Answer :
Sure! Let's go through a detailed, step-by-step explanation of the solution for the given serial dilution problem:
1. Understanding pH and Serial Dilution:
- The pH of a solution is a measure of its acidity or alkalinity, calculated as the negative logarithm (base 10) of the hydrogen ion concentration [tex]\([\text{H}^+]\)[/tex].
- A lower pH means higher acidity and a higher [tex]\([\text{H}^+]\)[/tex] concentration.
- In a serial dilution, each dilution typically reduces the concentration of [tex]\([\text{H}^+]\)[/tex] by a factor of 10, which increases the pH by 1 unit.
2. Initial Conditions:
- Beaker #1 has a pH of 2.
3. Predicting the pH for Beaker #2:
- After a serial dilution, Beaker #2's pH will increase by 1 unit.
- Therefore, the pH of Beaker #2 is 3.
4. Predicting the pH for Beaker #3:
- Beaker #3 undergoes another serial dilution similar to Beaker #2.
- This again increases the pH by 1 unit compared to Beaker #2.
- So, the pH of Beaker #3 is 4.
5. Calculating Concentration Difference:
- The hydrogen ion concentration [tex]\([\text{H}^+]\)[/tex] relationship with pH is given by [tex]\([\text{H}^+] = 10^{-\text{pH}}\)[/tex].
- Calculate [tex]\([\text{H}^+]\)[/tex] concentration for Beaker #1: [tex]\(10^{-2}\)[/tex].
- Calculate [tex]\([\text{H}^+]\)[/tex] concentration for Beaker #3: [tex]\(10^{-4}\)[/tex].
- To find how many times greater the concentration is in Beaker #1 compared to Beaker #3, divide the concentrations:
[tex]\[
\frac{10^{-2}}{10^{-4}} = 10^{4-2} = 10^2 = 100
\][/tex]
- Therefore, the concentration of [tex]\([\text{H}^+]\)[/tex] in Beaker #1 is 100 times greater than in Beaker #3.
Putting it all together, the predicted pH for Beaker #2 is 3, for Beaker #3 is 4, and the [tex]\([\text{H}^+]\)[/tex] concentration in Beaker #1 is 100 times greater than in Beaker #3.
1. Understanding pH and Serial Dilution:
- The pH of a solution is a measure of its acidity or alkalinity, calculated as the negative logarithm (base 10) of the hydrogen ion concentration [tex]\([\text{H}^+]\)[/tex].
- A lower pH means higher acidity and a higher [tex]\([\text{H}^+]\)[/tex] concentration.
- In a serial dilution, each dilution typically reduces the concentration of [tex]\([\text{H}^+]\)[/tex] by a factor of 10, which increases the pH by 1 unit.
2. Initial Conditions:
- Beaker #1 has a pH of 2.
3. Predicting the pH for Beaker #2:
- After a serial dilution, Beaker #2's pH will increase by 1 unit.
- Therefore, the pH of Beaker #2 is 3.
4. Predicting the pH for Beaker #3:
- Beaker #3 undergoes another serial dilution similar to Beaker #2.
- This again increases the pH by 1 unit compared to Beaker #2.
- So, the pH of Beaker #3 is 4.
5. Calculating Concentration Difference:
- The hydrogen ion concentration [tex]\([\text{H}^+]\)[/tex] relationship with pH is given by [tex]\([\text{H}^+] = 10^{-\text{pH}}\)[/tex].
- Calculate [tex]\([\text{H}^+]\)[/tex] concentration for Beaker #1: [tex]\(10^{-2}\)[/tex].
- Calculate [tex]\([\text{H}^+]\)[/tex] concentration for Beaker #3: [tex]\(10^{-4}\)[/tex].
- To find how many times greater the concentration is in Beaker #1 compared to Beaker #3, divide the concentrations:
[tex]\[
\frac{10^{-2}}{10^{-4}} = 10^{4-2} = 10^2 = 100
\][/tex]
- Therefore, the concentration of [tex]\([\text{H}^+]\)[/tex] in Beaker #1 is 100 times greater than in Beaker #3.
Putting it all together, the predicted pH for Beaker #2 is 3, for Beaker #3 is 4, and the [tex]\([\text{H}^+]\)[/tex] concentration in Beaker #1 is 100 times greater than in Beaker #3.
