1. **State the problem:** Find the concentration of hydrogen ions (H⁺) in moles per liter when the pH of the liquid is 3.97. 2. **Recall the formula:** pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration: $$\text{pH} = -\log_{10}[\text{H}^+]$$ 3. **Rearrange the formula to find** $[\text{H}^+]$: $$[\text{H}^+] = 10^{-\text{pH}}$$ 4. **Substitute the given pH value:** $$[\text{H}^+] = 10^{-3.97}$$ 5. **Calculate the value:** $$10^{-3.97} = 10^{-4 + 0.03} = 10^{-4} \times 10^{0.03}$$ 6. **Evaluate $10^{0.03}$ approximately:** Using the approximation $10^{0.03} \approx 1.0715$ 7. **Multiply:** $$[\text{H}^+] = 10^{-4} \times 1.0715 = 1.0715 \times 10^{-4}$$ 8. **Final answer:** The concentration of hydrogen ions is approximately $$[\text{H}^+] = 1.07 \times 10^{-4} \text{ moles per liter}$$