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AP®︎/College Chemistry
Course: AP®︎/College Chemistry > Unit 12
Lesson 1: Acids, bases, and pH- Arrhenius acids and bases
- Arrhenius acids and bases
- pH, pOH, and the pH scale
- Brønsted-Lowry acids and bases
- Brønsted–Lowry acids and bases
- Autoionization of water
- Water autoionization and Kw
- Definition of pH
- Acid strength, anion size, and bond energy
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pH, pOH, and the pH scale
Definitions of pH, pOH, and the pH scale. Calculating the pH of a strong acid or base solution. The relationship between acid strength and the pH of a solution.
Key points
- We can convert between
and using the following equations:
- We can convert between
and using the following equations:
- For any aqueous solution at
:
.
- For every factor of
increase in concentration of , will decrease by unit, and vice versa. - Both acid strength and concentration determine
and .
Introduction
In aqueous solution, an acid is defined as any species that increases the concentration of , while a base increases the concentration of . Typical concentrations of these ions in solution can be very small, and they also span a wide range.
For example, a sample of pure water at contains of and . In comparison, the concentration of in stomach acid can be up to approximately . That means for stomach acid is approximately orders of magnitude larger than in pure water!
To avoid dealing with such hairy numbers, scientists convert these concentrations to or values. Let's look at the definitions of and .
Definitions of and
Relating and
The for an aqueous solution is calculated from using the following equation:
The lowercase indicates . You will often see people leave off the base part as an abbreviation.
For example, if we have a solution with , then we can calculate the using Eq. 1a:
Given the of a solution, we can also find :
Relating and
The for an aqueous solution is defined in the same way for :
For example, if we have a solution with , then we can calculate using Eq. 2a:
Given the of a solution, we can also find :
Relating and
Based on equilibrium concentrations of and in water, the following relationship is true for any aqueous solution at :
This relationship can be used to convert between and . In combination with Eq. 1a/b and Eq. 2a/b, we can always relate and/or to and . For a derivation of this equation, check out the article on the autoionization of water.
Example 1: Calculating the of a strong base solution
If we use of to make of an aqueous solution at , what is the of this solution?
We can find the of our solution by using the relationship between , , and . Let's go through the calculation step-by-step.
Step 1. Calculate the molar concentration of
Molar concentration is equal to moles of solute per liter of solution:
To calculate the molar concentration of , we can use the known values for the moles of and the volume of solution:
The concentration of in the solution is .
Step 2: Calculate based on the dissociation of
Because is a strong base, it dissociates completely into its constituent ions in aqueous solution:
This balanced equation tells us that every mole of produces one mole of in aqueous solution. Therefore, we have the following relationship between and :
Step 3: Calculate from using Eq. 2a
Now that we know the concentration of , we can calculate using Eq. 2a:
The of our solution is .
Step 4: Calculate from using Eq. 3
We can calculate from using Eq. 3. Rearranging to solve for our unknown, :
We can substitute the value of we found in Step 3 to find the :
Therefore, the of our solution is .
The scale: Acidic, basic, and neutral solutions
Converting to is a convenient way to gauge the relative acidity or basicity of a solution. The scale allows us to easily rank different substances by their value.
The scale is a negative logarithmic scale. The logarithmic part means that changes by unit for every factor of change in concentration of . The negative sign in front of the log tells us that there is an inverse relationship between and : when increases, decreases, and vice versa.
The following image shows a scale labeled with values for some common household substances. These values are for solutions at . Note that it is possible to have a negative value.
Some important terminology to remember for aqueous solutions at :
- For a neutral solution,
. - Acidic solutions have
. - Basic solutions have
.
The lower the value, the more acidic the solution and the higher the concentration of . The higher the value, the more basic the solution and the lower the concentration of . While we could also describe the acidity or basicity of a solution in terms of , it is a little more common to use . Luckily, we can easily convert between and values.
Concept check: Based on the scale given above, which solution is more acidic orange juice, or vinegar?
Example : Determining the of a diluted strong acid solution
We have of a nitric acid solution with a of . We dilute the solution by adding water to get a total volume of .
What is the of the diluted solution?
There are multiple ways to solve this problem. We will go over two different methods.
Method 1. Use properties of the log scale
Recall that scale is a negative logarithmic scale. Therefore, if the concentration of decreases by a single factor of , then the will increase by unit.
Since the original volume, , is one tenth the total volume after dilution, the concentration of in solution has been reduced by a factor of . Therefore, the of the solution will increase unit:
Therefore, the of the diluted solution is .
Method 2. Use moles of to calculate
Step 1: Calculate moles of
We can use the and volume of the original solution to calculate the moles of in the solution.
Step 2: Calculate molarity of after dilution
The molarity of the diluted solution can be calculated by using the moles of from the original solution and the total volume after dilution.
Step 3: Calculate from
Finally, we can use Eq. 1a to calculate :
Method 2 gives us the same answer as Method 1, hooray!
In general, Method 2 takes a few extra steps, but it can always be used to find changes in . Method 1 is a handy shortcut when changes in concentration occur as multiples of . Method 1 can also be used as a quick way to estimate changes.
Relationship between and acid strength
Based on the equation for , we know that is related to . However, it is important to remember that is not always directly related to acid strength.
The strength of an acid depends on the amount that the acid dissociates in solution: the stronger the acid, the higher at a given acid concentration. For example, a solution of strong acid will have a higher concentration of than a solution of weak acid . Thus, for two solutions of monoprotic acid at the same concentration, will be proportional to acid strength.
More generally though, both acid strength and concentration determine . Therefore, we can't always assume that the of a strong acid solution will be lower than the of a weak acid solution. The acid concentration matters too!
Summary
- We can convert between
and using the following equations:
- We can convert between
and using the following equations:
- For every factor of
increase in concentration of , will decrease by unit, and vice versa. - For any aqueous solution at
:
.
- Both acid strength and concentration determine
and .
Problem 1: Calculating the pH of a strong base solution at
We make of a solution with a concentration of . The solution is then diluted to by adding additional water.
What is the of the solution after dilution?
Want to join the conversation?
- How does the temperature affect the pH and pOH?(36 votes)
- At 100C the pH of water is 6.14, so higher temperature decreases the pH. The opposite is true for pOH: higher temperatures increases the pOH.(43 votes)
- What does M stand for in the unit labels?(15 votes)
- M stands for the unit of Molarity of the solution.(20 votes)
- Could someone explain the difference between acid strength and concentration? According to me, a strong acid will fully ionise in water compared to a weak acid which will partially ionise. Therefore a strong acid will contribute more H+ ions than a weak acid. Therefore, the pH of a strong acid solution will be higher than a weak acid solution.
Is this correct?(8 votes)- Nice question!! It is important that you don't confuse the words strong and weak with the terms concentrated and dilute. At the same concentration, a weak acid will be less acidic than a strong acid. However, if you have highly concentrated weak acid (almost pure) and compare this to a very diluted strong acid (like 1 drop of HCl in a swimming pool) then the pH of the weak acid will be much more acidic than that of the strong acid.(25 votes)
- Can someone please explain what are monoprotic and diprotic acids? Thanks.(13 votes)
- H2SO4 is a typical diprotic acid (2 protons can be released in aqueous solution, however one at that time)
H2SO4 +H20 gives HSO4- + H+/H3O+
then,
HSO4- +H2O gives SO42- + H+/H3O+(16 votes)
- how can we solve pH,pOH numericals without using scientific calculator during our examination?(8 votes)
- Unless you are using perfect numbers of base ten (e.g. 10^-7, 10^-2, etc.) there is no way to do it because you cannot easily do logarithms. If you are asked to do these calculations without a calculator, there is a good chance minimal if any extensive calculations are required.
Example: log(10^-6) = -6(7 votes)
- How can NaOH have a pH scale? How can a base add H+ ions to the solution? It adds OH- ions right?(5 votes)
- NaOH does not have a pH, but an aqueous solution of NaOH does.
Water contains both H⁺ and OH⁻ ions.
Adding NaOH increases the concentration of OH⁻ ions and decreases the concentration of H⁺ ions.
But there are always some H⁺ ions present, so aqueous NaOH solutions have a pH, usually between 7 and 14.(11 votes)
- How does pH+pOH= 14? Where does the random number come in?(3 votes)
- There is no random number.
The formula comes from the ion product for water.
[H⁺][OH⁻] = 1.00 × 10⁻¹⁴
∴ pH + pOH = 14.00(4 votes)
- Hi
I feel like there's a step missing.I'm not sure why the pH as an exponent is negative & where the minus sign comes from.I understand that the logarithm (of base 10) was changed to an exponent.What is this law of logarithms called?
pH= -log (H+)
10^-pH = (H+)
Also I was trying to figure it out with numbers pH=-(log 10^-4)
and I got 10^-pH =10^-4 and I'm not sure where to go from there to obtain the pH.Do I just cancel out the 10s & minuses that are on both sides to get a pH of 4,to cross off these I have to divide/multiply both sides by some number(s) would these numbers be 10 and multiplying the exponents by -1 to get rid of the minuses because the pH scale is usually positive numbers?
Thanks!(3 votes)- This is the power rule of logs. When you have a number in front of a log term, this is the same as raising the log term to that number. For example, 4log(3) is the same as log(3^4).
With pH, the number in front of the log is -1 (because pH = -log [H+]). Therefore, using the power rule, we can re-express this as pH = log ([H+]^-1).
Using another log rule, we can express each side of this equation as an exponent of 10 and we get:
10^pH = 10^log ([H+]^-1).
Using a definition of logs, the right hand side of this equation now just becomes [H+]^-1. So we have:
10^pH = [H+]^-1
The right hand side can be expressed as 1/[H+] giving us:
10^pH = 1/[H+]
Multiplying each side by [H+] and dividing each side by 10^pH gives:
[H+] = 1/10^pH which is the same as saying [H+] = 10^-pH.
As an example, if the pH is 7, then [H+] = 10^-7.(3 votes)
- what is -log? is it a number?(2 votes)
- Log is a maths function, it stands for logarithm.
We use a log scale so we can visualise the concentration of H+ ions easier as we don't without have to deal with lots of decimal places etc.(4 votes)
- Is it necessary that to calculate pH or pOH of a substance, we need to have the substance in aqueous physical state? What if the substance is already in aqueous state?
Is it possible to find the pH or pOH of a substance in solid physical state or even by melting it?
Also, we always calculate the pH or pOH of a solid substance by dissolving it in water and find its pH or pOH according to the [H+] or [OH-] produced by it .Why we don't take in consideration the [H+] or [OH-] present in water and only take [H+] or [OH-]of the dissolved substance?
Thankyou :)(3 votes)- Ok so while calculating the equilibrium constant for a reaction, we consider the active masses of substances involved in the reactants and products. Since the activity of pure solids and liquids is unity, adding them to the expression will make no difference and it is usually omitted.
Hope this helps!(1 vote)