How many moles of H3O+ or OH- must you add to a liter of strong base solution to adjust its PH from 9.870 to 7.980. Assume a negligible change in volume.
Convert pH = 7.980 to (H3O^+) = ? mols/L.
Convert pH = 9.870 to (H3O^+) = ? mols/L.
Subtract to see the difference in mols.
The pH is now 9.87 and you want to move it to 7.98, therefore, you must add acid and you want to add the mols difference.
Sub
To calculate the number of moles of H₃O⁺ or OH⁻ required to adjust the pH from 9.870 to 7.980, we first need to determine the concentration of H₃O⁺ or OH⁻ at each pH level.
The pH scale is logarithmic, where pH = -log[H₃O⁺]. Thus, we need to convert the given pH values to concentrations (or molarities) of H₃O⁺ or OH⁻.
For pH 9.870:
pH = -log[H₃O⁺]
9.870 = -log[H₃O⁺]
Taking the logarithm of both sides:
[H₃O⁺] = 10^(-pH)
[H₃O⁺] = 10^(-9.870)
Similarly, for pH 7.980:
[H₃O⁺] = 10^(-pH)
[H₃O⁺] = 10^(-7.980)
Since we are starting with a strong base solution, the concentration of OH⁻ ions will be high. To find the concentration of OH⁻, we can use the equation [H₃O⁺] × [OH⁻] = 1.0 x 10^-14 (at 25°C).
Remember, the concentration of H₃O⁺ (or [H₃O⁺]) is the same as the concentration of OH⁻ (or [OH⁻]) in a neutral solution.
From the equation [H₃O⁺] × [OH⁻] = 1.0 x 10^-14:
[H₃O⁺] = 10^(-9.870)
[OH⁻] = 1.0 x 10^-14 / [H₃O⁺]
Now, we can calculate the concentrations [H₃O⁺] and [OH⁻] at pH 9.870 and pH 7.980:
At pH 9.870:
[H₃O⁺] = 10^(-9.870)
[OH⁻] = 1.0 x 10^-14 / [H₃O⁺]
At pH 7.980:
[H₃O⁺] = 10^(-7.980)
[OH⁻] = 1.0 x 10^-14 / [H₃O⁺]
Finally, to determine the number of moles, we multiply the concentrations by the volume:
moles = concentration × volume
Since the volume is negligible in this case (given in the question), we can consider it to be 1 liter.
Therefore, the number of moles of H₃O⁺ or OH⁻ required to adjust the pH from 9.870 to 7.980 is equal to the concentrations calculated above.
To solve this problem, we need to apply the concept of pH and the relationship between pH and the concentration of H3O+ or OH- ions.
First, let's understand the relationship between pH and the concentration of H3O+ ions.
pH is a measure of acidity or alkalinity in a solution and is defined as the negative logarithm (base 10) of the concentration of H3O+ ions. The pH scale ranges from 0 to 14, where pH 7 is considered neutral, pH less than 7 is acidic, and pH greater than 7 is alkaline or basic.
The formula for calculating pH is:
pH = -log[H3O+]
Since we are given the initial and final pH values, we can use the equation to determine the initial and final H3O+ concentrations.
Step 1: Calculate the initial H3O+ concentration
pH = -log[H3O+]
9.870 = -log[H3O+]
[H3O+] = 10^(-9.870)
Step 2: Calculate the final H3O+ concentration
pH = -log[H3O+]
7.980 = -log[H3O+]
[H3O+] = 10^(-7.980)
Now we need to find the difference in concentration between the initial and final H3O+ ions.
Step 3: Calculate the concentration difference
Δ[H3O+] = [H3O+]final - [H3O+]initial
= 10^(-7.980) - 10^(-9.870)
Since the solution is a strong base, it will contain OH- ions. In a neutral solution, the concentration of H3O+ ions is equal to the concentration of OH- ions.
Step 4: Calculate the moles of OH- ions to be added
Δ[H3O+] = Δ[OH-] = moles of OH- ions / volume of the solution
Since we are given that the volume remains constant, we can directly calculate the moles of OH- ions to be added.
Step 5: Calculate the moles of OH- ions
moles of OH- ions = Δ[OH-] × volume = Δ[H3O+] × volume
Now, you can plug in the values to calculate the moles of OH- ions by substituting the value of Δ[H3O+] and the volume (which is given as 1 liter).
moles of OH- ions = (10^(-7.980) - 10^(-9.870)) × 1
Please note that the moles of OH- ions obtained will be the same as the moles of H3O+ ions required to adjust the pH.