The pH Scale - Online Tutor, Practice Problems & Exam Prep

The pH scale, ranging from 0 to 14, measures the acidity or basicity of aqueous solutions at room temperature (25 °C) and a molarity of one. A pH below 7 indicates acidity, with lower values signifying stronger acids, while a pH above 7 denotes basicity, with higher values indicating stronger bases. At pH 7, a solution is neutral, meaning the concentrations of H⁺ (hydrogen ions) and OH⁻ (hydroxide ions) are equal. The pH or pOH of a solution can be calculated if the molarity of H⁺ or OH⁻ is known, using the formulas:

$\mathrm{pH}=-\log \left[H_{+}\right]$

and

$\mathrm{pOH}=-\log \left[{\mathrm{OH}}_{-}\right]$

Additionally, H⁺ concentration can be found with 10 to the power of -pH, and OH⁻ concentration with 10 to the power of -pOH. The relationship between pH and pOH is such that their sum equals 14 under standard conditions. This framework is crucial for understanding acid-base chemistry and for performing calculations related to solution concentration and acidity.

The pH Scale

So here we're going to say that the pH scale is used to classify the acidity or the basicity of a GUID solutions. And we're going to say that the pH scale normally ranges from zero to 14 under normal conditions. Now when we say normal conditions we mean the temperature is around room temperature, which is approximately 25°C and a molarity of one. If we go outside a molarity of one, then the pH scale can be outside the range of 0 to 14.

Now here with the pH scale we have zero to 14. We can see here that at pH of seven we are classified as being neutral. If it's below 7 then it becomes acidic and the lower we go in terms of a pH, the more acidic we become. Above seven were basic and the higher we go up the more basic we become. O here we're going to say the stronger the acid the lower the pH and the stronger the base the higher the pH could be.

Here we have examples of acidic, acidic, neutral and basic types of solutions. In the first one we have vinegar. Here vinegar is acidic. Since it's acidic, that would mean that it's acidic component, which is your H⁺ ion, would be greater in amount than the concentration of OH⁻, which is typically reserved for basic compounds. Here the pH of vinegar is around 3, now neutral.

What we can think of here is purified water. It's pH is equal to 7. For it to be neutral, the hydronium ion concentration H⁺ and hydroxide ion concentration OH⁻ have to be roughly equal to each other. So they're equal and then finally basic. Here we have ammonia cleaner or to be basic the amount of hydroxide ion concentration has to be greater than the H⁺ concentration. Here for this example the pH of the ammonia cleaner is around 12.

So remember under normal conditions where temperatures around room temperature and the molarity is up to one molar, our pH scales from zero to 14. Remember below 7 is acidic, above 7 is basic, at 7 is neutral.

The pH Scale Example

Given the H concentration of the following solutions, which one is the least acidic? So here we have nitric acid with the H concentration of 1.2 molar. HCL is 0.025 molar, so uric acid is 0.27 molar and then we have perchloric acid at 0.019 molar.

We want the least acidic. This would translate to the one with the lowest concentration of H plus ions. For the numbers that we see, the smallest concentration for H ions would be with our perchloric acid solution.

So here our answer would be option D. It has the lowest H plus concentration, which would translate to the being the least acidic solution out of the options present.

pH and pOH

We can determine pH or POH of a solution if concentrations which means molarity of either the H⁺ and OH^- concentrations are known and vice versa. So basically if we take a look here we have our pH and our POH formulas. First of all P just is a stand in for negative log. So when I say pH I really mean negative log of your H⁺ concentration.

Here we could rework this in which we can determine the concentration of H⁺ from our known pH value. So here we would take the inverse log. We divide both sides by -1. They give me negative pH equals log of concentration of H⁺. You will take the inverse log of both sides. Doing that would help you realize that H⁺ concentration equals 10 to the negative pH. So this is a way of us going between pH and H⁺ back and forth.

So if I know my H⁺ concentration, I can use it to find my pH. If I know my pH, I can use it to find my H⁺ concentration. The same method can be applied to POH with POH. Again, remembering P equals negative log POH just means negative log of my OH^- concentration. By dividing both sides by -1 and taking the inverse log, we can see that OH^- concentration is equal to 10 to the negative POH.

So again, if I know my OH^- concentration I can find POH. Or if I know my POH value, I can use it to find my OH^- concentration. So just keep in mind the relationship between pH and POH with their concentrations of H⁺ and OH^-.

The pH Scale Example

A solution is prepared by dissolving hydrocyanic acid in 2 liters of water if the H concentration was found to be equal to 0.34 moles. Calculate the pH of this hydrocyanic acid solution. All right, so remember pH is equal to the negative log of our H plus concentration. Another name for concentration is molarity.

So here we're going to say molarity equals moles over liters. We're going to take the moles of H plus ion given to us divided by the 2 liters, so that gives me 0.17 molar. We're then just going to say now pH equals the negative log of 0.17 molar here. When we work that out, that's going to give me 0.77 at the pH of this solution.

Here the numbers a little bit high because we're able to generate quite a bit of H ion for 0.17. Molar is a pretty large number. Remember when we're dealing with the pH scale from zero to 14, we can go up to one molar to fall within that range. 0.17 is pretty high up there along the way to towards one molar.

Again, we figured out the concentration of H plus ions here, plugged it into the formula, and we're able to deduce what our pH is at 0.77.

A solution of NaOH was prepared in a chemistry lab and the pOH was determined to be 9.3. What is the concentration of OH⁻ ions of this basic solution?

• A. 5 × 10⁻¹¹ M
• B. 5 × 10⁻¹⁰ M
• C. 2 × 10⁹ M
• D. 2 × 10⁸ M

Additional pH and pOH Calculations

Now recall that we say the pH scale can go up to 14 at temperature of 25°C and up to a concentration of one molar. Because of this, we can calculate pH from POH or vice versa using the following equation. That equation is that pH plus POH equals 14 itself.

In addition to this, we have on the right side some equations that we've seen before where pH equals negative log of H⁺ and therefore H⁺ concentration equals 10 to the negative pH. POH equals negative log of OH⁻ and therefore the concentration of OH⁻ equals 10 to the negative POH.

So we're starting quite a collection of different formulas that are connecting pH and POH to one another. Just remember the addition between pH and POH equals 14.

pH + pOH = 14 pH = - log ⁡ ( H + ) H + = 10 - pH pOH = - log ⁡ ( OH - ) OH - = 10 - pOH

The pH Scale Example

You prepare a solution of hydrochloric acid with a pH of 2.3 at 25°C. What will be the pOH and the concentration of hydronium ions of the solution? All right, so remember that pH plus pOH equals 14. We know the pH is 2.3, so subtract 2.3 from both sides so pOH equals 11.7.

Now for hydronium ion concentration. Remember hydronium ion is just H⁺ or H₃O⁺. We can determine this since we know the pH. That's because H⁺ equals 10 to the negative pH. So take the pH that we found and plug it in. When we do that, we get 5.01187 * 10 to the -3 molar or our hydronium ion concentration.

Here we round into sig figs and that'll be your answer. OK, so 5.0 * 10 to the -3 and actually we should round to one sig fig, so 5 * 10 to the -3 concentration because we don't need all those extra digits. So here our OH, not pH, is 11.7 and our pH is. From that, we can determine our H as being 5 * 10 to the -3 molar.

Calculate [OH⁻] of a lemon juice solution at 25°C with a [H⁺] = 5.7 × 10⁻⁴ M.

• A. 5.7 × 10¹⁰ M
• B. 4.7 × 10⁻¹¹ M
• C. 2.7 × 10⁻¹⁸ M
• D. 1.8 × 10⁻¹¹ M

A 345 mL bottle of antacid (Mg(OH)₂) contains 1.45 × 10⁻² moles of hydroxide ions. Determine pH and pOH of the antacid.

• A. pH = 12.384
  pOH = 1.616
• B. pH = 12.623
  pOH = 1.377
• C. pH = 12.161
  pOH = 1.839
• D. pH = 12.338
  pOH = 1.662

Which of the following statement(s) on aqueous solutions is/are correct?

a) aqueous solutions have a pH of 7

b) as concentration of hydronium ion increases, concentration of hydroxide ion decreases

c) solutions of weaker acids generally have a higher pOH then solutions of stronger acids

d) pH of pure water equals to 7 at 35º C.

• A. aqueous solutions have a pH of 7
• B. as concentration of hydronium ion increases, concentration of hydroxide ion decreases
• C. solutions of weaker acids generally have a higher pOH then solutions of stronger acids
• D. pH of pure water equals to 7 at 35º C.

Here’s what students ask on this topic:

What is the pH scale?

The pH scale is a measure of how acidic or basic (alkaline) a solution is. It ranges from 0 to 14, with 7 being neutral. Solutions with a pH less than 7 are considered acidic, while those with a pH greater than 7 are considered basic or alkaline. The scale is logarithmic, meaning each whole pH value below 7 is ten times more acidic than the next higher value, and each whole pH value above 7 is ten times more alkaline than the next lower value. For example, a solution with a pH of 6 is ten times more acidic than a solution with a pH of 7, and a solution with a pH of 8 is ten times more alkaline than a solution with a pH of 7. This scale is crucial in chemistry, biology, and environmental science, as it affects chemical reactions, biological processes, and the health of ecosystems.

How do you calculate pH?

To calculate the pH of a solution, you need to know the concentration of hydrogen ions (H⁺) or hydronium ions (H₃O⁺) in moles per liter (Molarity). The pH is calculated using the following formula:

$\mathrm{pH}=-\log \left[H^{+}\right]$

Here's a step-by-step process:

1. Determine the concentration of hydrogen ions in the solution in molarity (M). This is often given, but if not, you may need to derive it from the concentration of an acid or base.
2. Take the negative logarithm (base 10) of the hydrogen ion concentration. This means you use a scientific calculator to find the log of the H⁺ concentration and then multiply that number by -1.

For example, if the hydrogen ion concentration is 1 x 10^-7 M, the pH is:

$\mathrm{pH}=-\log (1x{10}^{-7})=7$

Remember that a pH less than 7 is acidic, a pH of 7 is neutral, and a pH greater than 7 is basic or alkaline. The pH scale typically ranges from 0 to 14.

What is the relationship between the pH scale and concentration?

The pH scale is a measure of the acidity or alkalinity of a solution, which is determined by the concentration of hydrogen ions (H+) present. The scale ranges from 0 to 14, with 7 being neutral. A pH less than 7 indicates an acidic solution, while a pH greater than 7 indicates an alkaline (basic) solution.

The relationship between pH and hydrogen ion concentration is logarithmic, not linear. This means that each unit change in pH represents a tenfold change in H+ concentration. A decrease in pH by 1 unit reflects a tenfold increase in acidity (more H+ ions), while an increase in pH by 1 unit reflects a tenfold decrease in acidity (fewer H+ ions).

For example, a solution with a pH of 6 has ten times more hydrogen ions than a solution with a pH of 7. Conversely, a solution with a pH of 8 has ten times fewer hydrogen ions than a solution with a pH of 7. This logarithmic relationship allows the pH scale to cover a wide range of hydrogen ion concentrations in a compact scale.

How do you calculate H⁺ from pH?

To calculate the concentration of hydrogen ions (H⁺) from pH, you can use the following formula:

$\left[H^{+}\right]={10}^{-\mathrm{pH}}$

Here, [H⁺] represents the concentration of hydrogen ions in moles per liter (M), and pH is the measure of acidity or alkalinity of a solution.

The pH scale typically ranges from 0 to 14, with 7 being neutral. A pH less than 7 indicates an acidic solution, while a pH greater than 7 indicates a basic (alkaline) solution. The pH scale is logarithmic, which means each whole pH value below 7 is ten times more acidic than the next higher value. For example, a solution with a pH of 3 is ten times more acidic than a solution with a pH of 4.

To perform the calculation, simply take the negative of the pH value and use it as the exponent for 10. For instance, if the pH of a solution is 3.5, the concentration of H⁺ ions is:

$\left[H^{+}\right]={10}^{-3.5}=3.16\times {10}^{-4}\text{M}$

This means there are 3.16 × 10^-4 moles of hydrogen ions per liter of solution.

How to calculate OH^- from pH?

To calculate the concentration of hydroxide ions (OH^-) from the pH, you can use the following steps:

1. Remember that pH is a measure of the hydrogen ion concentration [H⁺], and it is related to [H⁺] by the formula: $\mathrm{pH}=-\log \left[H\right]$.
2. Understand that the product of the concentrations of hydrogen ions [H⁺] and hydroxide ions [OH^-] in water at 25°C is always $1.0x{10}^{-14}$. This is known as the ion-product constant for water (K_w).
3. Use the pH to find the [H⁺] by reversing the pH formula: $\left[H\right]={10}^{-pH}$.
4. Once you have [H⁺], use the ion-product constant to find [OH^-]: $\left[\mathrm{OH}\right]=K$_w/[H].
5. Plug in the values: $\left[\mathrm{OH}\right]=1.0x{10}^{-14}/\left[H\right]$.
6. Calculate the [OH^-] using the [H⁺] you found from the pH.

For example, if the pH is 7, $\left[H\right]={10}^{-7}$ M. To find [OH^-], you would calculate $\left[\mathrm{OH}\right]=1.0x{10}^{-14}/{10}^{-7}={10}^{-7}$ M. Therefore,