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Answer :
To find the new pH after dilution, convert the original pH to molarity, then calculate the new molarity after dilution and convert back to pH. The new pH after adding 1.5 liters of distilled water to a 2L solution of HI with pH of 1.37 is approximately 1.61.
To calculate the new pH after diluting a 2L solution of HI with a pH of 1.37 by adding 1.5 liters of distilled water, we need to understand the change in concentration of the hydronium ions (H3O+) in the solution.
The pH is a measure of the acidity of a solution, indicating the concentration of H3O+ ions.
The pH is calculated using the formula: pH = -log[H3O+].
First, we calculate the concentration of H3O+ in the original solution using the given pH.
Since pH = -log[H3O+], by inverse, [H3O+] = 10-pH.
For a pH of 1.37, [H3O+] = 10-1.37 which equals approximately 4.27 x 10-2 M. In a 2L solution, this corresponds to 2L * 4.27 x 10-2 mol/L = 8.54 x 10-2 moles of H3O+.
After adding 1.5L of water, the total volume becomes 3.5L.
The number of moles of H3O+ remains the same, but the concentration changes due to the increased volume.
The new concentration of H3O+ is 8.54 x 10-2 moles / 3.5L = approximately 2.44 x 10-2 M.
The new pH is then calculated: pH = -log(2.44 x 10-2) which is approximately 1.61.
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