Using the provided data for the rainfall sample, estimate the molar concentration of H+ in the rainfall assuming that H+ and OH− are the only two species present that are not liste... Using the provided data for the rainfall sample, estimate the molar concentration of H+ in the rainfall assuming that H+ and OH− are the only two species present that are not listed. Determine the activity coefficient for H+ based on the calculated ionic strength, and compare the calculated pH value to that measured by the electrode. Read more

Steps to Solve

1. Calculate Molar Concentration of H⁺ Ions

To find the molar concentration of H⁺ ions, we can use the given concentration of soluble ions in the rainfall sample. If the concentration of H⁺ is given directly or can be inferred from the composition, we can state it as: $$ [H^+] = \text{Concentration of H^+ in the sample (mol/L)} $$

2. Calculate Ionic Strength (I)

The ionic strength is calculated using the formula: $$ I = \frac{1}{2} \sum c_i z_i^2 $$ where $c_i$ is the concentration of each ion and $z_i$ is the charge of each ion. Sum the contributions from all ions in the sample.

3. Estimate Activity Coefficient for H⁺

Use the Debye-Hückel equation to estimate the activity coefficient ($\gamma_{H^+}$): $$ \log \gamma = \frac{-A z^2 \sqrt{I}}{1 + B a \sqrt{I} } $$ where:

• $A$ and $B$ are constants depending on the temperature and solvent
• $z$ is the charge of the ion ($z = +1$ for H⁺)
• $I$ is ionic strength
• $a$ is the effective diameter of the ion in nanometers

4. Calculate pH from Molar Concentration

Finally, calculate the pH using the relationship: $$ \text{pH} = -\log [H^+] $$

5. Compare Calculated pH to Measured pH

Compare the calculated pH to the measured pH value from the sample.

• If they are close, your calculations are likely correct. If not, review the previous steps for any errors.