600 gallons of 15 M nitric acid were added to a lake. The initial pH of the lake was 5.90 and the final pH was 3.70. What is the volume of the lake?
Convert 5.90 pH to H^+.
Convert 3.70 pH to H^+ = z
I would convert 600 gallons to L. It's approx 2E3 L but you should do that exactly.
L1 x M1 = L2 x M2
2E3L x 15M = L2(lake)*z
Solve for L2. L2 will be the total volume and you should subtract the volume of the 600 gallons you added but I think the 600 gallons will be insignificant compared to the volume of the lake and it won't make any difference.
To find the volume of the lake, we can use the fact that the change in pH is related to the concentration of the acid added.
1. Determine the initial hydrogen ion concentration ([H+]) of the lake. The pH is given as 5.90, so we can convert it to [H+] using the formula: [H+] = 10^(-pH). In this case, [H+] = 10^(-5.90).
2. Determine the final hydrogen ion concentration ([H+]) of the lake after the acid is added. The pH is given as 3.70, so we can convert it to [H+] using the same formula: [H+] = 10^(-pH). In this case, [H+] = 10^(-3.70).
3. Calculate the difference in hydrogen ion concentration ([H+]) between the initial and final states of the lake: Δ[H+] = [H+]final - [H+]initial.
4. Use the volume relationship between the acid solution and the lake water to find the volume of the lake. Since we know the volume and concentration of the acid solution added, as well as the change in hydrogen ion concentration, we can set up the following equation:
Initial [H+] * Volume of the lake + Δ[H+] * Volume of the lake (due to acid addition) = Final [H+] * Volume of the lake.
However, since we are trying to find the volume of the lake, we can simplify the equation to:
Δ[H+] * Volume of the lake = Final [H+] * Volume of the lake - Initial [H+] * Volume of the lake.
5. Solve the equation to find the volume of the lake. In this case, Δ[H+] * Volume of the lake = (10^(-3.70) - 10^(-5.90)) * Volume of the lake.
Once you calculate the right side of the equation, you can divide both sides by Δ[H+] to solve for the volume of the lake.
By following these steps, you can find the volume of the lake by plugging in the given values for initial and final pH.