Calculate the pH Level of 1.5 × 10-2 M NaOH
Use this premium calculator to find pOH, pH, hydroxide concentration, and hydrogen ion concentration for a sodium hydroxide solution. By default, it is prefilled for 1.5 × 10-2 M NaOH at 25°C.
Visual Result Chart
The chart compares pH and pOH for the current NaOH concentration. It also highlights the logarithmic concentration relationship for strong bases.
- NaOH is treated as a strong base with complete dissociation in dilute aqueous solution.
- For monobasic hydroxides, [OH⁻] is approximately equal to the base molarity.
- At 25°C, pH + pOH = 14.
How to calculate the pH level of 1.5 × 10-2 M NaOH
If you need to calculate the pH level of 1.5 × 10-2 M NaOH, the process is straightforward once you remember that sodium hydroxide is a strong base. In water, NaOH dissociates essentially completely into sodium ions and hydroxide ions:
Because there is one hydroxide ion released for each formula unit of NaOH, the hydroxide concentration is the same as the NaOH molarity for this problem. That means:
From there, you calculate pOH first and then convert to pH. This is the standard method used in introductory chemistry, general chemistry, water chemistry, and many analytical chemistry contexts. The key equations are:
Plugging in the value:
Why NaOH is handled as a strong base
Sodium hydroxide is one of the classic strong bases taught in chemistry because it dissociates very efficiently in water under ordinary dilute conditions. That matters because weak bases require an equilibrium calculation involving a base dissociation constant, but NaOH does not. For a strong base like NaOH, KOH, or LiOH, you can generally assume complete dissociation and directly convert the concentration of the compound into hydroxide concentration.
This is why the problem “calculate the pH level of 1.5 10 2 m naoh” is usually interpreted in standard scientific notation as “calculate the pH level of 1.5 × 10-2 M NaOH.” Once that notation is cleaned up, the math becomes simple and reliable.
Step by step method
- Interpret the concentration correctly as 1.5 × 10-2 M.
- Convert scientific notation to decimal form: 0.015 M.
- Assume complete dissociation because NaOH is a strong base.
- Set [OH⁻] = 0.015 M.
- Compute pOH using pOH = -log10[OH⁻].
- Find pH from pH = 14 – pOH at 25°C.
- Round reasonably, usually to 2 or 3 decimal places depending on class or lab expectations.
Detailed worked example
Let us work through the exact values carefully. The concentration is 1.5 × 10-2 M, which means:
Since sodium hydroxide is a strong base:
Now calculate pOH:
Using the common 25°C relationship:
Therefore, the pH is about 12.18. This value makes sense chemically because a 0.015 M NaOH solution is strongly basic, so the pH should be significantly above 7 and typically above 12.
Quick reference table for common NaOH concentrations
The table below shows how the pH changes for several common sodium hydroxide concentrations at 25°C. These values are calculated using the standard strong-base approximation. This helps you see where 1.5 × 10-2 M fits on the broader scale.
| NaOH concentration (M) | [OH⁻] (M) | pOH | pH at 25°C | Interpretation |
|---|---|---|---|---|
| 1.0 × 10^-4 | 0.0001 | 4.000 | 10.000 | Mildly basic laboratory solution |
| 1.0 × 10^-3 | 0.001 | 3.000 | 11.000 | Clearly basic |
| 1.5 × 10^-2 | 0.015 | 1.824 | 12.176 | Strongly basic |
| 1.0 × 10^-2 | 0.01 | 2.000 | 12.000 | Strongly basic |
| 1.0 × 10^-1 | 0.1 | 1.000 | 13.000 | Very strongly basic |
| 1.0 | 1.0 | 0.000 | 14.000 | Idealized upper-limit textbook case |
How this compares with real-world pH ranges
A pH of about 12.18 is far outside the normal range of drinking water and most environmental waters. The U.S. Environmental Protection Agency notes a recommended secondary drinking water pH range of 6.5 to 8.5, which is much lower than the result for 0.015 M NaOH. That makes sense because sodium hydroxide solutions are corrosive and strongly alkaline, not suitable for direct consumption.
| Reference material or benchmark | Typical pH or range | Comparison with 1.5 × 10^-2 M NaOH |
|---|---|---|
| Pure water at 25°C | 7.0 | NaOH solution is over 5 pH units more basic |
| EPA secondary drinking water guidance | 6.5 to 8.5 | NaOH solution is far above the recommended range |
| Human blood | About 7.35 to 7.45 | NaOH solution is dramatically more alkaline |
| Household ammonia solutions | About 11 to 12 | 1.5 × 10^-2 M NaOH is in a similar strongly basic region, often slightly higher |
| Concentrated drain cleaner formulations | Often above 13 | NaOH at 0.015 M is basic, but typically below highly concentrated cleaners |
Common mistakes students make
- Using pH = -log[OH⁻]. That is incorrect. The negative logarithm of hydroxide concentration gives pOH, not pH.
- Forgetting the dissociation step. You first identify that NaOH releases OH⁻ completely.
- Misreading scientific notation. 1.5 × 10-2 is 0.015, not 0.0015 and not 0.15.
- Assuming all bases behave like NaOH. Weak bases such as NH₃ require equilibrium calculations, not just direct conversion.
- Ignoring temperature assumptions. The simple relationship pH + pOH = 14 is standard at 25°C.
When the simple method works best
The direct method used here is appropriate when all of the following are true:
- The base is strong, such as NaOH.
- The solution is reasonably dilute to moderate in concentration.
- You are working under standard classroom conditions, usually 25°C.
- You only need the theoretical pH from molarity, not an activity-corrected value for advanced physical chemistry work.
In more advanced settings, especially at higher ionic strengths, measured pH can deviate from ideal textbook values because pH meters respond to activity rather than simple concentration. However, for general chemistry, the result of 12.18 is the accepted answer.
Why the answer is reasonable chemically
A useful way to sanity-check your answer is to compare it to benchmark values. A 10-2 M strong base has pOH of 2 and pH of 12. Since 1.5 × 10-2 M is slightly more concentrated than 1.0 × 10-2 M, its pOH should be slightly lower than 2, and its pH should be slightly higher than 12. That is exactly what we got: pOH ≈ 1.824 and pH ≈ 12.176.
Formula summary
- Convert scientific notation: 1.5 × 10-2 = 0.015
- Strong base rule: [OH⁻] = 0.015 M
- Calculate pOH: pOH = -log(0.015) = 1.8239
- Convert to pH: pH = 14 – 1.8239 = 12.1761
Authoritative references for pH and hydroxide chemistry
For further reading, consult these reliable educational and government resources:
- U.S. EPA: Secondary Drinking Water Standards and pH guidance
- Chemistry LibreTexts educational chemistry resources
- NCBI Bookshelf: chemistry and aqueous equilibrium references
FAQ: calculate the pH level of 1.5 × 10-2 M NaOH
Is the pH exactly 12.18?
In standard textbook calculations, yes, approximately 12.18. In real laboratory measurement, the observed value can differ slightly because of temperature, calibration, ionic strength, and activity effects.
Why do we calculate pOH first?
Because the given quantity is hydroxide concentration. pOH directly relates to [OH⁻], and then pH follows from the 25°C relationship.
Would KOH give the same result at the same molarity?
Under the same ideal assumptions, yes. KOH is also a strong monohydroxide base, so 0.015 M KOH would produce approximately the same pH.
Can pH be greater than 14?
In advanced chemistry contexts, yes, measured values can extend outside 0 to 14. But in standard introductory aqueous problems at 25°C, the 0 to 14 framework is typically used.