Calculate the pH of a 200 mL Solution of Pure Water
Use this premium calculator to determine the pH, hydrogen ion concentration, hydroxide ion concentration, and moles present in 200 mL of pure water. The key chemistry principle is that for pure water, pH depends on temperature, not on sample volume, as long as the water remains pure.
Calculator
Enter the water sample volume.
200 mL is the standard example.
Neutral pH changes with temperature.
Air exposure can lower pH due to dissolved carbon dioxide.
For classroom problems, pH 7.00 at 25 degrees C is often assumed unless temperature effects are being discussed.
Results
Expert Guide: How to Calculate the pH of a 200 mL Solution of Pure Water
When students first encounter a chemistry problem asking them to calculate the pH of a 200 mL solution of pure water, the question can seem trickier than it actually is. The reason is simple: many acid-base problems train you to focus on concentration, moles, dilution, and volume changes. In this specific case, however, the chemistry of pure water is governed by water’s own autoionization equilibrium. That means the result is not driven by the fact that the sample is 200 mL. Instead, the pH is determined primarily by temperature and whether the water is truly pure or has absorbed gases such as carbon dioxide from the air.
At the standard classroom condition of 25 degrees C, pure water is neutral with a hydrogen ion concentration of 1.0 x 10^-7 mol/L and a hydroxide ion concentration of 1.0 x 10^-7 mol/L. From this, the pH is:
So if the question is simply asking for the pH of 200 mL of pure water at 25 degrees C, the answer is 7.00. The 200 mL value matters only if you are also asked to compute the actual number of moles of H+ or OH- present in that sample.
Why Volume Does Not Change the pH of Pure Water
pH is a measure of concentration, not total amount. Specifically, pH depends on the concentration of hydrogen ions in moles per liter. If a liquid remains chemically identical, then taking a smaller sample or a larger sample does not change that concentration. A cup of truly pure water and a tank of truly pure water at the same temperature have the same pH, because their [H+] values are the same.
This is one of the most important concepts for solving the problem correctly. A 200 mL sample contains less total material than 1 liter, but the concentration remains constant. The concentration of H+ in pure water at 25 degrees C is still 1.0 x 10^-7 mol/L. Therefore, the pH remains 7.00.
Key idea
- pH depends on concentration of H+, not volume.
- Moles depend on volume, because moles = concentration x volume.
- Neutral pH depends on temperature, so pure water is not always exactly pH 7.00 at every temperature.
Step-by-Step Calculation for 200 mL of Pure Water at 25 Degrees C
- Recognize that the water is described as pure.
- At 25 degrees C, pure water has [H+] = [OH-] = 1.0 x 10^-7 mol/L.
- Apply the pH formula: pH = -log10[H+].
- Substitute the hydrogen ion concentration: pH = -log10(1.0 x 10^-7) = 7.00.
- If needed, convert volume to liters: 200 mL = 0.200 L.
- Calculate moles of hydrogen ions: (1.0 x 10^-7 mol/L) x (0.200 L) = 2.0 x 10^-8 mol.
- Conclude that the sample contains 2.0 x 10^-8 mol of H+, but its pH is still 7.00.
Autoionization of Water Explained
Pure water undergoes a very slight self-ionization process called autoionization or self-ionization. In this equilibrium, one water molecule donates a proton to another:
In introductory chemistry, hydronium concentration is usually represented simply as [H+]. At 25 degrees C, the ion-product constant for water is:
For pure water, [H+] and [OH-] are equal. Therefore:
That is the direct chemical reason the pH of pure water is 7.00 at 25 degrees C. The sample size does not appear anywhere in this derivation because Kw is an equilibrium constant expressed in terms of concentration.
Comparison Table: pH, Concentration, and Moles in a 200 mL Sample
| Property | Value at 25 degrees C | Why It Matters |
|---|---|---|
| Volume | 200 mL = 0.200 L | Needed for calculating moles, not pH directly. |
| [H+] | 1.0 x 10^-7 mol/L | Defines pH of pure neutral water at 25 degrees C. |
| [OH-] | 1.0 x 10^-7 mol/L | Equal to [H+] in pure water. |
| pH | 7.00 | Neutral at 25 degrees C. |
| Moles of H+ in 200 mL | 2.0 x 10^-8 mol | Shows total ion amount in the sample. |
| Moles of OH- in 200 mL | 2.0 x 10^-8 mol | Matches H+ because the sample is pure water. |
Temperature Matters More Than Volume
One subtle but important point is that the neutral pH of pure water changes with temperature because Kw changes with temperature. As water gets warmer, autoionization becomes more extensive, so [H+] increases and neutral pH decreases. This does not mean the water becomes acidic in the usual sense. It still remains neutral because [H+] equals [OH-]. The value simply shifts below 7.00 at higher temperatures and above 7.00 at lower temperatures.
This is why good chemistry teaching emphasizes the phrase neutral means [H+] = [OH-], not simply “neutral means pH 7.” A pH of 7.00 is the neutral value specifically at 25 degrees C.
Approximate neutral pH values of pure water by temperature
| Temperature | Approximate pKw | Neutral pH |
|---|---|---|
| 0 degrees C | 14.94 | 7.47 |
| 10 degrees C | 14.53 | 7.27 |
| 25 degrees C | 14.00 | 7.00 |
| 40 degrees C | 13.54 | 6.77 |
| 50 degrees C | 13.26 | 6.63 |
| 60 degrees C | 13.02 | 6.51 |
| 100 degrees C | 12.26 | 6.13 |
These values are approximate educational references, but they clearly show the trend: neutral pH decreases as temperature rises. Therefore, if someone asks for the pH of pure water without stating temperature, many classroom settings assume 25 degrees C and answer 7.00.
What If the Water Is Exposed to Air?
In the real world, water that has been sitting in an open container is often not truly “pure” in the strict chemical sense. It can absorb carbon dioxide from the atmosphere. Dissolved carbon dioxide forms carbonic acid, which slightly lowers the pH. As a result, typical rainwater or air-exposed distilled water may have a pH closer to 5.6 to 6.0, depending on conditions.
This is why laboratory-grade pure water measurements can be tricky. Very pure water has low ionic strength, and even small contamination, dissolved gases, or contact with surfaces can affect measured pH. For textbook chemistry, however, the intended answer to “calculate the pH of a 200 mL solution of pure water” is generally still 7.00 at 25 degrees C.
Common Mistakes Students Make
- Using the 200 mL volume to change pH directly. Volume changes moles, not concentration, unless dilution or reaction occurs.
- Assuming pH 7.00 is always neutral. Neutrality depends on equal [H+] and [OH-], and the neutral pH changes with temperature.
- Confusing concentration with amount. A smaller sample has fewer moles but can have the same pH.
- Ignoring air exposure. Real samples may not behave like ideal pure water if carbon dioxide dissolves into them.
Worked Mini Example
Suppose you have 200 mL of pure water at 25 degrees C and need both the pH and the moles of hydrogen ions.
- Write the concentration of H+ for pure water: 1.0 x 10^-7 mol/L.
- Find pH: pH = -log10(1.0 x 10^-7) = 7.00.
- Convert volume: 200 mL = 0.200 L.
- Find moles: (1.0 x 10^-7 mol/L) x 0.200 L = 2.0 x 10^-8 mol.
Answer: pH = 7.00, moles of H+ = 2.0 x 10^-8 mol, moles of OH- = 2.0 x 10^-8 mol.
Practical Interpretation of the Result
This problem is often used to teach a foundational acid-base concept: concentration and total quantity are different ideas. In a 200 mL sample of pure water, there are indeed very few hydrogen ions in absolute terms, but the ratio relative to the total volume is what sets the pH. That ratio is fixed by water’s equilibrium at a given temperature. Once you understand that pH is logarithmic and concentration-based, the problem becomes straightforward.
It also highlights why laboratory chemistry relies on carefully controlled conditions. If you truly want to measure the pH of highly purified water, you must account for temperature, dissolved gases, instrument calibration, electrode limitations, and sample handling. But if you are solving a general chemistry homework problem, the expected answer is usually clean and elegant: 200 mL of pure water has pH 7.00 at 25 degrees C.
Authoritative References
For deeper reading on water chemistry, pH, and acid-base principles, review these reliable academic and government resources:
- USGS Water Science School: pH and Water
- Chemistry LibreTexts educational chemistry resources
- Princeton University chemistry pH reference material
Final Takeaway
If you need to calculate the pH of a 200 mL solution of pure water, the most important thing to remember is this: the 200 mL sample size does not determine the pH. At 25 degrees C, pure water has [H+] = 1.0 x 10^-7 mol/L, so the pH is 7.00. The volume is only relevant when calculating the total moles of H+ and OH- in the sample. If temperature changes, the neutral pH changes too. Therefore, the best complete answer is: for 200 mL of pure water at 25 degrees C, pH = 7.00, with 2.0 x 10^-8 mol of H+ and 2.0 x 10^-8 mol of OH- present in the sample.