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

The pH scale, ranging from 0 to 14, measures acidity and basicity, with pH < 7 indicating acidity and pH > 7 indicating basicity. The relationship between pH and hydroxide ion concentration (pOH) is expressed as pH+pOH=14. The concentration of hydrogen ions can be calculated using [H⁺]=10^-pH, while hydroxide ions are found using [OH^-]=10-pOH.

The pH Scale Concept 1

Hey, guys. In this new video, we're going to take a close look at pH and pOH. So, we're going to say that when it comes to the concentrations of H⁺ and OH^-, they usually come as very small numbers. And what we need to realize here is that the pH scale was invented to basically turn these very small numbers into more manageable ones. So, we're going to say under normal conditions, the pH scale operates within the range of 0 to 14. But what we need to realize here is that the pH scale could be less than 0 or it could be greater than 14. All we would need to do is increase the concentration of our acid or base. So remember, 0 to 14 are not the only numbers that your pH or pOH could be. They could be greater or less than that. It all again depends on upping the concentration of your compound. If you make your concentration very high, like over 1 molar, then it'll give you a very high or very low pH. Now, we're going to say by taking the negative log of H⁺ and OH^- we can find pH and pOH. pH just means negative log of H⁺concentration or negative log of H₃O⁺ because remember, we said this before, H⁺ and H₃O⁺ are the same exact thing. pOH is the negative log of OH^-, so that means that p represents negative log.

The pH Scale Concept 2

What we should realize here is that by recognizing the relationship between H⁺ and OH^-, we can find a new way to express them in terms of pH and pOH. We come back here, we say that pH equals negative log of H⁺. We could divide both sides by negative one to get rid of this negative. So negative pH equals log of H⁺. Now, we want to just isolate the H⁺, so we're going to divide out the log. When you divide anything by log, it becomes 10 to that whatever the variable is. So, we just found a new relationship. We can say that H⁺, the concentration of H⁺ ions is equal to 10 to the negative pH. We could do the same thing with pOH. Divide both sides by negative one where negative pOH equals log of OH^-, Divide both sides by log. So OH^- equals 10 to the negative pOH. Just remember the relationship we have here with these first two equations and how we have the relationship with their concentrations. Because sometimes you'll be asked to find H⁺ concentration if they give you pH. Sometimes you may be asked to find OH^- concentration if they give you pOH. You have to know the relationship both frontward and backward.

The pH Scale Concept 3

Now we're going to say, a species with a pH greater than 7 is classified as basic. If you're basic, you're going to say that your H⁺ concentration is less than your OH^- concentration. And we can also say that the stronger the base, then the higher the pH. And the higher the pH, the greater your hydroxide concentration. We can understand this relationship as strongly as a base would have the lowest pH, I mean highest pH. And therefore have the highest OH^- concentration. And remember, we already went over this several videos ago. How do we determine if something is weak or strong? You still need to know those in order to do the following questions. Because again, I've said it so many times before. Why do we need to know the strength of things? Because eventually we're going to have to use ICE charts to find pH if we're given a weak acid or a weak base. That's why it's important to know what our species is. Is it weak or is it strong?

Now, we're going to say a species with a pH less than 7 is termed acidic. And if you're acidic, your H⁺ concentration is greater than your OH^- concentration. Here we can say the stronger the acid then the lower the pH. The strongest acid has the lowest pH which means you have the highest H⁺. And then finally, we're going to say species with a pH equal to 7 is neutral. Remember, this is only true at 25 degrees Celsius because remember at 25 degrees Celsius, K_w equals 1.0×10^-14. If they were to change the temperature, that would change our K_w and then neutral pH would become a new number. It doesn't always equal 7. And we're going to say here, if you're neutral, then your H⁺ concentration is equal to your OH^- concentration.

The pH Scale Concept 4

We're going to say here, we've talked about pH and pOH and just realize their relationship is connected together by this equation. We're going to say pH plus pOH equals 14. This arises by the fact that we have Kw = H⁺∙OH⁻. And if you take the negative log of H⁺ it gives you pH. If you take the negative log of OH⁻, it gives you pOH. And Kw = 1.0×10-14. If you took the negative log of Kw, it would give you 14. That's where this equation comes from. It comes from taking the negative log of all of this. And remember, if you have 2 things multiplying like H⁺ and OH⁻ are multiplying, and you take the negative log of that whole thing, then it becomes the addition between them. These guys are related. These two equations that I circled are related because they're connected together by negative log. So just remember that relationship and you'll be able to remember this formula. And remember, pH scale 0 to 14, you can be below 0 or higher than 14 depending on the concentration of the acid or base you're using.

The pH Scale Example 1

Hey guys. In this new video, we're going to put to practice some of the concepts we learned about pH and pOH. So let's take a look at the first example. Here it says, what is the hydroxide ion? So, what's the OH^- and the hydrogen ion concentration or hydronium ion concentration actually? That's H⁺ of an aqueous solution that has a pH equal to 6.12. So, we have pH, we need to find OH^- and H⁺. Remember, we're able to derive a formula that connects us between H⁺ and pH. Remember that H⁺ = 10^-pH. All we have to do now is just take that number and plug it in. When we do that, we get 7.59x10^-7. Now we could find OH^- now and we can find OH^- in 2 different ways.

Now, the first way we could find OH^- is by simply using this equation, K_w = H⁺OH^-. We know what K_w is. We assume the temperature is 25 degrees Celsius since they don't tell us what it is. This will be 1.0x10^-14. We just found out what H⁺ is. It's 7.59x10^-7. Now we have to find OH^-. OH^- is our only missing variable, so just isolate it. Here, OH^- would equal 1.32x10^-8. So that'd be one way we can find OH^-.

Now, the second way we could find it is if we know pOH, we can make a connection between pOH and OH^-. So first, we'd say that pH + pOH = 14. We know pH is 6.12, so let's just isolate our pOH. Subtract 6.12 from both sides. So pOH equals 7.88. And remember, what's the connection between pOH and OH^-? You can just simply say that, OH^- = 10^-pOH. And if you did 10^-7.88, you get the same exact answer for OH^-. So, 2 different methods to find the same exact missing variable. So it's basically your choice on deciding which way you want to go. Personally, I like to just find pOH and just do 10^-pOH. Because remember, if you don't put these 2 in brackets, your calculator may give you the incorrect answer. So it's probably always safer just to say OH^- = 10^-pOH.

Which of the following statements about aqueous solutions is/are true?

• A. For an basic solution the concentration of H₃O⁺ is greater than the concentration of OH^-.
• B. The pH of a neutral aqueous solution is 7.00 at all temperatures.
• C. An acidic solution under normal conditions has a pH value less than 7.00.
• D. If the concentration of H₃O⁺ decreases then the concentration of OH^- will also decrease.
• E. The pH of aqueous solutions is less than 7.

The pH Scale Example 2

Hey guys, in this new video, we're going to continue with our calculations dealing with pH and pOH. In this question, it says a solution is prepared by dissolving 0.235 moles of strontium hydroxide in water to produce a solution with a volume of 750 ml. Now, I'm asking you to find the concentration of OH^-. Now remember, these brackets mean concentration. Another name for concentration is molarity. And remember, molarity equals moles of solute over liters of solution. Here we need the moles of OH^- divided by the liters of solution. Let's do the easier part first. The easier part is we have 750 ml of solution. Let's just change that to liters. We're going to say we have 750 ml. You can say here, for every 1 liter, there's 1000 milliliters or you could say for every 1 ml, there's 10 to the negative 3 liters. That gives me 0.750 liters. That'll go on the bottom. Now, the harder part, we have to isolate moles of just hydroxide ion. All we're going to do here is we're going to take these 0.235 moles of strontium hydroxide and convert them into moles of hydroxide ion only. We're going to say we have 0.235 moles of strontium hydroxide and then just simply say here, for every one mole of strontium hydroxide, how many hydroxides are in the formula? You're going to notice that there are 2 of them, so there's 2 hydroxides for every one mole of strontium hydroxide. So that's going to give me 0.470 moles OH^-. So we're going to take those moles and plug them up top. So 0.470 divided by 0.750 will give me 0.627 molar OH^-. That'll be our answer here.

Now, for part b, I want us to find the H⁺ concentration. Remember, all we need to realize here is if I know my OH^- concentration, then I know my H⁺ concentration because remember, they're connected by this formula. Kw=H⁺∙OH^-. Plug in what we know for K_w and then fill in what we know for OH^-. So all we got to do now is divide both sides by 0.627, and we'll know what H⁺ is. H⁺ comes out to be 1.59x10^-14. Hope you guys were able to follow along. This question just has to do with a little bit of unit conversions and some little bit of stoichiometric relationships. For every 1 mole of strontium hydroxide, we have 2 moles of OH^-. So now that we've seen that one, I want you guys to attempt to do this practice question here. So remember, go back and see what the relationships are in order to find this correct answer. And just realize here when I say pure water, just understand pure water means neutral water. So if your water is pure, your water is neutral. And remember, what does that mean in terms of H⁺ OH^-? Knowing that will be the key to solving this question. Good luck, guys.

What is the Kw of pure water at 20.0°C, if the pH is 7.083?

• A. 8.26 × 10^-8
• B. 6.82 × 10^-15
• C. 7.23 × 10^-14
• D. 1.00 × 10^-14

Here’s what students ask on this topic:

What is the pH scale and how does it work?

The pH scale measures the acidity or basicity of a solution, ranging from 0 to 14 under normal conditions. A pH of 7 is neutral, below 7 is acidic, and above 7 is basic. The scale is logarithmic, meaning each whole number change represents a tenfold change in hydrogen ion concentration. The pH is calculated using the formula:

$\mathrm{pH}=-\log \left(H_{+}\right)$

where $H_{+}$ is the concentration of hydrogen ions. This scale helps to simplify the representation of very small or very large concentrations of hydrogen ions.

How do you calculate the pH of a solution?

To calculate the pH of a solution, you need to know the concentration of hydrogen ions (H⁺). The formula to find pH is:

$\mathrm{pH}=-\log \left(H_{+}\right)$

For example, if the concentration of H⁺ is 1.0 × 10^-3 M, the pH is:

$\mathrm{pH}=-\log (1.0\times {10}^{-3})$

This simplifies to:

$\mathrm{pH}=3$

Thus, the pH of the solution is 3, indicating it is acidic.

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 equation arises from the ion product of water (K_w), which is:

$K_w=H_{+}\times {\mathrm{OH}}_{-}$

At 25°C, K_w is 1.0 × 10^-14. Taking the negative logarithm of both sides, we get:

$-\log \left(K_w\right)=-\log \left(H_{+}\right)-\log \left({\mathrm{OH}}_{-}\right)$

Which simplifies to:

$\mathrm{pH}+\mathrm{pOH}=14$

This relationship helps in calculating either pH or pOH if one is known.

How do you determine if a solution is acidic, basic, or neutral?

A solution's pH determines whether it is acidic, basic, or neutral. If the pH is less than 7, the solution is acidic, meaning it has a higher concentration of hydrogen ions (H⁺) than hydroxide ions (OH^-). If the pH is greater than 7, the solution is basic, indicating a higher concentration of OH^- ions than H⁺ ions. A pH of exactly 7 is neutral, meaning the concentrations of H⁺ and OH^- are equal. This neutrality is typically true at 25°C, where the ion product of water (K_w) is 1.0 × 10^-14.

What is the formula to find the concentration of hydrogen ions from pH?

The concentration of hydrogen ions (H⁺) can be found from the pH using the formula:

$H_{+}={10}^{-}$

For example, if the pH of a solution is 4, the concentration of H⁺ is:

$H_{+}={10}^{-}$

This simplifies to:

$H_{+}=1.0\times 10-4$

Thus, the concentration of hydrogen ions is 1.0 × 10^-4 M.