Calculate The Ph In 1.67 M Ch3Co2H

Use this interactive weak acid calculator to determine the pH of acetic acid solution, verify each equilibrium step, and visualize the resulting concentrations of CH3CO2H, H+, and CH3CO2-. The default values are set for 1.67 M acetic acid, so you can calculate the answer instantly or explore how changing Ka affects the result.

Results

How to calculate the pH in 1.67 M CH3CO2H

To calculate the pH in 1.67 M CH3CO2H, you treat acetic acid as a weak acid rather than as a strong acid that dissociates completely. This is the key idea that controls the entire problem. CH3CO2H, also written as HC2H3O2, exists mostly in molecular form in water, and only a small fraction ionizes to produce hydrogen ions. Because pH depends on the hydrogen ion concentration, the correct calculation must use the acid dissociation constant, Ka, instead of assuming that the hydrogen ion concentration is equal to the formal molarity.

At 25 degrees C, a commonly used value for the acid dissociation constant of acetic acid is 1.8 x 10^-5. The dissociation equilibrium is:

CH3CO2H ⇌ H+ + CH3CO2-

If the initial concentration of acetic acid is 1.67 M, and x represents the amount that dissociates, the equilibrium concentrations become:

• [CH3CO2H] = 1.67 – x
• [H+] = x
• [CH3CO2-] = x

You then substitute these values into the equilibrium expression:

Ka = x^2 / (1.67 – x)

Using Ka = 1.8 x 10^-5 gives:

1.8 x 10^-5 = x^2 / (1.67 – x)

Because acetic acid is weak and the concentration is fairly large, x is much smaller than 1.67. That means many chemistry students first use the common approximation:

x ≈ √(Ka x C)

Substituting the values:

x ≈ √(1.8 x 10^-5 x 1.67) ≈ 5.48 x 10^-3 M

Then:

pH = -log10(5.48 x 10^-3) ≈ 2.26

If you solve the quadratic exactly, the answer is almost identical:

[H+] ≈ 5.47 x 10^-3 M and pH ≈ 2.26

So the pH in 1.67 M CH3CO2H is approximately 2.26 at 25 degrees C, using Ka = 1.8 x 10^-5. This value makes chemical sense. Even though the formal concentration is high, acetic acid does not fully dissociate, so the pH is much higher than the pH of a 1.67 M strong acid, which would be negative or close to zero depending on activity corrections.

Why acetic acid must be handled as a weak acid

Many pH calculation mistakes happen when learners confuse concentration with ionization. A 1.67 M strong monoprotic acid would contribute nearly 1.67 M hydrogen ions, giving a very low pH. But acetic acid is fundamentally different because its Ka is small. The Ka value tells you the equilibrium strongly favors the undissociated form. In practical terms, acetic acid molecules remain mostly intact in solution, and only a small percentage release H+.

That is why a weak acid calculation requires an ICE setup, where ICE means Initial, Change, and Equilibrium. It gives a systematic way to connect the known starting concentration to the unknown hydrogen ion concentration. Once [H+] is found, converting to pH is straightforward using the logarithm definition.

Step by step solution using the ICE table

1. Write the balanced acid dissociation equation: CH3CO2H ⇌ H+ + CH3CO2-.
2. Set the initial concentration of CH3CO2H to 1.67 M and assume initial H+ and CH3CO2- from the acid are 0.
3. Let x be the amount dissociated.
4. Write equilibrium concentrations as 1.67 – x, x, and x.
5. Substitute into Ka = [H+][A-]/[HA].
6. Use Ka = 1.8 x 10^-5 to solve for x.
7. Set [H+] = x.
8. Compute pH = -log10[H+].

This is the standard approach taught in general chemistry, analytical chemistry, and introductory equilibrium theory. It is also highly reusable. Once you understand the method for acetic acid, you can adapt the same logic to propionic acid, benzoic acid, hydrofluoric acid, and many other weak acids.

Exact solution versus approximation

For weak acid calculations, instructors often show two approaches. The approximate method assumes x is negligible compared with the initial concentration, so 1.67 – x is replaced with 1.67. The exact method solves the quadratic equation directly. In this problem, both methods produce nearly the same answer because the acid dissociation is very small relative to the starting concentration.

Method	Hydrogen Ion Concentration, [H+]	Calculated pH	Comment
Approximation	5.48 x 10^-3 M	2.261	Fast and appropriate when x is much smaller than 1.67
Exact quadratic	5.47 x 10^-3 M	2.262	Most rigorous textbook method for weak acid equilibrium
Difference	About 0.00001 M	Less than 0.001 pH unit	Negligible for most educational and practical uses

This tiny difference shows why the square root shortcut is so popular in chemistry classes. However, if your concentration is very low, or if your Ka is not especially small compared with the starting concentration, the approximation may fail. In those cases the quadratic equation is safer.

Percent ionization of 1.67 M CH3CO2H

Percent ionization helps explain why the pH remains much higher than that of a strong acid. It is calculated as:

Percent ionization = ([H+] / initial concentration) x 100

Using the exact value:

(5.47 x 10^-3 / 1.67) x 100 ≈ 0.33%

That means only about one-third of one percent of the acetic acid molecules ionize under these conditions. More than 99.6% remain in the protonated CH3CO2H form. This is the chemical reason the pH does not remotely approach the pH of a 1.67 M strong acid.

Comparison with other acetic acid concentrations

One useful way to understand weak acid behavior is to compare pH across several concentrations while keeping the same Ka. The values below are based on Ka = 1.8 x 10^-5 at 25 degrees C and are representative textbook calculations using the weak acid equilibrium relationship.

Acetic Acid Concentration	Approximate [H+]	Approximate pH	Approximate Percent Ionization
0.010 M	4.24 x 10^-4 M	3.37	4.24%
0.100 M	1.34 x 10^-3 M	2.87	1.34%
1.00 M	4.24 x 10^-3 M	2.37	0.42%
1.67 M	5.48 x 10^-3 M	2.26	0.33%

This table illustrates an important equilibrium trend: as the concentration of a weak acid increases, the pH decreases, but the percent ionization also decreases. In other words, stronger concentration does not mean proportionally stronger dissociation. The equilibrium suppresses the fraction ionized as more undissociated acid is present.

Ka, pKa, and what they tell you

The Ka of acetic acid is about 1.8 x 10^-5, and its pKa is about 4.74 to 4.76 depending on the source and temperature used. Ka and pKa are simply two ways of expressing acid strength. A larger Ka means stronger dissociation. A smaller pKa means stronger acidity. Acetic acid is weak compared with mineral acids such as hydrochloric acid, nitric acid, or perchloric acid, but it is still acidic enough to produce a pH in the low twos at high concentrations.

Because pH is logarithmic, it is worth appreciating what a pH of 2.26 actually means. Relative to pure water at pH 7, the hydrogen ion concentration is about 10^(7 – 2.26), or roughly 55,000 times higher. So even though acetic acid dissociates only slightly, a concentrated acetic acid solution is still strongly acidic in ordinary laboratory handling terms.

Common errors students make

• Assuming [H+] = 1.67 M because the acid concentration is 1.67 M.
• Forgetting that CH3CO2H is a weak acid and must be solved with Ka.
• Using pKa directly without first converting to [H+] or using the proper equilibrium relationship.
• Ignoring the logarithm sign when converting [H+] to pH.
• Rounding Ka too aggressively, which can slightly shift the final pH.

If you avoid these mistakes and use an ICE table consistently, weak acid pH problems become much more manageable.

When the simple model begins to break down

For many classroom calculations, using concentration instead of activity is acceptable. However, at higher ionic strengths, especially in concentrated solutions, activity effects can make the measured pH differ somewhat from the ideal equilibrium prediction. In advanced chemistry, the distinction between concentration and activity becomes important, and a pH meter may not exactly match the textbook number. Still, for standard educational problem solving, the accepted answer remains approximately 2.26 for 1.67 M CH3CO2H.

Practical conclusion: using Ka = 1.8 x 10^-5 and standard weak acid equilibrium assumptions, the pH of 1.67 M acetic acid is approximately 2.26.

Authoritative references for acid dissociation and pH concepts

For deeper reading on pH, acid-base equilibrium, and water chemistry fundamentals, consult these reliable educational sources:

• USGS: pH and Water
• University of Wisconsin Chemistry Netorial: Acids and Bases
• MIT OpenCourseWare: Acid-Base Equilibrium

Final answer summary

If the question is simply “calculate the pH in 1.67 M CH3CO2H,” the standard chemistry answer is:

1. Use acetic acid Ka = 1.8 x 10^-5.
2. Set up Ka = x^2 / (1.67 – x).
3. Solve for x to find [H+] ≈ 5.47 x 10^-3 M.
4. Compute pH = -log10(5.47 x 10^-3) ≈ 2.26.

The final pH is 2.26, which reflects weak acid behavior, not complete dissociation. This distinction is the heart of the problem and the reason equilibrium chemistry matters.

Educational note: values may vary slightly depending on the Ka source, temperature, and whether ideal concentration or activity corrections are used. For most general chemistry contexts, 2.26 is the correct reported result.