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Consider an exceptionally weak acid, HA, with a Ka = 1x10 -20 . You make a 0.1M solution of the salt Na

What is the pH?

2 Answers

5 votes

Answer:

pH = 13

Step-by-step explanation:

Dissociation constant, Ka, of an acid HA in water, is written as:

HA(aq) + H₂O(l) ⇄ H₃O⁺(aq) + A⁻(aq)

Ka = [H₃O⁺][A⁻] / [HA] = 1x10⁻²⁰

Now, knowing the equilibrium of water is:

2H₂O ⇄ OH⁻ + H₃O⁺

Kw = [OH⁻] [H₃O⁺] = 1x10⁻¹⁴

Now, subtracting the equilibrium of water - the dissociation of the acid:

A⁻(aq) + H₂O ⇄ OH⁻ + HA

And the equilibrium constant, Kb, is:

Kb = Kw / Ka = 1x10⁻¹⁴ / 1x10⁻²⁰ = 1x10⁶

And is defined as:

Kb = 1x10⁶ = [OH⁻] [HA] / [A⁻]

If you make a solution of 0.1M NaA (A⁻ in water), the equilibrium concentrations are:

[A⁻] = 0.1M - X

[OH⁻] = X

[HA] = X

Where X is the reaction coordinate

Replacing in Kb formula:

1x10⁶ = [X] [X] / [0.1-X]

1x10⁵ - 1x10⁶X = X²

0 = X² + 1x10⁶X - 1x10⁵

Solving for X:

X = -1 → Wrong solution. There is no negative concentrations

X = 0.09999999M → Right solution.

As [OH⁻] = X, [OH⁻] = 0.09999999M,

Defining pOH = -log [OH⁻]

pOH = 1

As pH = 14- pOH

pH = 14 - 1

pH = 13

User Joshua P Nixon
by
7.7k points
3 votes

Answer:


pH=13

Step-by-step explanation:

Hello,

In this case, given the acid, we can suppose a simple dissociation as:


HA\rightleftharpoons H^+ + A^-

Which occurs in aqueous phase, therefore, the law of mass action is written by:


Ka=([H^+][A^-])/([HA])

That in terms of the change
x due to the reaction's extent we can write:


1x10^(-20)=(x*x)/(0.1M-x)

But we prefer to compute the Kb due to its exceptional weakness:


Kb=(Kw)/(Ka)=(1x10^(-14))/(1x10^(-20)) =1x10^(-6)

Next, the acid dissociation in the presence of the base we have:


Kb=([OH^-][HA])/([A^-])=1x10^(6)=(x*x)/(0.1-x)

Whose solution is
x=0.0999M which equals the concentration of hydroxyl in the solution, thus we compute the pOH:


pOH=-log([OH^-])=-log(0.0999)=1

Finally, since the maximum scale is 14, we can compute the pH by knowing the pOH:


pH+pOH=14\\\\pH=14-pOH=14-1\\\\pH=13

Regards.

User Tue Nguyen
by
7.3k points