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Chapter 47: Problem 5

Describe how to determine the value of \(K_{\mathrm{b}}\) for a base-given the value of \(K_{\mathrm{a}}\) for its conjugate acid.

Short Answer

Expert verified
Firstly, understand that \(K_{a} \ imes K_{b} = K_{w}\). Then calculate \(K_{b}\) using the equation \(K_{b} = \frac{K_{w}}{K_{a}}\). Use the known \(K_{w}\) value (typically, \(1.0 \ imes 10^{-14}\) at room temperature, 25掳C) and the given \(K_{a}\) value. The result is the value of \(K_{b}\).

Step by step solution

01

Understand the relationship between \(K_{a}\), \(K_{b}\), and \(K_{w}\)

The ion constant of water (\(K_{w}\)) is always equal to the product of the acid ionization constant (\(K_{a}\)) and the base ionization constant (\(K_{b}\)). The equilibrium relationship can be written as: \(K_{w} = K_{a} \ imes K_{b}\)
02

Calculate \(K_{b}\)

Since \(K_{w} = K_{a} \ imes K_{b}\), we can solve for \(K_{b}\) to find: \(K_{b} = \frac{K_{w}}{K_{a}}\). Now, plug in the given value of \(K_{a}\) and the known value of \(K_{w}\) at a given temperature to find the value of \(K_{b}\). The most common value for \(K_{w}\) at room temperature (25 degrees Celsius) is \(1.0 \ imes 10^{-14}\).
03

Verify the magnitude and units of \(K_{b}\)

Depending on the given \(K_{a}\) value and the known \(K_{w}\) value, calculate the \(K_{b}\) value. Make sure the obtained value of \(K_{b}\) is sensible and that the units are correctly expressed (or unitless, as the case may be).

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Most popular questions from this chapter

Which of the following ions are potential bases: \(\mathrm{Fe}^{3+} ; \mathrm{NH}_{4}^{+} ; \mathrm{F}^{-} ?\)

Which of the following ions are potential acids: \(\mathrm{Al}^{3+} ; \mathrm{CH}_{3} \mathrm{NH}_{3}^{+} ; \mathrm{HPO}_{4}^{2-} ; \mathrm{F}^{-}\) \(\mathrm{C} \mathrm{H}_{3}^{-} ?\)

Explain why the conjugate bases of the strong acids do not produce basic solutions when dissolved in water.

Consider two acids, HA and HX, with HA being a stronger acid than HX. a) Which acid has a larger value of \(K_{\mathrm{a}}\) ? b) Which conjugate base, \(\mathrm{A}^{-}\) or \(\mathrm{X}^{-}\), has a larger value of \(\mathrm{K}_{\mathrm{b}}\) ? c) Provide a qualitative description of the relationship between the relative strength of an acid and the relative strength of its conjugate base.

The chloride ion is the conjugate base of hydrochloric acid. Explain why \(\mathrm{Cl}^{-}\) does not produce a basic solution when dissolved in water.
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