1. **State the problem:** Find the concentration of hydrogen ions (H⁺) in moles per liter when the pH of the liquid is 8.23. 2. **Recall the formula:** The relationship between pH and hydrogen ion concentration is given by: $$\text{pH} = -\log[H^+]$$ which can be rearranged to find $[H^+]$: $$[H^+] = 10^{-\text{pH}}$$ 3. **Substitute the given pH value:** $$[H^+] = 10^{-8.23}$$ 4. **Calculate the concentration:** Using a calculator or logarithm tables, $$10^{-8.23} = 10^{-8} \times 10^{-0.23}$$ 5. **Evaluate $10^{-0.23}$:** $$10^{-0.23} = \frac{1}{10^{0.23}} \approx \frac{1}{1.698} \approx 0.589$$ 6. **Multiply:** $$[H^+] = 10^{-8} \times 0.589 = 0.589 \times 10^{-8} = 5.89 \times 10^{-9}$$ **Final answer:** The concentration of hydrogen ions is $$[H^+] = 5.89 \times 10^{-9} \text{ moles per liter}$$