a solution contains h+ 2.9×10-4 m calculate the ph
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Interactive ChartHow to solve: a solution contains h+ 2.9×10-4 m calculate the ph
If you are asked, “a solution contains h+ 2.9×10-4 m calculate the ph,” you are working with one of the most common introductory chemistry calculations. The problem gives you the hydrogen ion concentration, written as [H+], and asks for the pH. Because pH is a logarithmic measure of acidity, you do not subtract or divide in the usual way. Instead, you apply the pH formula directly:
pH = -log10[H+]
In this question, the concentration of hydrogen ions is 2.9 × 10-4 M. The unit M means molarity, or moles of solute per liter of solution. To calculate pH, substitute that concentration into the formula:
pH = -log10(2.9 × 10-4)
When evaluated, this becomes approximately 3.5376. Rounded to two decimal places, the pH is 3.54. Because this value is less than 7, the solution is acidic.
Step by step breakdown
- Identify the given concentration: [H+] = 2.9 × 10-4 M.
- Use the pH formula: pH = -log10[H+].
- Substitute the value: pH = -log10(2.9 × 10-4).
- Compute the logarithm using a calculator.
- Round appropriately: pH ≈ 3.54.
Why the answer is acidic
The pH scale classifies aqueous solutions by acidity and basicity. At 25°C, a neutral solution has pH 7, which corresponds to [H+] = 1.0 × 10-7 M. In this problem, the hydrogen ion concentration is much larger than 10-7 M, so the pH must be below 7. That is why the final answer of 3.54 clearly indicates an acidic solution.
The pH scale is logarithmic, not linear. That means a one unit change in pH corresponds to a tenfold change in hydrogen ion concentration. A solution with pH 3 is ten times more acidic than a solution with pH 4 and one hundred times more acidic than a solution with pH 5. This is why even seemingly small differences in pH are chemically significant.
Using logarithm rules to understand the calculation
Some students like to see the scientific notation split into parts. You can rewrite the expression using log rules:
log10(2.9 × 10-4) = log10(2.9) + log10(10-4)
Since log10(10-4) = -4 and log10(2.9) ≈ 0.4624:
log10(2.9 × 10-4) ≈ 0.4624 – 4 = -3.5376
Therefore:
pH = -(-3.5376) = 3.5376 ≈ 3.54
This approach helps explain why the pH is not just 4. The coefficient 2.9 shifts the answer upward from exactly 4 to about 3.54 after the negative sign is applied.
Common mistakes students make
- Forgetting the negative sign in the formula pH = -log10[H+].
- Typing 2.9×10-4 incorrectly into a calculator instead of using scientific notation keys properly.
- Confusing [H+] with pH and assuming the answer is simply 4 because the exponent is -4.
- Rounding too early and losing precision.
- Mixing up pH and pOH.
Calculator entry tips
On most scientific calculators, you should enter the value as 2.9 EXP -4 or 2.9 EE -4, depending on the device. Then apply the logarithm base 10 and the negative sign. If your calculator uses natural log by default, make sure you choose log base 10, not ln.
| pH Value | [H+] in M | Classification | Approximate Example |
|---|---|---|---|
| 1 | 1.0 × 10-1 | Strongly acidic | Strong acid solutions |
| 2 | 1.0 × 10-2 | Very acidic | Lemon juice range |
| 3.54 | 2.9 × 10-4 | Acidic | This problem’s solution |
| 7 | 1.0 × 10-7 | Neutral | Pure water at 25°C |
| 10 | 1.0 × 10-10 | Basic | Mild alkaline cleaners |
| 13 | 1.0 × 10-13 | Strongly basic | Strong base solutions |
How pH and pOH are related
At 25°C, pH and pOH are linked by the relationship:
pH + pOH = 14
Once you know the pH is 3.54, you can find the pOH:
pOH = 14 – 3.54 = 10.46
You can then estimate the hydroxide ion concentration:
[OH-] = 10-10.46 ≈ 3.45 × 10-11 M
This low hydroxide concentration is another confirmation that the solution is acidic.
Significant figures and reporting the final answer
In pH calculations, the number of decimal places in the pH generally corresponds to the number of significant figures in the concentration. The given concentration, 2.9 × 10-4, has two significant figures. That means the pH is usually reported with two digits after the decimal, which gives 3.54. If your teacher or textbook wants more detail, you may show the unrounded intermediate value first and then present the final rounded answer.
Comparison table: pH of common substances
| Substance | Typical pH | Relative Acidity Compared with pH 7 | Interpretation |
|---|---|---|---|
| Battery acid | 0 to 1 | 1,000,000 to 10,000,000 times more acidic | Extremely acidic |
| Lemon juice | 2 to 3 | 10,000 to 100,000 times more acidic | Strong food acid |
| This solution | 3.54 | About 2,884 times more acidic | Moderately acidic |
| Black coffee | 5 | 100 times more acidic | Mildly acidic |
| Pure water | 7 | Baseline | Neutral |
| Seawater | About 8.1 | About 12.6 times less acidic | Mildly basic |
| Household ammonia | 11 to 12 | 10,000 to 100,000 times less acidic | Clearly basic |
How to check whether your answer makes sense
A good chemistry habit is to estimate before finalizing your result. Since [H+] = 2.9 × 10-4 M, and 10-4 would correspond to pH 4, the coefficient 2.9 tells you the pH should be a bit less than 4. Any answer around 3.5 is reasonable. If you got 4.46, 0.29, or 10.46 for the pH, that would signal a mistake in sign, logarithm entry, or formula choice.
Why pH matters in real science
pH is more than an exercise for chemistry class. It is one of the most important measurable properties in environmental science, biology, medicine, agriculture, water treatment, and industrial manufacturing. Water quality standards, soil fertility, enzyme activity, corrosion control, and food processing all depend on correct pH measurements. That is why even a simple problem like “a solution contains h+ 2.9×10-4 m calculate the ph” introduces a concept with broad practical importance.
In environmental monitoring, pH is tracked to protect aquatic life. In biology, blood pH is tightly regulated because enzymes and metabolic pathways depend on narrow pH ranges. In laboratories, pH determines reaction rates, solubility, and equilibrium behavior. Understanding how to move between ion concentration and pH is a foundational skill that supports more advanced chemistry.
Authoritative references for pH and water chemistry
For trusted reference material, review: U.S. Environmental Protection Agency on alkalinity and water chemistry, U.S. Geological Survey pH and water science overview, and university-level chemistry learning materials hosted by LibreTexts.
Quick answer summary
- Given: [H+] = 2.9 × 10-4 M
- Formula: pH = -log10[H+]
- Calculation: pH = -log10(2.9 × 10-4)
- Result: pH ≈ 3.54
- Conclusion: The solution is acidic
Final takeaway
To solve “a solution contains h+ 2.9×10-4 m calculate the ph,” simply apply the standard pH equation. The hydrogen ion concentration of 2.9 × 10-4 M gives a pH of 3.54. Once you understand that pH is the negative base 10 logarithm of [H+], these questions become much easier. The main things to remember are correct scientific notation entry, careful use of the negative sign, and appropriate rounding based on significant figures.