Calculate The Ph Of 0.050 M C5H5N

Use this premium pyridine solution calculator to find pH, pOH, hydroxide concentration, and ionization percentage for a C5H5N solution. The default example is 0.050 M pyridine at 25°C using a standard weak-base equilibrium model.

Default answer for 0.050 M C5H5N: the pH is approximately 8.965 when Kb = 1.7 × 10^-9 at 25°C.

How to calculate the pH of 0.050 M C5H5N

To calculate the pH of 0.050 M C5H5N, you treat C5H5N, better known as pyridine, as a weak base in water. Unlike strong bases such as NaOH, pyridine does not dissociate completely. Instead, it reacts only partially with water to form its conjugate acid, C5H5NH+, and hydroxide ions, OH-. Because the pH of a basic solution depends on the amount of OH- produced, the core of the problem is a weak-base equilibrium calculation.

The relevant reaction is:

C5H5N + H2O ⇌ C5H5NH+ + OH-

The base dissociation constant for pyridine at 25°C is commonly taken as Kb = 1.7 × 10^-9. Starting with an initial concentration of 0.050 M, you can define the change in concentration as x, where x equals the equilibrium concentration of OH-. The equilibrium expression is:

Kb = [C5H5NH+][OH-] / [C5H5N]

If the initial concentration of pyridine is 0.050 M and x is small relative to 0.050, then:

1.7 × 10^-9 = x² / 0.050

Solving for x gives:

x = √(1.7 × 10^-9 × 0.050) = 9.22 × 10^-6 M

That means [OH-] = 9.22 × 10^-6 M. From there:

• pOH = -log(9.22 × 10^-6) ≈ 5.035
• pH = 14.000 – 5.035 = 8.965

So the pH of a 0.050 M pyridine solution is approximately 8.97. This is basic, but only mildly so, because pyridine is a weak base with a very small Kb.

Why pyridine does not produce a high pH like a strong base

Students often expect every base-containing solution to have a very high pH. That assumption works for strong bases, but not for weak bases. Pyridine contains a nitrogen atom with a lone pair, so it can accept a proton. However, the lone pair in pyridine is influenced by the aromatic ring structure, and that reduces its basicity compared with simpler amines. As a result, only a tiny fraction of pyridine molecules react with water at equilibrium.

That is why a 0.050 M pyridine solution has a pH under 9, even though 0.050 M sounds fairly concentrated. The equilibrium simply does not favor hydroxide production strongly enough to push the solution into strongly basic territory.

Key chemical facts about C5H5N

• Pyridine is a weak base and a heteroaromatic compound.
• Its conjugate acid is pyridinium, written as C5H5NH+.
• Its base dissociation constant at 25°C is about 1.7 × 10^-9.
• Its pKb is about 8.77, while the pKa of pyridinium is about 5.23.
• Because Kb is small, the percent ionization remains very low even at 0.050 M.

Step-by-step method using an ICE table

An ICE table is one of the most reliable ways to organize weak-acid and weak-base equilibrium problems. For the pyridine problem, the table looks like this:

Species	Initial (M)	Change (M)	Equilibrium (M)
C5H5N	0.050	-x	0.050 – x
C5H5NH+	0	+x	x
OH-	0	+x	x

Insert those equilibrium concentrations into the Kb expression:

Kb = x² / (0.050 – x)

For highly accurate work, solve the quadratic exactly. For typical general chemistry homework, the approximation 0.050 – x ≈ 0.050 is acceptable because x is much smaller than 0.050. In this case the approximation is excellent, since the ionization percentage is only around 0.018%.

Exact quadratic solution

Using the exact form:

1.7 × 10^-9 = x² / (0.050 – x)

Rearranging:

x² + (1.7 × 10^-9)x – (8.5 × 10^-11) = 0

Solving the quadratic gives essentially the same positive root:

x ≈ 9.22 × 10^-6 M

That confirms the approximation is valid here.

Comparison table: weak base versus strong base at the same initial concentration

The following comparison helps explain why pyridine behaves so differently from a strong base. These values assume 25°C and idealized aqueous behavior.

Solution	Initial concentration (M)	Characteristic constant	Approximate [OH-] at equilibrium	Approximate pH
Pyridine, C5H5N	0.050	Kb = 1.7 × 10^-9	9.22 × 10^-6 M	8.97
Ammonia, NH3	0.050	Kb = 1.8 × 10^-5	9.40 × 10^-4 M	10.97
Sodium hydroxide, NaOH	0.050	Strong base, near-complete dissociation	5.0 × 10^-2 M	12.70

This table shows how dramatically equilibrium strength affects pH. Pyridine and ammonia are both weak bases, but ammonia is far stronger than pyridine, so it generates much more OH-. NaOH, as a strong base, produces hydroxide essentially equal to its formal concentration.

Percent ionization of 0.050 M pyridine

Percent ionization tells you what fraction of the original base actually reacts with water:

Percent ionization = ([OH-] / initial concentration) × 100

Substitute the numbers:

(9.22 × 10^-6 / 0.050) × 100 = 0.0184%

That tiny percentage is the reason the weak-base approximation works so well. Because less than two hundredths of one percent of the pyridine reacts, the initial concentration barely changes.

What the low ionization means in practice

• The solution is basic, but only mildly basic.
• The concentration of unreacted pyridine remains essentially 0.050 M.
• The hydroxide concentration is many thousands of times smaller than the formal pyridine concentration.
• Small changes in Kb or temperature can shift the calculated pH slightly, but not enough to make the solution strongly basic.

Common mistakes when solving this problem

1. Treating pyridine as a strong base. If you assume complete dissociation, you would wrongly set [OH-] = 0.050 M and obtain a pH near 12.70, which is far too high.
2. Using Ka instead of Kb. Pyridine is a base, so use Kb unless you are working from the conjugate-acid Ka and converting through Kw.
3. Confusing pOH and pH. After finding [OH-], you calculate pOH first, then convert to pH using pH + pOH = 14.00 at 25°C.
4. Using the wrong logarithm sign. Remember that pOH = -log[OH-].
5. Ignoring units and significant figures. For chemistry coursework, 8.97 or 8.965 is typically appropriate depending on the requested precision.

How pH changes with pyridine concentration

As the concentration of a weak base increases, pH rises, but not linearly. Because the approximation gives [OH-] ≈ √(KbC), hydroxide concentration scales with the square root of concentration rather than matching it directly. That means doubling concentration does not double [OH-]. It increases OH- by a factor of about √2, and the pH changes more gradually than students sometimes expect.

Pyridine concentration (M)	Estimated [OH-] (M)	Estimated pOH	Estimated pH
0.005	2.92 × 10^-6	5.535	8.465
0.050	9.22 × 10^-6	5.035	8.965
0.500	2.92 × 10^-5	4.535	9.465

This pattern is very useful when checking whether an answer is physically reasonable. A tenfold increase in concentration raises the pH by only about 0.5 unit for this weak base under the approximation.

When to use the exact method instead of the approximation

The approximation is usually acceptable if x is less than 5% of the initial concentration. In this pyridine example, x is far below that threshold, so the approximation is excellent. However, if you work with very dilute weak-base solutions or with stronger weak bases, it is safer to solve the quadratic exactly. The calculator above offers both methods so you can compare them directly.

Quick rule of thumb

• Use the approximation when Kb is small and the initial concentration is not extremely low.
• Use the exact quadratic if your instructor requires rigorous treatment or if the 5% rule looks questionable.
• For pyridine at 0.050 M, both methods give essentially identical pH values.

Authoritative chemistry references

If you want to verify equilibrium constants, acid-base concepts, or pH definitions from highly credible sources, these references are useful:

• NIST Chemistry WebBook
• Chemistry LibreTexts hosted by higher-education institutions
• U.S. Environmental Protection Agency
• NCBI Bookshelf chemistry and biochemistry references
• Encyclopaedia Britannica overview of pH

.gov and .edu resources for deeper study

For readers who specifically want government and university references, the following sources are especially relevant to acid-base chemistry, water chemistry, and chemical data:

• National Institute of Standards and Technology (NIST) Chemistry WebBook
• U.S. EPA overview of pH and water chemistry
• LibreTexts chemistry courses used by many colleges and universities

Final answer

Using Kb = 1.7 × 10^-9 for pyridine at 25°C, the pH of a 0.050 M C5H5N solution is:

pH ≈ 8.97

That answer comes from calculating the equilibrium hydroxide concentration, converting to pOH, and then subtracting from 14.00. Because pyridine is a weak base, the solution is only mildly basic, and the percent ionization is extremely small.