Calculate the pH of 7.5 × 10-2 M HCl
Use this interactive strong acid calculator to solve the pH of hydrochloric acid step by step, visualize the result, and understand the chemistry behind the answer.
pH Calculator
Enter the concentration in scientific notation. This page is preloaded for 7.5 × 10-2 M HCl, which is the standard interpretation of the problem.
How to calculate the pH of 7.5×10-2 M HCl
When students are asked to calculate the pH of 7.5×10-2 M HCl, the problem is usually testing two core ideas from general chemistry: first, that hydrochloric acid is a strong acid that dissociates essentially completely in water, and second, that pH is the negative base 10 logarithm of the hydronium ion concentration. Once those two ideas are in place, the problem becomes direct and elegant. You convert the scientific notation to a decimal concentration, assume complete dissociation because HCl is a strong monoprotic acid, and then apply the pH formula.
The notation 7.5×10-2 M means a concentration of 0.075 moles per liter. The minus 2 in the exponent moves the decimal point two places to the left. So before you even think about logarithms, the concentration of the acid is already known in standard decimal form. Since HCl contributes one hydrogen ion for each formula unit dissolved, the hydrogen ion concentration is also 0.075 M. Then you calculate pH using:
pH = -log10[H+]
Substituting the hydronium concentration gives:
pH = -log10(0.075) ≈ 1.12
That is the accepted classroom answer in most introductory chemistry contexts. The value is acidic, as expected, because the pH is far below 7. In fact, a pH of about 1.12 indicates a highly acidic solution, much stronger than mildly acidic substances like coffee or rainwater, but still within a range regularly used in chemistry instruction and laboratory calculations.
Step by step breakdown
- Identify the acid: HCl is hydrochloric acid, a strong acid.
- Recognize that HCl dissociates completely in water: HCl → H+ + Cl–.
- Convert scientific notation to decimal: 7.5×10-2 = 0.075.
- Set [H+] equal to the acid concentration because HCl is monoprotic: [H+] = 0.075 M.
- Apply the pH formula: pH = -log(0.075).
- Round appropriately: pH ≈ 1.12.
Why HCl is treated differently from a weak acid
One of the biggest reasons this problem is straightforward is that HCl is considered a strong acid in aqueous solution. In classroom and most practical calculations, strong acids are assumed to ionize completely. This means there is no need to set up an equilibrium ICE table as you would for a weak acid like acetic acid or hydrofluoric acid. For a weak acid, you would need an acid dissociation constant, usually written as Ka, and then solve for the equilibrium hydrogen ion concentration. With HCl, none of that is necessary for standard pH calculations at this level.
That complete dissociation assumption is what allows the direct statement:
- [HCl] = 0.075 M
- [H+] = 0.075 M
- pH = 1.12
It is also worth noting that HCl is monoprotic. Each mole of HCl releases one mole of hydrogen ions. If you were dealing with a strong diprotic acid and assuming full dissociation of both protons, the relation between acid concentration and hydrogen ion concentration would be different. That distinction matters in more advanced acid-base problems.
Common student mistakes
Even though the calculation is short, students often lose points because of small but important errors. The most frequent mistake is misreading the exponent in scientific notation. If the problem says 7.5×10-2 M and a student enters 7.5×102 M instead, the concentration changes from 0.075 M to 750 M, which is completely different and physically unrealistic in ordinary aqueous chemistry. Another common mistake is forgetting the negative sign in the pH formula. Since logarithms of numbers less than 1 are negative, the minus sign in front is essential to produce a positive pH value.
Here are a few errors to watch for:
- Converting 7.5×10-2 incorrectly to 0.0075 or 0.75.
- Using pH = log[H+] instead of pH = -log[H+].
- Forgetting that HCl is a strong acid and trying to use Ka.
- Reporting too many or too few significant figures.
Worked example with interpretation
Let us work the full problem in plain language. Start with 7.5×10-2 M HCl. This means the solution contains 0.075 moles of hydrochloric acid per liter. Since HCl dissociates essentially 100 percent in water, the hydronium concentration is also 0.075 M. Using a calculator, log10(0.075) is approximately -1.1249. Applying the negative sign from the pH definition gives +1.1249. Rounded to two decimal places, the pH is 1.12.
This number is chemically reasonable. A lower pH means a higher hydrogen ion concentration. Because 0.075 M is a fairly high concentration of hydrogen ions compared with neutral water at 1.0×10-7 M, the pH must be much lower than 7. A pH near 1 is exactly what we would expect.
| HCl Concentration (M) | Hydrogen Ion Concentration (M) | Calculated pH | Relative Acidity vs 1.0×10-7 M Neutral Water |
|---|---|---|---|
| 7.5×10-1 | 0.75 | 0.125 | 7.5 million times higher [H+] |
| 7.5×10-2 | 0.075 | 1.125 | 750,000 times higher [H+] |
| 7.5×10-3 | 0.0075 | 2.125 | 75,000 times higher [H+] |
| 7.5×10-4 | 0.00075 | 3.125 | 7,500 times higher [H+] |
The role of pOH and water autoionization
Many instructors also like students to connect pH with pOH. At 25°C, the standard relation is:
pH + pOH = 14.00
So if the pH is 1.12, then the pOH is:
pOH = 14.00 – 1.12 = 12.88
This relation comes from the ionic product of water, often written as Kw = 1.0×10-14 at 25°C. In very dilute acid or base calculations, the autoionization of water can matter. In this problem it does not, because 0.075 M is enormously larger than 1.0×10-7 M. Therefore, nearly all of the hydrogen ion concentration comes from the HCl, not from water itself.
How strong is 0.075 M HCl compared with everyday substances?
A pH of 1.12 is strongly acidic. Everyday acidic items such as black coffee, tomato juice, or acid rain usually have much higher pH values. That means they are far less acidic in terms of hydrogen ion concentration. This comparison can help make logarithmic pH values feel more intuitive. A difference of 1 pH unit corresponds to a factor of 10 in hydrogen ion concentration. A difference of 2 pH units corresponds to a factor of 100, and so on.
| Substance or Reference Point | Approximate pH | Approximate [H+] in M | Comparison to 0.075 M HCl |
|---|---|---|---|
| 0.075 M HCl | 1.12 | 0.075 | Reference |
| Gastric acid range | 1 to 3 | 0.1 to 0.001 | Comparable acidic environment |
| Lemon juice | 2 | 0.01 | About 7.5 times less [H+] |
| Coffee | 5 | 0.00001 | 7,500 times less [H+] |
| Pure water at 25°C | 7 | 0.0000001 | 750,000 times less [H+] |
Significant figures and reporting your answer correctly
In acid-base chemistry, pH reporting follows the decimal places rule connected to significant figures in the concentration. The concentration 7.5×10-2 has two significant figures. Therefore, the pH is commonly reported with two digits after the decimal, which gives 1.12. If your instructor uses a different convention, follow that class rule, but in most cases 1.12 is the best final answer.
What if the original problem was written ambiguously?
Sometimes a typed prompt appears as “7.5×10 2 M HCl” without superscripts or a visible minus sign. In chemistry, context matters. Most educational pH problems of this form are intended to be read as 7.5×10-2 M, not 7.5×102 M, because the latter would imply 750 M, which is not a realistic ordinary aqueous concentration. If you are completing an assignment and the notation looks unclear, it is always wise to verify the exponent with your teacher, textbook, or source material.
Useful formulas for this and related problems
- pH = -log[H+]
- pOH = -log[OH–]
- pH + pOH = 14.00 at 25°C
- [H+] = acid concentration for strong monoprotic acids like HCl
Authoritative references for acid-base chemistry
If you want to study the underlying chemistry from authoritative educational and government sources, these references are useful starting points:
- General chemistry explanations at LibreTexts are widely used, though not a .gov or .edu domain.
- U.S. Environmental Protection Agency – pH overview
- National Institute of Standards and Technology – scientific reference resources
- Massachusetts Institute of Technology Chemistry Department
Final answer
For 7.5×10-2 M HCl, assume complete dissociation because HCl is a strong monoprotic acid. Then:
[H+] = 0.075 M
pH = -log(0.075) = 1.12
So, the pH of 7.5×10-2 M HCl is approximately 1.12.