Calculate The Ph Of 0.20 M Nacn

Chemistry Calculator

Solve the pH of a sodium cyanide solution using cyanide hydrolysis, the acid dissociation constant of HCN, and the ionic product of water. This tool shows pH, pOH, Kb, hydroxide concentration, and percent hydrolysis.

NaCN pH Calculator

Core chemistry used: CN⁻ + H₂O ⇌ HCN + OH⁻ and Kb = Kw / Ka.

How to calculate the pH of 0.20 M NaCN

If you need to calculate the pH of 0.20 M NaCN, the key idea is that sodium cyanide is a salt of a strong base and a weak acid. The sodium ion, Na⁺, is essentially a spectator ion in water. The cyanide ion, CN⁻, is the chemically important species because it behaves as a weak base and reacts with water to generate hydroxide ions. Since hydroxide is produced, the solution becomes basic and the pH rises above 7.

The correct equilibrium begins with complete dissociation of the salt:

NaCN(aq) → Na⁺(aq) + CN⁻(aq)

Once cyanide is in solution, it hydrolyzes water:

CN⁻(aq) + H₂O(l) ⇌ HCN(aq) + OH⁻(aq)

This is why a sodium cyanide solution is basic. Cyanide is the conjugate base of hydrocyanic acid, HCN. Because HCN is a weak acid, its conjugate base has measurable basic strength. At 25 C, a commonly used Ka value for HCN is about 6.2 × 10^-10. From this, you can calculate the base dissociation constant for cyanide:

Kb = Kw / Ka = (1.0 × 10^-14) / (6.2 × 10^-10) = 1.61 × 10^-5

Now set up the ICE table for a 0.20 M cyanide solution. At the start, the cyanide concentration is 0.20 M, and the hydroxide produced from hydrolysis is effectively zero compared with what the reaction will generate.

Initial: [CN⁻] = 0.20, [HCN] = 0, [OH⁻] = 0 Change: [CN⁻] = -x, [HCN] = +x, [OH⁻] = +x Equil.: [CN⁻] = 0.20 – x, [HCN] = x, [OH⁻] = x

Insert these equilibrium terms into the Kb expression:

Kb = [HCN][OH⁻] / [CN⁻] = x² / (0.20 – x)

For many classroom problems, the weak base approximation is acceptable because x is much smaller than 0.20. Using that approximation:

x ≈ √(KbC) = √((1.61 × 10^-5)(0.20)) = √(3.22 × 10^-6) ≈ 1.79 × 10^-3 M

That x value is the hydroxide concentration:

[OH⁻] ≈ 1.79 × 10^-3 M

Then calculate pOH:

pOH = -log[OH⁻] = -log(1.79 × 10^-3) ≈ 2.75

Finally:

pH = 14.00 – 2.75 ≈ 11.25

Final answer at 25 C: the pH of 0.20 M NaCN is approximately 11.25 when Ka for HCN is taken as 6.2 × 10^-10.

Why NaCN is basic in water

Students often ask why a salt can make water basic. The answer depends on the acid and base from which the salt was formed. Sodium hydroxide is a strong base, while hydrocyanic acid is a weak acid. A salt formed from a strong base and weak acid usually gives a basic aqueous solution because the anion hydrolyzes water. Here, CN⁻ pulls a proton from water to produce HCN and OH⁻. The extra hydroxide raises pH.

• Na⁺ is neutral in water for general acid base calculations.
• CN⁻ is a weak base.
• OH⁻ production makes the solution basic.
• HCN is weak, so cyanide remains a meaningfully reactive conjugate base.

Exact solution versus approximation

For 0.20 M NaCN, the approximation works very well because the amount hydrolyzed is under 1 percent of the initial concentration. Still, if you want the most rigorous value, solve the quadratic equation directly:

Kb = x² / (C – x) → x² + Kbx – KbC = 0

Using Kb = 1.61 × 10^-5 and C = 0.20 M:

x = [-Kb + √(Kb² + 4KbC)] / 2

This gives an OH⁻ concentration very close to the approximation result, and the pH remains about 11.25. In practical educational settings, both methods lead to the same reported answer when rounded to two decimal places.

Step by step method you can use on exams

1. Write the salt dissociation equation: NaCN → Na⁺ + CN⁻.
2. Identify the reactive ion: CN⁻ is the conjugate base of weak acid HCN.
3. Write the hydrolysis reaction: CN⁻ + H₂O ⇌ HCN + OH⁻.
4. Convert Ka to Kb using Kb = Kw / Ka.
5. Set up an ICE table with initial CN⁻ concentration equal to the salt concentration.
6. Solve for x to find [OH⁻].
7. Compute pOH = -log[OH⁻].
8. Compute pH = 14.00 – pOH at 25 C.

Reference values relevant to the calculation

The exact numerical pH depends on accepted equilibrium constants and temperature. In many textbooks and lab manuals, the HCN Ka is reported close to 6.2 × 10^-10 at 25 C. Since Kb is found by dividing Kw by Ka, a small change in Ka slightly changes the final pH. This is why you may see answers such as 11.24, 11.25, or 11.26 in different sources.

Quantity	Typical value at 25 C	Role in the pH calculation
NaCN concentration	0.20 M	Sets the initial [CN⁻] after complete dissociation.
Ka of HCN	6.2 × 10^-10	Used to determine the strength of the conjugate base CN⁻.
Kw	1.0 × 10^-14	Connects Ka and Kb through Kb = Kw / Ka.
Kb of CN⁻	1.61 × 10^-5	Determines the extent of cyanide hydrolysis.
[OH⁻]	1.79 × 10^-3 M	Leads directly to pOH and then pH.
Calculated pH	11.25	Final answer for 0.20 M NaCN at 25 C.

How concentration affects the pH of cyanide solutions

A useful insight is that stronger formal concentration leads to higher hydroxide concentration and therefore higher pH, though the increase is not linear on the pH scale because pH is logarithmic. For weak bases, [OH⁻] often scales approximately with the square root of concentration when the approximation is valid.

NaCN concentration (M)	Approximate [OH⁻] (M)	Approximate pOH	Approximate pH at 25 C
0.010	4.01 × 10^-4	3.40	10.60
0.050	8.97 × 10^-4	3.05	10.95
0.10	1.27 × 10^-3	2.90	11.10
0.20	1.79 × 10^-3	2.75	11.25
0.50	2.84 × 10^-3	2.55	11.45

These values show a common pattern in weak base chemistry: increasing concentration raises pH, but not by the same number of pH units per concentration step. This is one reason logarithmic thinking is so important in acid base work.

Common mistakes when solving NaCN pH problems

• Treating NaCN as neutral. It is not neutral because CN⁻ hydrolyzes water.
• Using Ka directly without converting to Kb. The reactive species is CN⁻, so you need Kb or an equivalent expression based on Ka and Kw.
• Forgetting to calculate pOH first. Since hydrolysis produces OH⁻, it is often easiest to find pOH and then convert to pH.
• Assuming x is always negligible without checking. The approximation is excellent here, but in other problems it may not be.
• Ignoring temperature. If Kw changes, the relationship between pH and pOH changes slightly.

Why different sources may report slightly different pH values

If you compare published examples, you may notice minor variations. That usually comes from one or more of the following:

• Different accepted Ka values for HCN.
• Different rounding practices.
• Approximation versus exact quadratic solution.
• Different temperature assumptions.

For example, using Ka values around 4.9 × 10^-10 to 6.2 × 10^-10 changes Kb enough to shift the final pH by a few hundredths. In a classroom setting, that is usually acceptable as long as the method is chemically correct and the constants are clearly stated.

Safety and handling context for cyanide chemistry

Cyanide chemistry appears in analytical chemistry, industrial chemistry, environmental chemistry, and toxicology discussions. However, sodium cyanide is highly hazardous and should never be handled outside properly equipped professional settings. The calculator and explanation here are for educational chemistry only. For toxicology and safety information, consult official institutional guidance.

Authoritative references

For deeper study, review acid base and cyanide information from authoritative sources:

• PubChem, U.S. National Library of Medicine: Hydrogen Cyanide
• U.S. Environmental Protection Agency: Cyanide Information
• Chemistry educational materials hosted by academic institutions via LibreTexts

Bottom line

To calculate the pH of 0.20 M NaCN, focus on cyanide hydrolysis, not on sodium. Convert the weak acid constant of HCN to the base constant of CN⁻, solve for the hydroxide concentration, then convert to pOH and pH. With Ka(HCN) = 6.2 × 10^-10 and Kw = 1.0 × 10^-14 at 25 C, the solution gives a pH of about 11.25. That value is fully consistent with NaCN being a basic salt in water.