A 10 ml of hydrochloric acid solution of concentration equal to 0.1 mol per litre is added 90 ml of pure water. What's the pH of the final solution?
Assuming the volumes are additive, the final concn of the HCl is
0.1 x (10/100) = 0.01 M so pH = = log(H^+). The H^+ contributed by the H2O is small enough to be ignored in this case.
To determine the pH of the final solution, we need to calculate the concentration of the resulting hydrochloric acid solution after it is diluted with water.
Step 1: Calculate the moles of hydrochloric acid in the initial 10 ml solution.
Using the equation: Concentration (mol/L) = moles (mol) / volume (L)
0.1 mol/L = moles (in the initial 10 ml solution) / 0.01 L (10 ml converted to L)
Rearranging the equation, we find:
moles (in the initial 10 ml solution) = 0.1 mol/L * 0.01 L = 0.001 mol
Step 2: Calculate the total moles of hydrochloric acid after dilution.
Since the initial 10 ml solution is diluted with 90 ml of pure water:
Total volume = 10 ml + 90 ml = 100 ml = 0.1 L
The moles of hydrochloric acid after dilution will remain the same, as no chemical reaction has occurred. Therefore, we have:
moles (after dilution) = 0.001 mol
Step 3: Calculate the concentration of the resulting hydrochloric acid solution after dilution.
Using the equation: Concentration (mol/L) = moles (mol) / volume (L)
Concentration (after dilution) = moles (after dilution) / volume (after dilution)
Concentration (after dilution) = 0.001 mol / 0.1 L = 0.01 mol/L = 0.01 M
Step 4: Calculate the pH of the resulting solution.
pH is a measure of the acidity or basicity of a solution.
The formula to calculate pH is: pH = -log[H+]
Since hydrochloric acid is a strong acid, it dissociates completely, and the concentration of H+ ions is equal to the concentration of the hydrochloric acid solution. Therefore:
[H+] = 0.01 M
Using the formula, we find:
pH = -log(0.01) = -(-2) = 2
Thus, the pH of the final solution is 2.
To determine the pH of the final solution, we need to calculate the concentration of the resulting acid solution after the dilution. Here's how you can do it step by step:
1. Find the moles of hydrochloric acid initially present:
Concentration of hydrochloric acid = 0.1 mol/L
Volume of hydrochloric acid solution = 10 mL = 10/1000 L = 0.01 L
Moles of hydrochloric acid = Concentration × Volume = 0.1 mol/L × 0.01 L = 0.001 mol
2. Determine the volume of the final solution:
The volume of pure water added = 90 mL = 90/1000 L = 0.09 L
Volume of the final solution = Volume of hydrochloric acid + Volume of water = 0.01 L + 0.09 L = 0.1 L
3. Calculate the new concentration of hydrochloric acid in the final solution by dividing the moles of the acid by the volume of the solution:
Concentration of the final solution = Moles of hydrochloric acid / Volume of the final solution
Concentration = 0.001 mol / 0.1 L = 0.01 mol/L
4. Convert the concentration to pH:
pH = -log[H+]
Since hydrochloric acid (HCl) is a strong acid and fully dissociates in water, the concentration of [H+] ions is equal to the concentration of hydrochloric acid.
pH = -log(0.01) = 2
Therefore, the pH of the final solution is 2.