516-x)*6.3*10^(-5) - x^(2) = 0`

From which by factorizing gives (x+3.42×10⁻⁴)×(x-2.79×10⁻⁴) = 0

That is x = -3.42×10⁻⁴ or 2.79×10⁻⁴ which gives x= 2.79×10⁻⁴ since we are dealing with concentration

However x = [OH⁻] = 2.79×10⁻⁴

pOH = -log[OH⁻] = -log(2.79×10⁻⁴) = 3.5538

pH = 14 - pOH = 14 - 3.5538 = 10.446 ≈ 10.4

the pH of a solution containing an amphetamine concentration of 205 mg/l = 10.4.