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

pH and pOH

When it comes to most solutions, the concentrations of H⁺ and OH^- tend to be very small numbers. In order to deal with these very small numbers, the pH scale was invented. We're going to say here that under normal conditions, which means that our concentrations of H⁺ and OH^- are less than 1 molar, the pH scale will range between 0 to 14. So if your H⁺ concentration were greater than 1 molar, you'd get a pH less than 0. If your OH^- concentration were greater than 1 molar, then you would get a pH greater than 14. The whole thing about the pH scale being from 0 to 14, that's only true if these two ions are less than 1 molar. Now we're going to say by taking the negative log of H⁺ and OH^- you can get pH and pOH, respectively. pH is just negative log of H⁺ or H₃O⁺ because remember they're the same thing, and pOH equals negative log of OH^-. This is just telling us that 'p' just means negative log. Now, if we can recognize the relationship between H⁺ and OH^-, we can establish relationships between pH and pOH as well. So for example, pH equals negative log of H⁺. If we divide both sides by negative one, then we would get that negative pH equals log of H⁺. We would take the antilog in order to get rid of that log. And when I take the antilog of the other side, it becomes 10 to that value. So it's 10 to the negative pH. So what this is saying is if I know what my pH value is, I just do 10 to the negative pH, and I'll have my H⁺ concentration. In the same way, we can establish the relationship between pOH and OH^-. So again, we divide both sides here by negative one. So now we're going to get negative pOH equals log of OH^-. We would take the antilog of both sides again. So 10 to the negative pOH equals OH^-. So if you know pOH, you know what OH^- is. Now we're going to say, in general, as the pH value increases, our pH is getting higher, there's going to be a decrease in my H⁺ concentration and an increase in my OH^- concentration in classifications of solutions, we're going to say species with a pH equal to 7 is classified as neutral. Now, if we're talking about a neutral solution, that means that H⁺ and OH^- are equal to one another. But more specifically, they're equal to the number of 1.0 times 10 to the negative 7 molar at neutral pH. That's because K_w equals H⁺ times OH^-. If they're both equal to each other, they're both equal to x, which is x K_w, which is your ion product constant for water, is 1.0 times 10 to the negative 14 at 25 degrees Celsius. Solving for x, that's where this number here comes into play. When you're neutral, all of them are equal to one another. Now, if your pH is greater than 7, you're classified as a basic solution. If you're basic, that means your OH^- concentration will be greater than your H⁺ concentration, and that's because OH^- would be greater than this value of 1.0 times 10 to negative 7 molar, which in turn would be greater than H⁺. Finally, if your pH is less than 7, you're acidic. Now H⁺ concentration will be greater than both of them. It would be greater than the value of 1.0 times 10 negative 7 molar, and which in turn is greater than OH^- concentration. Finally, if you know pH, you know pOH. If you know pOH, you know pH because together they're connected to pH + pOH equals 14. These are some of the fundamental ideas behind the relationships between your K_w, which is your ion product constant, your H⁺ and OH^- concentrations, as well as pH and pOH. As we delve deeper into the different types of acids and bases, we'll learn different approaches in order to calculate their pH and pOH values respectively. Now that we've seen all of that, look to see if you can attempt the example question left at the bottom of the page. Attempt it on your own, but if you get stuck, just go to the next video and see how I approach that question.

pH and pOH

Here it asks, what is the hydroxide ion and hydronium ion concentration of a solution with a pH equal to 5.88? All right. So we need to determine what our OH^- concentration is and what our H⁺ or H₃O⁺ concentration is. Recall, up above I said that if you know pH, you know what your H⁺ concentration is because H⁺ is equal to 10 to the negative pH. So it's 10-5.88. When you punch that into your calculator, that'll give you the concentration of your hydronium ion. So here that gives me 1.32 times 10-6 molar as my answer. Now, we need to figure out what OH^- is. We can find it in two different ways. So one method we can use is to realize that pH + pOH equals 14. So pOH would equal 14 minus my pH which gives me 8.12. If we know what the pOH is, then we know what OH^- is because OH^- equals 10-pOH. Plug that in. So when we do that, we get an answer of 7.59 times 10-9 molar as the concentration for hydroxide ion. Another method we could have used to figure out my hydroxide ion concentration is to realize that K_w equals H⁺ times OH^-. K_w, since that'll give us a temperature, we assume it's room temperature, so 25 degrees Celsius. So that's 1.0 times 10-14 for my K_w value. We just found out what H⁺ is earlier, so plug that in. And all we have to do now is isolate OH^-. So you divide both sides here by the value we got for H⁺. Remember, anytime you have a number times 10 to any power, you should put them in parentheses to avoid any computer or calculator errors that could happen. So if you do this correctly, you would get the same exact value here for OH^-. So 2 different approaches to find your hydroxide ion concentration. Use the method that you're most comfortable with to get your final answer. So remember, there are connections that exist between H⁺ and OH^- and their relationships to pH and pOH respectively. Remembering them is key to getting your final answer when doing any types of these calculations. We'll continue with our discussion of pH and pOH as we delve deeper and deeper into discussions of different types of acids and bases.

pH and pOH Calculations 1

It states that among the following options, a solution with which pH would have the greatest concentration of hydronium ions. On the previous page, we mentioned that increasing our pH concentration would lead to a drop in the amount of H₊ ions available. Here, we want the opposite. We seek the greatest amount of H₊ ions available. Therefore, the lowest pH would translate into the highest amount of H₊ ions and the lowest amount of hydroxide ions. So for this question, it's simply option 4. Now remember, we're dealing with a log function here.

So if you're comparing a pH of 4 to a pH of 5, just realize here that increasing the pH by 1 unit means a 10-fold increase in OH^- concentration and a 10-fold decrease in H₊ concentration. Conversely, if you went from pH equals 4 to pH equals 2, every 1 unit that we move up and down the pH scale, there's a 10-fold increase or decrease for H₊ or OH^- concentration. Here we're going to a pH of 2, so we're becoming more acidic. That means we're increasing the amount of H₊ concentration. But here, we're moving down by 2 units. Every pH unit we go down, we increase H₊ tenfold. Since we're moving down by 2 units, that'd be 10 times 10, which results in a 100-fold increase for H₊ concentration and a 100-fold decrease for OH^- concentration. This question itself was simple.

Here I added a couple more details to it. Just remember, when you're moving up and down the pH scale by units of 1, that translates to a 10-fold increase or decrease in either your H₊ concentration or your OH^- concentration. Use the two examples I gave here as a roadmap to understand what happens to their concentration as we go up and down the pH scale.

Now that we've attempted this one, try to do example 2. Here HBr is a strong acid, so we have to understand that in order to find its true mass at the end. Attempt it on your own, but if you get stuck, come back and see how I approach that same exact question.

pH and pOH Calculations 1

So here it says what mass of HBr should a student mix into 250 ml's of water to make a solution with a pH of 3.850. All right, so they're asking us to find mass, so we're looking for the grams of HBr. Now, realize here that because we know what pH is and we're dealing with an acid, we can figure out what our H⁺ concentration is. So with this information, I'll be able to find the molarity of H⁺. Realize that we have molarity and we also have volume involved. Molarity equals moles over liters. I can figure out my molarity from the pH. I can change milliliters to liters. With those two pieces of information, I can isolate moles because moles equals liters times molarity. So what I'm going to do first is remember that H⁺ equals 10 to the negative pH. So that's 10-3.850. When we plug that in, that gives me 1.4124 times 10-4 molar of H⁺. Here, try not to round it to the very end to avoid any types of rounding errors. Here, we have 250 ml's. So what I'm going to do here is I'm going to convert ml's into liters. So 1 milliliter is 10-3 liters. You could also say that 1 liter is a 1000 milliliters. So use whichever convention is more familiar to you. Molarity means moles over liters. So this molarity that we found really means 1.41254 times 10-4 moles of H⁺ over 1 liter. So anytime we have molarity, it's that number in moles over 1 liter. Liters cancel out. Now I have moles of HBr. Because we're dealing with a strong acid in the form of HBr, remember here that strong acids and strong bases dissociate completely when in solution. This will give me H⁺ and Br^- and I'll form 100% of these. Because of that, we can say that there is a one-to-one relationship between the acid and these ions. So we're going to say here that for every one mole of HBr, there's exactly 1 mole of H⁺ within that compound. It's this connection that allows us to go from H⁺ to HBr. Finally, because we have the moles of HBr, we can figure out our grams of HBr for the end. So HBr has in it 1 hydrogen and 1 bromine. If we look at the periodic table, we'll see the atomic masses of hydrogen and bromine respectively. So H on the periodic table is 1.00794 grams and Br weighs 79.904 grams. One mole of HBr here. Add those two numbers for the mass of hydrogen and Br. Together, it comes out as 80.9119 grams of HBr when I add these two numbers together. So moles of HBr cancel out, so I'll have grams at the end. That comes out to 0.002857 grams of HBr. And when we round that, that simply gives us option a as the correct choice. So just remember here they're asking for the mass of the acid. We need to pick up on cues being given to us within the question. We had volume given to us. If they give us pH, we can find concentration. So remember, concentration, which is molarity, times liters gives me moles. By knowing moles, I can figure out what my grams will be at the end. Now that we've attempted this question, try to do the practice question left at the bottom of the page. Attempt it on your own. We've done examples that are similar to it. Once you've done that come back and take a look at my video and see if your answer matches mine.

What is the hydronium ion concentration in a solution having a pOH of 3.62?

• A. 3.8 × 10⁻⁵ M
• B. 4.2 × 10⁻¹¹ M
• C. 3.8 × 10⁻⁴ M
• D. 2.6 × 10⁻¹¹ M
• E. 5.1 × 10⁻¹⁰ M

Here’s what students ask on this topic:

What is the pH scale and how is it used to measure acidity and basicity?

The pH scale ranges from 0 to 14 and measures the concentration of hydrogen ions (H⁺) in a solution. A pH of 7 is neutral, meaning the concentrations of H⁺ and hydroxide ions (OH^-) are equal at 1.0 × 10^-7 M. Solutions with pH < 7 are acidic (H⁺ > 1.0 × 10^-7 M), while those with pH > 7 are basic (OH^- > 1.0 × 10^-7 M). The pH is calculated using the formula: $\mathrm{pH}=-{\log }_{H_{+}}$. This scale helps determine the acidity or basicity of a solution, which is crucial in various chemical and biological processes.

How do you calculate pH from the concentration of hydrogen ions?

To calculate pH from the concentration of hydrogen ions (H⁺), use the formula: $\mathrm{pH}=-{\log }_{H_{+}}$. For example, if the concentration of H⁺ is 1.0 × 10^-3 M, the pH is calculated as follows: $\mathrm{pH}=-{\log }_{{\mathrm{1.0}}_{\times }}$, which simplifies to pH = 3. This method allows you to determine the acidity of a solution accurately.

What is the relationship between pH and pOH?

The relationship between pH and pOH is given by the equation: $\mathrm{pH}+\mathrm{pOH}=14$. This means that if you know either the pH or pOH of a solution, you can easily calculate the other. For example, if the pH of a solution is 5, the pOH can be calculated as follows: $\mathrm{pOH}=14-\mathrm{pH}$, which simplifies to pOH = 14 - 5 = 9. This relationship is crucial for understanding the balance between hydrogen and hydroxide ions in a solution.

How do you determine if a solution is acidic, basic, or neutral based on its pH?

A solution's pH determines whether it is acidic, basic, or neutral. A pH of 7 is neutral, indicating equal concentrations of H⁺ and OH^- ions at 1.0 × 10^-7 M. If the pH is less than 7, the solution is acidic, meaning the concentration of H⁺ ions is greater than 1.0 × 10^-7 M. Conversely, if the pH is greater than 7, the solution is basic, indicating a higher concentration of OH^- ions than H⁺ ions. This classification helps in understanding the chemical nature and potential reactivity of the solution.

What is the significance of the ion product constant for water (Kw) in the pH scale?

The ion product constant for water (K_w) is significant in the pH scale as it defines the relationship between H⁺ and OH^- concentrations in water. At 25°C, K_w is 1.0 × 10^-14. This means that the product of the concentrations of H⁺ and OH^- ions in water is always 1.0 × 10^-14. Mathematically, $K_w=H_{+}\times {\mathrm{OH}}_{-}$. This constant helps in calculating pH and pOH and understanding the equilibrium state of water and aqueous solutions.