The pH or acidity of liquid is measured in pH, where pH is given by the equation pH=- log C, with C being the concentration of [H+] in multiples of M=1mol/L. Suppose you are given a solution of hydrochloric acid with a pH of 1.7 and asked to increase the pH solution by 1.4. Determine by how much you must dilute the solution if the ratio of the concentration of two acids is c2/c1 . Does your answer differ if you start with pH of 2.2
If pH(1) = 1.7 => [H+]=10^-1.7 = 0.020M
If pH(2) = 1.7 + 1.4 = 3.1 => [H+]=10^-3.1 = 0.0008
pH(1)/pH(2) = 0.020/0.00080 = 25X dilution
If pH(3) = 2.2 => [H+]=10^-2.2 = 0.0063M
If pH(4)= 2.2 + 1.4 = 3.6 => [H+]= 0.00025
pH(3)/pH(4)= 0.0063/0.00025 = 25X dilution
No
To determine by how much you must dilute the solution in order to increase the pH by 1.4, we need to first find the concentration of hydrogen ions ([H+]) in the original solution.
The equation to calculate pH is given as:
pH = -log [H+]
Rearranging the equation, we get:
[H+] = 10^(-pH)
Using the given pH value of 1.7, we can calculate the original concentration of hydrogen ions:
[H+] = 10^(-1.7)
Now, to increase the pH by 1.4, we need to calculate the new concentration of hydrogen ions:
New [H+] = 10^(-1.7 + 1.4) = 10^(-0.3)
Next, we are given the ratio of the concentration of the two acids, c2/c1. Let's assume that c1 represents the original concentration of hydrochloric acid and c2 represents the new concentration after dilution.
According to the dilution formula, the ratio of the concentrations of two solutions is equal to the ratio of their volumes:
c2/c1 = V1/V2
We want to find out by how much we need to dilute the solution, which means we need to find the ratio of the final volume to the original volume.
Plugging in the known values, we have:
10^(-0.3)/10^(-1.7) = V1/V2
Simplifying the equation:
10^(-0.3 + 1.7) = V1/V2
10^1.4 = V1/V2
V1/V2 = 25.12
Therefore, you need to dilute the solution by a ratio of approximately 25.12.
Now, let's consider if we start with a pH of 2.2 instead. Using the same approach as above, we calculate the original concentration as:
[H+] = 10^(-2.2)
To increase the pH by 1.4, we calculate the new concentration:
New [H+] = 10^(-2.2 + 1.4) = 10^(-0.8)
Applying the dilution formula with the new values:
10^(-0.8)/10^(-2.2) = V1/V2
10^(-0.8 + 2.2) = V1/V2
10^1.4 = V1/V2
V1/V2 = 25.12
As you can see, the answer remains the same regardless of whether we start with a pH of 1.7 or 2.2. The dilution ratio in both cases is approximately 25.12.