To find the value of the base dissociation constant (Kb) for the weak base, we follow these steps:
1. Determine pOH from pH:
- Recall the relationship between pH and pOH:
[tex]\[
\text{pH} + \text{pOH} = 14
\][/tex]
- Given that the pH = 10.30, we can find the pOH by rearranging the equation:
[tex]\[
\text{pOH} = 14 - \text{pH} = 14 - 10.30 = 3.70
\][/tex]
2. Find the concentration of OH⁻ ions:
- pOH is related to the hydroxide ion concentration [tex]\([\text{OH}^-]\)[/tex] by the formula:
[tex]\[
[\text{OH}^-] = 10^{-\text{pOH}}
\][/tex]
- Substituting the calculated pOH value:
[tex]\[
[\text{OH}^-] = 10^{-3.70} \approx 0.0001995 \, \text{M}
\][/tex]
3. Use the concentration of OH⁻ ions to find [tex]\( K_b \)[/tex]:
- For a weak base, the dissociation in water can be represented as:
[tex]\[
\text{B} + \text{H}_2\text{O} \leftrightharpoons \text{BH}^+ + \text{OH}^-
\][/tex]
Where [tex]\([ \text{OH}^- ]\)[/tex] is the concentration of hydroxide ions at equilibrium.
- The expression for [tex]\( K_b \)[/tex] (base dissociation constant) is given by:
[tex]\[
K_b = \frac{[\text{OH}^-]^2}{[\text{Base}]}
\][/tex]
- Substituting the known concentrations into the formula:
[tex]\[
K_b = \frac{(0.0001995)^2}{0.12} \approx 3.32 \times 10^{-7}
\][/tex]
Thus, the value of the base dissociation constant [tex]\( K_b \)[/tex] for this weak base is approximately [tex]\( 3.32 \times 10^{-7} \)[/tex].
