A solution has a pH of 3.90. What is the hydroxide ion concentration? I know that I need to find H30+ first but my teacher doesn't allow calculators on the test. So how would I find the answer WITHOUT a calculator?
Let me clarify something:
As you might notice, it doesn't matter what the pH is, if it is x.50 (where x= 1,2,3,4,5,6,7,8,9,etc) then you can guarantee that the answer will look like: 3.16E-(x+1).
To determine the hydroxide ion concentration without a calculator, you can use the relationship between pH and pOH. The pH and pOH are related by the equation:
pH + pOH = 14
Given that the pH of the solution is 3.90, we can solve for the pOH as follows:
pOH = 14 - pH
= 14 - 3.90
= 10.10
Now that we have the pOH value, we can use the relationship between pOH and hydroxide ion concentration to find the value of hydroxide ion concentration (OH-). The relationship is given by the equation:
pOH = -log[OH-]
Taking the antilogarithm (inverse of logarithm) of both sides, we have:
10^pOH = OH-
Now, using the value of pOH obtained earlier (10.10), we can calculate the hydroxide ion concentration:
OH- = 10^pOH
= 10^10.10
To evaluate this without a calculator, you can use the fact that 10^1 = 10 and 10^0 = 1. Therefore, we can rewrite the expression as follows:
10^10.10 = 10^(10 + 0.10)
= 10^10 × 10^0.10
≈ 10^10 × 1.259
Approximating 10^10 as 10 billion (10,000,000,000), we can calculate the hydroxide ion concentration:
OH- ≈ 10,000,000,000 × 1.259
≈ 12,590,000,000
Therefore, the hydroxide ion concentration in the solution is approximately 12,590,000,000.
To find the hydroxide ion concentration without a calculator, you can use the relationship between pH and pOH. The pH and pOH values are related to each other by the equation:
pH + pOH = 14
Therefore, if the pH of a solution is given, you can find the pOH by subtracting the pH from 14. In this case, the pH is 3.90, so the pOH would be:
pOH = 14 - 3.90 = 10.10
Now that you have the pOH value, you can calculate the hydroxide ion concentration by taking the antilog of the pOH value. The antilog is the inverse operation of taking a logarithm.
In this case, since we want the hydroxide ion concentration, we want to find the value of [OH-]. The antilog of the pOH value can be found using the formula:
[OH-] = 10^(-pOH)
Substituting the value of pOH into the equation:
[OH-] = 10^(-10.10)
Now, you can approximate the value of 10^(-10.10) without using a calculator by using scientific notation and manipulating the equation. Notice that 10^(-10.10) is equivalent to 1/(10^10.10).
To approximate this value, you can begin by noting that 10^2 = 100. So, 10^4 = 10,000, and 10^8 = 100,000,000.
Using this information, you can estimate that 10^10 is roughly 1,000,000,000 or 10^9.
Now, 10^10.10 can be estimated as slightly larger than 10^10, so it can be approximated as roughly 10 times larger than 10^9, or approximately 10^10.
Therefore, the hydroxide ion concentration is approximately:
[OH-] ≈ 10^(-10) = 1 x 10^(-10) M
Please note that this is an approximate value, since we rounded during the approximation process. However, it should be sufficient for most purposes without a calculator.
First off, hydroxide ion is OH-. H3O+ is actually the hydrogen ion concentration. Ummm...without a calculator, this is a tough one. You can estimate, by first finding the pOH:
pOH = 14-pH = 10.10
Then you can extrapolate into how the log was formed:
So if the pOH = 10 then the concentration of OH- in the solution would be 1E-10 M, and if the pOH = 11 then the concentration of OH- in the solution would be 1E-11.
However, the only way to do this without a calculator is to know the math behind logs and anti-logs...or memorize the tables for values. For example:
Lets say pH = 3.50, you know that if the pH was 3 then the concentration of H+ would be 1E-3 M. Also, if it was 4 then H+ concentration would be 1E-4 M. Here's where memorizing is helpful, once you know the range you can just memorize some numbers:
pH = 3.50; H+ conc = 3.16E-4
pH = 4.50; H+ conc = 3.16E-5
pH = 10.50; H+ conc = 3.16E11
As you might notice, it doesn't matter what the pH is, if it is xx.50 then you can guarantee that the answer will look like 3.16E-xx.
So having a table of these values memorized is helpful and thus a pOH = 10.10 gives you a concentration of about 7.94E-11 M
If you have any more questions or are confused about a certain part then just ask.