To calculate the volume of sodium hydroxide required to neutralize the contaminated water, we need to first determine the number of moles of acid present in the tank.
Step 1: Convert the volume of water to liters
The volume of water is given as 1.6x10^4 Liters. Since the standard unit for volume in calculations is liters, no conversion is required in this step.
Step 2: Calculate the number of moles of acid
To calculate the number of moles of acid, we need to use the equation for pH:
pH = -log[H+]
where [H+] represents the concentration of hydrogen ions in moles per liter.
In this case, we are given the pH as 3.78. To find [H+], we use the equation:
[H+] = 10^(-pH)
[H+] = 10^(-3.78)
[H+] = 1.58x10^(-4) moles per liter
Now, to calculate the number of moles in the entire tank, we need to multiply the concentration by the volume:
moles of acid = [H+] x volume of water
moles of acid = (1.58x10^(-4) moles/L) x (1.6x10^4 L)
moles of acid = 2.53 moles
Step 3: Convert moles of acid to moles of sodium hydroxide
Since nitric acid (HNO3) is a strong acid and sodium hydroxide (NaOH) is a strong base, the reaction between them is 1:1 in terms of moles. Therefore, the number of moles of sodium hydroxide required to neutralize the acid is also 2.53 moles.
Step 4: Calculate the volume of sodium hydroxide
To calculate the volume of sodium hydroxide, we need to use the equation:
volume (L) = moles / concentration (M)
In this case, the concentration given is 0.050 M (0.050 moles/L).
volume of sodium hydroxide = 2.53 moles / 0.050 moles/L
volume of sodium hydroxide = 50.6 Liters
Therefore, 50.6 Liters of 0.050 M sodium hydroxide are required to neutralize the contaminated water in the tank.