Question

the ph readings for wines vary from 3.2 to 4.2. find the corresponding range of hydrogen ion concentrations.
6.31 × 10⁻⁵ ≤ h⁺ ≤ 6.31 × 10⁻⁴
4.2 × 10⁻⁵ ≤ h⁺ ≤ 3.2 × 10⁻⁴
6.31 × 10⁻¹⁰ ≤ h⁺ ≤ 6.31 × 10⁻⁹
4.2 × 10⁻¹⁰ ≤ h⁺ ≤ 3.2 × 10⁻⁹
none of these

Explanation:

Step1: Recall pH formula

The formula relating pH and hydrogen ion concentration \([H^+]\) is \(pH = -\log_{10}[H^+]\), which can be rearranged to \([H^+]=10^{-pH}\).

Step2: Calculate for pH = 3.2

Substitute \(pH = 3.2\) into the formula: \([H^+]=10^{-3.2}\). Using a calculator, \(10^{-3.2}\approx6.31\times 10^{-4}\).

Step3: Calculate for pH = 4.2

Substitute \(pH = 4.2\) into the formula: \([H^+]=10^{-4.2}\). Using a calculator, \(10^{-4.2}\approx6.31\times 10^{-5}\).

Step4: Determine the range

Since a lower pH means a higher hydrogen ion concentration, the range of \([H^+]\) when pH is from 3.2 to 4.2 is \(6.31\times 10^{-5}\leq[H^+]\leq6.31\times 10^{-4}\).

Answer:

\(6.31\times 10^{-5}\leq[H^+]\leq6.31\times 10^{-4}\) (the first option)