pH of a solution of a strong acid is 5.0. What will be the pH of the solution obtained after diluting the given solution a 100 times?a)5.6999b)6.0090c)7.6907d)6.699Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Conc. of a strong Acid with pH=5 is 10^ -5 M. On diluting 100- times the concentration decreases to 10^-7.
But the water at 25 degree C will be having 10–7 M of H3O+ ions in solution. So the H3O+ ion concentration in 10^-7 M HCl is (10^-7+10^-7) M
= 2 x 10^ -7.
So it pH= - log (2 x 10^-7)
= 6.6987

Answer

pH of a solution of a strong acid is 5.0. What will be the pH of the solution obtained after diluting the given solution a 100 times?

When we dilute a solution, the concentration of the solute decreases. In this case, we are diluting a strong acid solution, which means the concentration of hydrogen ions (H+) will decrease.

pH is a measure of the concentration of hydrogen ions in a solution.

The pH scale ranges from 0 to 14. A pH of 7 is considered neutral, pH below 7 is acidic, and pH above 7 is basic. Each unit on the pH scale represents a tenfold change in the concentration of hydrogen ions. So, a solution with a pH of 5 is more acidic than a solution with a pH of 6.

To find the pH of the solution obtained after dilution, we need to consider the dilution factor.

The dilution factor is given as 100 times. This means that the volume of the original solution is diluted with 100 times the amount of solvent.

When we dilute a solution, the number of moles of the solute remains the same.

To calculate the new concentration of the solute, we can use the formula:

Concentration of solute in the diluted solution = Concentration of solute in the original solution / Dilution factor

Since the concentration of the solute (hydrogen ions) in the original solution is unknown, we need to consider the pH value.

pH is defined as the negative logarithm of the hydrogen ion concentration.

Mathematically, pH = -log[H+]

Where [H+] is the concentration of hydrogen ions in moles per liter.

Given that the pH of the original solution is 5.0, we can calculate the concentration of hydrogen ions using the pH formula.

pH = -log[H+]

5.0 = -log[H+]

log[H+] = -5.0

[H+] = 10^-5.0

[H+] = 1 x 10^-5 M

Now, we can calculate the concentration of hydrogen ions in the diluted solution:

Concentration of solute in the diluted solution = Concentration of solute in the original solution / Dilution factor

Concentration of solute in the diluted solution = (1 x 10^-5 M) / 100

Concentration of solute in the diluted solution = 1 x 10^-7 M

Finally, we can calculate the pH of the diluted solution using the concentration of hydrogen ions:

pH = -log[H+]

pH = -log(1 x 10^-7)

pH = -(-7)

pH = 7

Therefore, the pH

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