Question

Calculate the hydrogen ion concentration, in moles per liter, for solutions with each of the following pH values. a. \(\mathrm{pH}=8.34\) b. \(\mathrm{pH}=5.90\) c. \(\mathrm{pH}=2.65\) d. \(\mathrm{pH}=12.6\)

Short answer

Using the formula \( [\mathrm{H^+}] = 10^{-\mathrm{pH}}\), we find the hydrogen ion concentrations: a. \(4.57 \times 10^{-9}\) M b. \(1.26 \times 10^{-6}\) M c. \(0.0022\) M d. \(2.51 \times 10^{-13}\) M

Step-by-step solution

Applying the formula to find ion concentration from pH

Plug the given pH values into the equation \( [\mathrm{H^+}] = 10^{-\mathrm{pH}} \) to calculate the corresponding hydrogen ion concentrations. a. \[\mathrm{pH} = 8.34\] Substituting this into our formula gives: \[ [\mathrm{H^+}] = 10^{-8.34}\] This yields a Hydrogen ion concentration of approximately \(4.57 \times 10^{-9}\) M b. \[\mathrm{pH} = 5.90\] Substituting this into our formula gives: \[ [\mathrm{H^+}] = 10^{-5.90}\] This yields a Hydrogen ion concentration of approximately \(1.26 \times 10^{-6}\) M c. \[\mathrm{pH} = 2.65\] Substituting this into our formula gives: \[ [\mathrm{H^+}] = 10^{-2.65}\] This yields a Hydrogen ion concentration of approximately \(0.0022\) M d. \[\mathrm{pH} = 12.60\] Substituting this into our formula gives: \[ [\mathrm{H^+}] = 10^{-12.6}\] This yields a Hydrogen ion concentration of approximately \(2.51 \times 10^{-13}\) M

Interpretation of the results

The Hydrogen ion concentration results show that solutions with lower pH values have higher Hydrogen ion concentrations. Conversely, solutions with higher pH values have lower Hydrogen ion concentrations. Hence, we can conclude that there is an inverse relationship between pH and [\(\mathrm{H^+}\)]. The more acidic a solution is, the higher its hydrogen ion concentration will be.