320.0 gallons of 15 M nitric acid were added to a lake. The initial pH p the lake was 6.30 and the final pH was 4.60. What is the volume of the lake?
Convert pH 4.60 to (H^+) = M2
gallons1 x M1 = gallons2 x M2
320 x 15 = gallons2 x 2.51E-5
Solve for gallons2
gallons 2 includes the 320 gallons that were added.
To solve this problem, we need to use the concept of dilution and the equation representing the relationship between initial and final pH values. Here is the step-by-step explanation:
Step 1: Determine the change in pH.
The change in pH is calculated by subtracting the final pH from the initial pH:
Change in pH = Final pH - Initial pH = 4.60 - 6.30 = -1.70
Step 2: Calculate the concentration of H+ ions in the acidic solution.
The pH of a solution is equal to the negative logarithm (base 10) of the concentration of H+ ions:
[H+] = 10^(-pH) = 10^(-4.60) = 2.51 x 10^(-5) M
Step 3: Use the concept of dilution to find the concentration of H+ ions in the diluted lake.
In dilution, the moles of solute remain constant, so we can use the equation:
Initial moles of H+ ions = final moles of H+ ions
Volume x Initial concentration = Final volume x Final concentration
We are trying to find the volume of the lake, so we can rearrange the equation as follows:
Volume of the lake = (Final volume x Final concentration) / Initial concentration
Step 4: Calculate the Final Volume of the solution.
The final volume of the solution can be calculated by using the equation:
Final volume = Initial volume + Volume of acid added
Since we know the initial volume of the solution (the lake) and the volume of acid added, we can substitute the values and calculate the final volume.
Step 5: Calculate the Volume of the lake.
Now that we have the final volume, we can substitute all the known values into the equation and calculate the volume of the lake.
Let's put all the steps together and solve the problem:
Step 1: Change in pH = 4.60 - 6.30 = -1.70
Step 2: [H+] = 10^(-4.60) = 2.51 x 10^(-5) M
Step 3: Volume of the lake = (Final volume x Final concentration) / Initial concentration
Step 4: Final volume = Initial volume + Volume of acid added
Step 5: Volume of the lake = Final volume
Please provide the initial volume of the lake and the volume of the acid added so we can proceed with the calculation.