To find the number of hydroxide ions in a solution, you need to know the concentration of the hydroxide ions. The concentration is usually expressed in moles per liter (mol/L). Here are some quick answers to common questions about finding hydroxide ion concentration:
– The hydroxide ion concentration is equal to the hydroxide ion molarity.
– You can calculate the hydroxide ion molarity if you know the pH of the solution.
– To calculate hydroxide molarity from pH, use the formula: Hydroxide molarity = 10^(-pH)
– So if you know the pH is 12, the hydroxide molarity is 10^(-12) = 0.0000000001 mol/L
– Once you have the molarity, you can calculate the number of hydroxide ions by multiplying the molarity by Avogadro’s number.
– Avogadro’s number is 6.022 x 10^23.
– So if the molarity is 0.0000000001 mol/L, multiply by Avogadro’s number to get 6.022 x 10^11 hydroxide ions per liter.
Calculating Hydroxide Ion Concentration from pH
As mentioned above, the concentration of hydroxide ions in a solution can be determined from the pH. Here is a more in-depth look at the relationship between pH and hydroxide ion concentration:
The pH Scale
The pH scale ranges from 0 to 14 and measures the acidity or alkalinity of a solution. It is based on the concentration of hydrogen ions (H+) in the solution.
– Solutions with a pH below 7 are acidic. This means they have a high concentration of H+ ions.
– Solutions with a pH above 7 are basic or alkaline. They have a low concentration of H+ and a high concentration of OH- ions.
– At pH 7, the solution is neutral. The concentrations of H+ and OH- are equal.
The pH is calculated as the negative logarithm of the H+ ion concentration:
pH = -log[H+]
So as the H+ concentration increases, the pH decreases, and vice versa.
The Relationship Between H+ and OH-
In any aqueous solution, the concentrations of H+ and OH- are related:
[H+][OH-] = 10^-14
This is known as the ion product of water. At neutral pH of 7:
[H+] = 10^-7 M
[OH-] = 10^-7 M
So if you know the concentration of either H+ or OH-, you can calculate the other using this relationship.
Calculating Hydroxide Concentration
Putting this together with the pH equation, we get:
pH = -log[H+]
And
[H+][OH-] = 10^-14
So:
[OH-] = 10^(-pH)
This is the formula for calculating the hydroxide ion concentration from the pH.
Let’s do an example:
If the pH is 12, then:
[OH-] = 10^(-12) = 0.0000000001 M or 1 x 10^-12 M
So a pH of 12 corresponds to a hydroxide concentration of 0.0000000001 mol/L.
Converting Hydroxide Molarity to Number of Ions
Once you’ve calculated the molarity of hydroxide ions in a solution, you can determine the actual number of OH- ions present by using Avogadro’s number.
Avogadro’s Number
Avogadro’s number (NA) is a constant equal to 6.022 x 10^23 mol^-1. This number represents the number of molecules or ions in one mole of a substance.
So for our purposes:
– 1 mole of OH- ions contains 6.022 x 10^23 ions
– 0.5 moles of OH- contains (0.5)(6.022 x 10^23) ions
– etc.
We can use Avogadro’s number to interconvert between molarity and number of ions.
Calculating Ions from Molarity
The calculation is:
Number of ions = Molarity x Avogadro’s number x Volume
Let’s walk through an example:
* Hydroxide molarity is 0.0000000001 mol/L
* Volume of solution is 1.0 L
* Avogadro’s number is 6.022 x 10^23 ions/mol
Number of OH- ions:
= Molarity x Avogadro’s number x Volume
= 0.0000000001 mol/L x 6.022 x 10^23 ions/mol x 1.0 L
= 6.022 x 10^11 ions
So for a 1 L solution with a hydroxide molarity of 0.0000000001 mol/L, there are 6.022 x 10^11 hydroxide ions present.
You can use variations of this calculation to determine the number of ions for any molar concentration and solution volume.
Practice Examples
Let’s go through a few more practice examples of finding hydroxide ion numbers from concentration data:
Example 1
If you are told that a solution has a hydroxide ion concentration of 0.000001 mol/L, how many hydroxide ions are present in 0.5 L of the solution?
| Given: | |
| OH- molarity | 0.000001 mol/L |
| Volume | 0.5 L |
| Avogadro’s number | 6.022 x 10^23 ions/mol |
Number of OH– ions = Molarity x Avogadro’s number x Volume
= 0.000001 mol/L x 6.022 x 10^23 ions/mol x 0.5 L
= 3.011 x 10^17 ions
Therefore, there are 3.011 x 10^17 hydroxide ions present in the 0.5 L solution.
Example 2
If a solution has a pH of 11, how many hydroxide ions are in 2.0 L of the solution?
| Given: | |
| pH | 11 |
| Volume | 2.0 L |
[OH–] = 10^(-pH) = 10^(-11) = 0.0000000001 mol/L
Number of OH– ions = Molarity x Avogadro’s number x Volume
= 0.0000000001 mol/L x 6.022 x 10^23 ions/mol x 2.0 L
= 1.204 x 10^17 ions
For a pH of 11, there are 1.204 x 10^17 hydroxide ions in 2.0 L of solution.
Example 3
What is the concentration of hydroxide ions in a solution with a pH of 13? If there is 0.25 L of this solution, how many OH– ions are present?
| Given: | |
| pH | 13 |
| Volume | 0.25 L |
[OH–] = 10^(-pH) = 10^(-13) = 0.0000000000001 mol/L
Number of OH– ions = Molarity x Avogadro’s number x Volume
= 0.0000000000001 mol/L x 6.022 x 10^23 ions/mol x 0.25 L
= 1.505 x 10^16 ions
For a pH of 13, the hydroxide molarity is 0.0000000000001 mol/L. In 0.25 L of this solution, there are 1.505 x 10^16 OH– ions.
Using Calculations to Balance Equations
One of the useful applications of determining hydroxide ion numbers is balancing chemical equations. Let’s look at an example:
Balance the following reaction equation in acidic solution:
Fe(s) + H2O(l) → Fe3+(aq) + H2(g)
Strategy
First, calculate the number of ions produced for one Fe atom reacting.
* 1 Fe produces 3 Fe3+ ions
* 1 H2O produces 2 H+ (since this is an acidic solution)
* Need to balance number of Fe and H+
Calculations
* If there is 1 Fe, there are 3 Fe3+ produced
* For 3 Fe3+, need 3 H2O to produce 6 H+
* So for 1 Fe, need 3/1 = 3 H2O
This gives balanced coefficients:
Fe(s) + 3H2O(l) → Fe3+(aq) + 3H2(g)
By calculating the ion numbers, we can ensure the equation balances appropriately.
Using Molar Ratios
Molar ratios provide another useful approach for relating the quantities of different ions in a balanced chemical equation. This can be helpful when calculating relative ion amounts.
The molar ratio is the coefficient in the balanced equation for each substance. Looking again at the previous example:
Fe(s) + 3H2O(l) → Fe3+(aq) + 3H2(g)
The molar ratios are:
| Fe : H2O | 1:3 |
| Fe : H2 | 1:3 |
| Fe3+ : H2 | 1:3 |
This tells us:
– For every 1 Fe, there are 3 H2O and 3 H2
– For every 1 Fe3+, there are 3 H2
We can use these whole number ratios to calculate relative ion amounts. For example, if we know there are 5 Fe atoms, we can determine:
– There must be 5 x 3 = 15 H2O
– There must be 5 x 3 = 15 H2 produced
– There must be 5 x 1 = 5 Fe3+ ions formed
So molar ratios give us mole-to-mole conversion factors between substances in a balanced equation. This provides another useful approach for calculating hydroxide and other ion numbers.
Limiting Reactant Concepts
When calculating the amount of hydroxide or other ions produced in a reaction, it is important to consider which reactant is limiting. The limiting reactant is the reactant that gets completely consumed first in the reaction. This places a limit on how much product can be formed.
Let’s look at an example reaction:
Fe(s) + 3H2O(l) → Fe3+(aq) + 3H2(g)
Imagine this reaction occurs with 5 moles of Fe and 8 moles of H2O. Which is limiting?
Using the molar ratio, we know:
– 5 moles Fe requires 5 x 3 = 15 moles H2O
– But we only have 8 moles H2O available
Therefore, H2O is the limiting reactant. There is not enough H2O to react with all the Fe present.
In this case:
– The 8 moles of H2O will be completely consumed
– According to the ratio, 8 moles H2O can only react with 8/3 = 2.67 moles of Fe
So the amount of products formed will be limited by the H2O availability:
– 2.67 moles of Fe will react
– Producing 2.67 moles of Fe3+
– Consuming 8 moles of H2O
– Producing 8 x 3 = 24 moles of H2
Considering limiting reactants prevents overcalculation of product amounts. This is key for accurately determining hydroxide and other ion numbers produced in chemical reactions.
Conclusion
In summary, here are the key steps for finding the number of hydroxide ions in a solution:
1. Use the pH to calculate the molarity of hydroxide ions:
[OH–] = 10^(-pH)
2. Convert moles OH– to number of ions using Avogadro’s number:
Ions = Molarity x Vol x Avogadro’s number
3. Consider limiting reactants when relevant to avoid overcalculation
4. Use balanced equations and molar ratios to relate quantities of ions
Mastering these calculation techniques allows quantitative determination of hydroxide ion numbers, a key skill in many chemical applications. With a bit of practice, you can become adept at finding the number of OH– ions in any solution.
