Weak Acids and Bases

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TABLE OF CONTENTS

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Hydrochloric acid and ethanoic acid are both acids, as their names suggest. Acids are molecules that donate protons when in solution by dissociating into positive hydrogen ions and negative ions. However, whilst hydrochloric acid is a strong acid, ethanoic acid is weak.

This article is about weak acids and bases in chemistry.
First of all, we'll define weak acids and bases.
We'll then consider the pH of weak acids and bases.
To consolidate our learning, we'll compare strong and weak acids and bases, before looking at a weak acid and base chart.
After that, we'll explore K_a and K_b.
Finally, we'll turn our attention to weak acid and base titrations.

Defining weak acids and bases

What are weak acids and bases? Let's look at a few definitions to make this clear.

Weak acids

To understand weak acids, we first need to define strong acid, so that you can accurately compare the two.

A strong acid is an acid that dissociates fully in solution.

All acids are proton donors. Every molecule of a strong acid donates a proton when it reacts. We can represent this using the following equation. Note how the reaction isn’t reversible:

$HA (aq) \to H^{+} (aq) + A^{-} (aq)$

On the other hand, weak acids behave a little differently.

A weak acid is an acid that only partially dissociates in solution.

Weak acids form an equilibrium, in which the majority of the molecules present are acid molecules and only a tiny fraction donate their protons and dissociate into ions. The stronger an acid is, the more the equilibrium shifts to the right and the greater the concentration of hydrogen ions in solution.

$HA (aq) ⇋ H^{+} (aq) + A^{-} (aq)$

Remember that acids in solution actually dissociate and react with water to form the hydronium ion, H₃O⁺. In order to simplify the equation, we omit the water and replace the hydronium ion with the hydrogen ion. Here's the original version of the equation:

$HA (aq) + H_{2} O (l) ⇋ H_{3} O^{+} (aq) + A^{-} (aq)$

In contrast, here is the simplified version:

$HA (aq) ⇋ H^{+} (aq) + A^{-} (aq)$

In fact, whenever you see the hydrogen ion in acid-base reactions, you should know that it actually represents the hydronium ion.

Weak bases

We can also find strong and weak bases. Remember that a base is a proton acceptor.

A strong base is a base that dissociates fully in solution.

An example of a strong base is sodium hydroxide, NaOH. Every molecule of NaOH accepts a proton from water, dissociating in solution to form sodium ions and hydroxide ions:

$NaOH (aq) + H_{2} O \to {NaH}^{+} (aq) + {OH}^{-} (aq)$

We also have a simplified way of representing this reaction. Once again, we omit the water molecule:

$NaOH (aq) \to {Na}^{+} (aq) + {OH}^{-} (aq)$

In contrast to sodium hydroxide, ammonia is only a weak base.

A weak base is a base that only partially dissociates in solution.

Like with weak acids, weak bases form an equilibrium in which the backward reaction is strongly favoured, and only a small proportion of the molecules ionise. This means not every molecule of the weak base accepts a proton. We represent the dissociation of ammonia with the following equation:

${NH}_{3} (aq) + H_{2} O (l) ⇋ {NH}_{4}^{+} (aq) + {OH}^{-} (aq)$

The general equations for the dissociation of a strong base and weak base are shown below, with the dissociation of a strong base first:

$B (aq) + H_{2} O (l) \to {BH}^{+} (aq) + {OH}^{-} (aq) B (aq) + H_{2} O (l) ⇋ {BH}^{+} (aq) + {OH}^{-} (aq)$

Don’t get strong and concentrated mixed up - they mean totally different things. Concentration is a measure of how many acid or base molecules are dissolved in solution, whilst strength is a measure of the proportion of these molecules that dissociate into ions. You can concentrated weak acids, as well as dilute strong acids!

Weak acids and bases strong weak concentrated dilute acids Vaia Fig. 1 - Strong and weak concentrated and dilute acids

pH of weak acids and bases

Weak acids have higher pH values than strong acids. Likewise, weak bases have lower pH values than strong bases. This is because weak acids and bases only partially ionise in solution.

Weak acids and bases pH studysmarter Fig. 2 - The pH of acids and bases

Remember that pH is a measure of hydrogen ion concentration in solution. Furthermore, a lower pH means there is a higher concentration of hydrogen ions.

Strong and weak acids and bases

Let's now take some time to compare strong and weak acids and bases. This table should recap the differences we've already mentioned, as well as introduce you to their reactions with metals and conductivities.

	Strong acid	Weak acid	Strong base	Weak base
Behaviour in solution	Fully ionises	Partially ionises	Fully ionises	Partially ionises
Equation	$HA \to H^{+} + A^{-}$	$HA ⇋ H^{+} + A^{-}$	$B + H_{2} O \to {BH}^{+} + {OH}^{-}$	$B + H_{2} O ⇋ {BH}^{+} + {OH}^{-}$
pH (colour range)	1-3 (red-orange)	4-6 (orange-yellow)	8-10 (aqua-blue)	11-13 (blue-purple)
Reaction with reactive metal	Vigorous reaction	Slow reaction	Vigorous reaction	Slow reaction
Conductivity	Very good	Good-poor	Very good	Good-poor
Example	HCl	CH₃COOH	NaOH	NH₃

Weak acids and bases chart

You’ll encounter both strong and weak acids and bases in everyday life. For example, concentrated hydrochloric acid, a strong acid, is used to remove algae from the bottoms of boats, whilst a more dilute solution is used in toilet cleaners. Hydrochloric acid is also the acid found in our stomachs that helps digest our food. Citric acid and ethanoic acid, the acids found in lemons and malt vinegar respectively, are both weak acids. Basic sodium bicarbonate is also known as baking soda, a useful leavening agent in baking, whilst the base calcium hydroxide is used to help neutralise acidic soil.

Here's a handy chart with common chemical examples of strong and weak acids and bases.

Weak acids and bases chart Vaia Fig. 3 - Strong and weak acid and base chart

Weak acids and K_a

Now let's move on to calculations involving weak acids and bases. We'll start by focusing on K_a.

In The Ionic Product of Water, we discussed K_w. K_w is a modified equilibrium constant for the dissociation of water. We can also get K_a, a modified equilibrium constant for the dissociation of weak acids.

The general equation of the equilibrium constant for the reaction $aA + bB ⇋ cC + dD$ is shown below:

$K_{c} = \frac{{[C]}^{c} {[D]}^{d}}{{[A]}^{a} {[B]}^{b}}$

Square brackets represent concentration, and the small letter represents the number of moles of each species in the chemical equation. For example, the equilibrium reaction, $H_{2} (g) + I_{2} (g) ⇌ 2 HI (g)$ , has the following equilibrium constant:

$K_{c} = \frac{{[HI]}^{2}}{[H_{2}] [I_{2}]}$

Let’s look at this from the point of view of a weak acid. It dissociates in solution with the equation $HA (aq) ⇋ H^{+} (aq) + A^{-} (aq)$ . The reactant is the acid and the products are the hydrogen ions and the negative ions. This gives us the following equilibrium constant, known as K_a:

$K_{a} = \frac{[H^{+} (aq)] [A^{-} (aq)]}{[HA (aq)]}$

You can remove the state symbols to simplify the equation if you want.

“But hang on!” We hear you cry. “How about the equation of a weak acid involving water and hydronium ions! Where have they gone?”

If we write out that equation, we get $HA (aq) + H_{2} O (l) ⇋ H_{3} O^{+} (aq) + A^{-} (aq)$ . This produces the following equation for the equilibrium constant:

$K_{c} = \frac{[H_{3} O^{+} (aq)] [A^{-} (aq)]}{[HA (aq)] [H 2 O (l)]}$

However, the concentration of water is so large that it completely dominates all the other values in the equation. To form K_a, we simply omit it.

You should also remember that we use the hydrogen ion to represent the hydronium ion in acid-base reactions. This gives us the familiar equation for K_a:

$K_{a} : \frac{[H^{+} (aq)] [A^{-} (aq)]}{[HA (aq)]}$

The units of K_a

To find the units of K_a, we multiply and cancel down the units of all the species involved in the equation. All three species, [H⁺], [A^-], and [HA], have the units mol dm^-3. The equation now looks like this:

$\frac{mol {dm}^{- 3} x mol {dm}^{- 3}}{mol {dm}^{- 3}}$

One of the mol dm^-3 from the top of the fraction cancels out with the one on the bottom, leaving just one mol dm^-3:

$\frac{mol {dm}^{- 3} x mol {dm}^{- 3}}{mol {dm}^{- 3}}$

K_a and pK_a

Just as pK_w is the negative log of K_w, pK_a is the negative log of K_a:

${pK}_{a} = - \log (K_{a}) K_{a} = 10^{- {pK}_{a}}$

You should note the following relationships between K_a, pK_a, acid strength and pH:

As K_a increases, pK_a and pH both decrease.
As K_a increases, acid strength increases.

Finding Ka from pH

To calculate the pH of weak acids, you use the relationships between K_a, PK_a, and the concentration of the acid in solution. You’ll be given information about the acid’s PK_a or K_a. There are a few more steps compared to working out the pH of a strong acid, but it isn’t too tricky. Let’s have a look at an example together.

Ethanoic acid, CH₃COOH, has K_a = 1.74 x 10^-5. Calculate the pH of a 0.100 mol dm^-3 solution of this weak acid.

First of all, let’s look at the equation for the dissociation of ethanoic acid:

${CH}_{3} COOH (aq) ⇋ H^{+} (aq) + {CH}_{3} {COO}^{-} (aq)$

To find pH, we need to know [H⁺], the concentration of hydrogen ions in solution. Well, what do we know about K_a? It is a modified equilibrium constant for the dissociation of a weak acid such as ethanoic acid and involves [H⁺]. For ethanoic acid, it looks like this:

$K_{a} = \frac{[{CH}_{3} {COO}^{-}] [H^{+}]}{[CH 3 COOH]}$

Let’s think about those values. The concentration of ethanoic acid was originally 0.100 mol dm^-3. At equilibrium, it will be a little less than that because some of the molecules will dissociate into ions. However, ethanoic is a weak acid and hardly any of the molecules dissociate - the equilibrium lies far to the left. We can therefore say that the concentration of ethanoic acid at equilibrium is still roughly 0.100 mol dm^-3. Let’s put that value into our equation:

$K_{a} = \frac{[CH 3 {COO}^{-}] [H^{+}]}{0.100}$

Look back at the equation. When one mole of ethanoic acid dissociates, it forms one mole of positive hydrogen ions, H⁺, and one mole of acetate ions, CH₃COO^-. This means that the number of hydrogen ions in solution equals the number of acetate ions in solution, and thus they have the same concentrations:

$K_{a} = [{CH}_{3} {COO}^{-}] = [H^{+}]$

We can replace [CH₃COO^-] with [H⁺] in our equation for K_a:

$K_{a} = \frac{{[H^{+}]}^{2}}{0.100}$

The question gives us K_a , so we can substitute that in. Now we have an equation where the only unknown is [H⁺]. We can solve it normally, as shown:

$1.74 x 10^{- 5} = \frac{{[H^{+}]}^{2}}{0.100} 1.74 x 10^{- 5} x 0.100 = {[H^{+}]}^{2} \sqrt{1.74 x 10^{- 5} x 0.100} = [H^{+}] 1.319 x 10^{- 3} = [H^{+}]$

You should remember the equation for pH. Substituting our value for [H⁺], we get our final answer:

$pH = - \log ([H^{+}]) = - \log (1.319 x 10^{- 3}) pH = 2.88$

Weak bases and K_b

We know what a weak base is - a base that only partially dissociates in solution. It forms an equilibrium reaction. Just like for acids, we can find an equilibrium constant, this time known as K_b. The equation for K_b is given below using B to represent the base:

$K_{b} = \frac{[{BH}^{+}] [{OH}^{-}]}{[B]}$

Units of K_b

Like K_a , K_b has the units mol dm^-3.

Kb and pKb

You can probably guess how we calculate pK_b. It is simply the negative log of K_b:

${pK}_{b} = - \log (K_{b}) K_{b} = 10^{- {pK}_{b}}$

There’s a special relationship between pK_w , pK_a and pK_b. It is very similar to the relationship we saw between pK_w, pH and pOH in The Ionic Product of Water:

${pK}_{w} = {pK}_{a} + {pK}_{b}$

Finding the pH of weak bases

Finding the pH of a weak base is similar to finding the pH of a weak acid. However, there are a few differences. Let’s look at an example together.

A 0.15 mol dm^-3 solution of NH₃has K_b = 1.77 x 10^-5. What is its pH at 25℃?

First of all, let’s take our equation for the dissociation of ammonia and our equation for K_b:

${NH}_{3} (aq) + H_{2} O (l) ⇌ {NH}_{4}^{+} (aq) + {OH}^{-} (aq) K_{b} = \frac{[{NH}_{4}^{+}] [{OH}^{-}]}{[{NH}_{3}]}$

We know from the first equation that the amounts of ammonium ions, NH₄⁺, and hydroxide ions, OH^-, are equal. They therefore have equal concentrations. This simplifies the equation for K_b:

$K_{b} = \frac{{[{OH}^{-}]}^{2}}{[{NH}_{3}]}$

We know the value for K_b and we know the concentration of ammonia, NH₃. Our original solution had a concentration of 0.15 mol dm^-3. Though the equilibrium solution will have a slightly lower concentration, the proportion of molecules that have dissociated into ions is so small that we can largely ignore it. Therefore, the equilibrium concentration of NH₃ molecules still roughly equals 0.15 mol dm^-3. We can substitute these values in to the equation and rearrange to find [OH^-]:

$1.77 x 10^{- 5} = \frac{{[{OH}^{-}]}^{2}}{0.15} \sqrt{1.77 x 10^{- 5} x 0.15} = [{OH}^{-}] = 1.63 x 10^{- 3} mol {dm}^{- 3}$

We can then use the relationships between [OH^-], pOH, pK_w and pH to work out the pH, just like we did to find the pH of a strong base. (If you aren’t too sure about this, check out Brønsted-Lowry Acids and Bases for a detailed explanation.)

$pOH = - \log ([{OH}^{-}]) pOH = - \log (1.63 x 10^{- 3}) = 2.79 pH = {pK}_{w} - pOH pH = 14 - 2.79 = 11.21$

Steps for finding the pH of weak acids and bases

Congratulations! You made it through some tricky calculations. You should now be able to work out the pH values for all sorts of acids, bases, and mixtures.

The following flowchart provides a summary of the steps taken to work out the pH of weak acids and bases. Remember to check out all of the other articles we mentioned here for more information about various acid-base calculations.

Weak acids and bases flow chart pH Vaia Fig. 4 - Finding the pH of weak acids and bases

Weak acid and base titrations

We've learned that weak acids have higher pH values than strong acids, whilst weak bases have lower pH values than storng bases. This means that they produce slightly different pH curves in titration experiments. You can explore this more in pH Curves and Titrations.

Weak Acids and Bases - Key takeaways

A weak acid is an acid that only partially dissociates in solution. These form an equilibrium represented by the equation $HA (aq) ⇋ H^{+} (aq) + A^{-} (aq)$
A weak base is a base that only partially dissociates in solution. These form an equilibrium represented by the equation $B (aq) + H_{2} O (l) ⇋ {BH}^{+} (aq) + {OH}^{-} (aq)$
K_a is a modified equilibrium constant for the dissociation of weak acids. It is represented by the equation $K_{a} = \frac{[H^{+}] [A^{-}]}{[HA]}$
K_b is a modified equilibrium constant for the dissociation of weak bases. It is represented by the equation $K_{b} = \frac{[{BH}^{+}] [{OH}^{-}]}{[B]}$
Both K_a and K_b take the units mol dm^-3.
${pK}_{a} = - \log (K_{a})$ and ${pK}_{b} = - \log (K_{b})$
We can use K_a and K_b to find the pH of solutions containing weak acids and bases.

Frequently Asked Questions about Weak Acids and Bases

You can identify weak acids and bases based on the fact that they only partially dissociate in solution. They tend to have pH values closer to 7 than strong acids and bases.

Weak acids and bases are, as the name suggests, types of acids and bases. They differ from strong acids and bases in that they only partially dissociate in solution.

To work out the pH of weak acids and bases, you use the equilibrium constants K_a and K_b to work out the concentrations of hydrogen ions or hydroxide ions in solution. You can then calculate pH.

Phenolphthalein would be a suitable indicator for a titration reaction between a weak acid and a strong base.

Strong acids fully dissociate in solution whereas weak acids only partially dissociate.

Final Weak Acids and Bases Quiz

Weak Acids and Bases Quiz - Teste dein Wissen

Question

What is a weak acid?

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Answer

An acid that only partially dissociates in solution.

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Question

What is a weak base?

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Answer

A base that only partially dissociates in solution.

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Question

Compare the terms concentrated and strong in terms of an acid.

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Answer

Concentrated means that there are lots of acid molecules dissolved in the solution.
Strong means that all of the acid molecules have dissociated into ions.

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Question

Qualitatively compare the pH values of strong and weak acids.

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Answer

Strong acids have lower pH values than weak acids.

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Question

Qualitatively compare the pH values of strong and weak bases.

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Answer

Strong bases have higher pH values than weak bases.

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Question

Give an example of a weak acid.

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Answer

Ethanoic acid, CH₃COOH.

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Question

What is Ka?

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Answer

An equilibrium constant that measures the extent of dissociation of a weak acid in solution at equilibrium.

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Question

What are the units of Ka?

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Answer

mol dm^-3

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Question

The higher the value of Ka, the ____.

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Answer

Stronger the acid.

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Question

The higher the value of pKa, the ____.

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Answer

Weaker the acid.

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Question

Outline the steps used to find Ka from pH.

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Answer

Write an expression for Ka.
Find [H⁺] using pH. Hence, find [A^-].
Find [HA].
Substitute values for [H⁺], [A^-], and [HA] into the expression for Ka and solve.

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Question

What two assumptions do we make when calculating Ka from pH?

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Answer

The concentration of HA molecules at equilibrium is the same as the original amount of acid added to the solution.
The entire equilibrium concentration of H⁺ is due to the dissociation of the weak acid, HA; we ignore any H⁺ions from the dissolution of water.

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Question

How do half-neutralisation and pH relate to Ka?

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Answer

The pH at the half-neutralisation point of a weak acid equals its pKa.

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Question

How do you find the pH at the half-neutralisation point on a titration curve?

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Answer

Locate the equivalence point. This point lies in the middle of the steep vertical section of the curve.
Use the equivalence point to find the equivalence point volume.
Use the equivalence point volume to find the half-neutralisation point volume.
Use the graph and the half-neutralisation point volume to identify the half-neutralisation pH.

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Question

What is a conjugate base?

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Answer

The base formed when an acid donates a proton in solution.

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Question

The higher the value of a weak acid's Ka, the ____ the value of its conjugate base's Kb.

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Answer

Lower

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Question

The higher the value of Ka, the ____ the percentage ionisation in solution.

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Answer

Greater

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Question

Which of the following give you enough information to find Ka?

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Answer

[H⁺], [A^-], and [HA].

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Weak Acids and Bases

Weak Acids and Bases

Weak Acids and Bases

Defining weak acids and bases

Weak acids

Weak bases

pH of weak acids and bases

Strong and weak acids and bases

Weak acids and bases chart

Weak acids and Ka

The units of Ka

Ka and pKa

Finding Ka from pH

Weak bases and Kb

Units of Kb

Kb and pKb

Finding the pH of weak bases

Steps for finding the pH of weak acids and bases

Weak acid and base titrations

Weak Acids and Bases - Key takeaways

Frequently Asked Questions about Weak Acids and Bases

How do you identify weak acids and bases?

What are weak acids and bases?

How do you find the pH of weak acids and weak bases?

What indicator is used for a weak acid and strong base?

What is the difference between strong and weak acids?

Final Weak Acids and Bases Quiz

Weak Acids and Bases Quiz - Teste dein Wissen

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Weak acids and K_a

The units of K_a

K_a and pK_a

Weak bases and K_b

Units of K_b