Question
The pH scale is a measure of the acidity of a solution. Its value is given by the formula:
\[ pH = -\log_{10}[H^+] \]
where \([H^+]\) is the concentration of hydrogen ions in the solution (measured in moles per litre).
(a) Calculate the pH value if the concentration of hydrogen ions is 0.0003.
The pH of milk is 6.6.
(b) Calculate the concentration of hydrogen ions in milk.
The strength of an acid is measured by its concentration of hydrogen ions.
A lemon has a pH value of 2 and a tomato has a pH value of 4.5.
(c) Calculate how many times stronger the acid in a lemon is when compared to the acid in a tomato.
▶️ Answer/Explanation
Detailed Solution
(a) Finding the pH Value
Using the given formula:
\[ pH = -\log_{10}(0.0003) \]
Using a calculator:
\[ pH = 3.52 \]
(b) Finding the Hydrogen Ion Concentration in Milk
We use the inverse logarithm to solve for \([H^+]\):
\[ [H^+] = 10^{-6.6} \]
Using a calculator:
\[ [H^+] = 2.51 \times 10^{-7} = 0.000000251 \text{ (moles per litre)} \]
(c) Comparing the Acidity of Lemon and Tomato
Using the inverse logarithm:
\[ \text{Lemon: } [H^+] = 10^{-2} = 0.01 \]
\[ \text{Tomato: } [H^+] = 10^{-4.5} = 0.0000316227… \]
Finding the ratio of acidity:
\[ \frac{10^{-2}}{10^{-4.5}} = \frac{0.01}{0.0000316227…} \]
Using a calculator:
\[ = 316.227… \approx 316 \]
Conclusion: The acid in a lemon is approximately 316 times stronger than the acid in a tomato.
……………………………Markscheme……………………………….
(a) pH value: 3.52
(b) Hydrogen ion concentration in milk: \( 2.51 \times 10^{-7} \) (or 0.000000251 moles per litre)
(c) Acid strength ratio (Lemon vs. Tomato): 316 times