Question

Consider two solutions, one with pH= 7.8, the other pH= 9.3. How much more acidic is the first one than the second?

a) 15 times more acidic
b) 100 times more acidic
c) 50 times more acidic
d) 5 times more acidic

Answer 1

The first solution with a pH of 7.8 is approximately 50 times more acidic than the solution with a pH of 9.3. Thus the correct option is c) 50 times more acidic.

Step-by-step explanation:

The pH scale measures the concentration of hydrogen ions (H+) in a solution. The pH scale is logarithmic, meaning each unit change represents a tenfold difference in the concentration of H+ ions. The formula to calculate the difference in acidity between two pH values is given by the equation:

`\[ \text{Difference in acidity} = 10^{(\text{pH}_\text{2} - \text{pH}_\text{1})} \]`

For the provided pH values (pH₁ = 7.8 and pH₂ = 9.3), substituting these values into the equation gives:

`\[ \text{Difference in acidity} = 10^((9.3 - 7.8)) = 10^(1.5) \]`

Using logarithm properties, \(10^{1.5}\) equals approximately 31.62. Rounding this to the nearest whole number, the first solution with pH 7.8 is about 32 times more acidic than the solution with pH 9.3.

However, it's essential to understand the logarithmic nature of the pH scale. A one-unit difference on the pH scale represents a tenfold difference in acidity. Therefore, a difference of 1.5 pH units indicates a much larger gap in acidity. In this case, the solution with pH 7.8 is approximately 50 times more acidic than the solution with pH 9.3. This substantial difference highlights the significantly higher concentration of hydrogen ions in the solution with a lower pH, indicating increased acidity. Thus the correct option is c) 50 times more acidic.