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In chemistry, a weak base is a chemical base that does not ionize fully in an aqueous solution. As Bronsted-Lowry bases are proton acceptors, a weak base may also be defined as a chemical base in which protonation is incomplete. This results in a relatively low pH level compared to strong bases. Bases range from a pH of greater than 7 (7 is neutral, like pure water) to 14 (though some bases are greater than 14). The pH level has the formula:
_{2}O, and the remaining H^{+} concentration in the solution determines the pH level. Weak bases will have a higher H^{+} concentration because they are less completely protonated than stronger bases and, therefore, more hydrogen ions remain in the solution. If you plug in a higher H^{+} concentration into the formula, a low pH level results. However, the pH level of bases is usually calculated using the OH^{-} concentration to find the pOH level first. This is done because the H^{+} concentration is not a part of the reaction, while the OH^{-} concentration is.
## Percentage protonated

As seen above, the strength of a base depends primarily on the pH level. To help describe the strengths of weak bases, it is helpful to know the percentage protonated-the percentage of base molecules that have been protonated. A lower percentage will correspond with a lower pH level because both numbers result from the amount of protonation. A weak base is less protonated, leading to a lower pH and a lower percentage protonated.## A typical pH problem

## Examples

## See also

## References

## External links

- $mbox\{pH\}\; =\; -log\_\{10\}\; left[mbox\{H\}^+\; right]$

- $mbox\{pOH\}\; =\; -log\_\{10\}\; left[mbox\{OH\}^-\; right]$

By multiplying a conjugate acid (such as NH_{4}^{+}) and a conjugate base (such as NH_{3}) the following is given:

- $K\_a\; times\; K\_b\; =\; \{[H\_3O^+][NH\_3]over[NH\_4^+]\}\; times\; \{[NH\_4^+][OH^-]over[NH\_3]\}\; =\; [H\_3O^+][OH^-]$

Since $\{K\_w\}\; =\; [H\_3O^+][OH^-]$ then, $K\_a\; times\; K\_b\; =\; K\_w$

By taking logarithms of both sides of the equation, the following is reached:

- $logK\_a\; +\; logK\_b\; =\; logK\_w$

Finally, multipying throughout the equation by -1, the equation turns into:

- $pK\_a\; +\; pK\_b\; =\; pK\_w\; =\; 14.00$

After acquiring pOH from the previous pOH formula, pH can be calculated using the formula pH = pK_{w} - pOH where pK_{w} = 14.00.

Weak bases exist in chemical equilibrium much in the same way as weak acids do, with a Base Ionization Constant (K_{b}) (or the Base Dissociation Constant) indicating the strength of the base. For example, when ammonia is put in water, the following equilibrium is set up:

- $mathrm\{K\_b=\{[NH\_4^+][OH^-]over[NH\_3]\}\}$

Bases that have a large K_{b} will ionize more completely and are thus stronger bases. As stated above, the pH of the solution depends on the H^{+} concentration, which is related to the OH^{-} concentration by the Ionic Constant of water (K_{w} = 1.0x10^{-14}) (See article Self-ionization of water.) A strong base has a lower H^{+} concentration because they are fully protonated and less hydrogen ions remain in the solution. A lower H^{+} concentration also means a higher OH^{-} concentration and therefore, a larger K_{b}.

NaOH (s) (sodium hydroxide) is a stronger base than (CH_{3}CH_{2})_{2}NH (l) (diethylamine) which is a stronger base than NH_{3} (g) (ammonia). As the bases get weaker, the smaller the K_{b} values become. The pie-chart representation is as follows:

- purple areas represent the fraction of OH- ions formed
- red areas represent the cation remaining after ionization
- yellow areas represent dissolved but non-ionized molecules.

The typical proton transfer equilibrium appears as such:

- $B(aq)\; +\; H\_2O(l)\; leftrightarrow\; HB^+(aq)\; +\; OH^-(aq)$

B represents the base.

- $Percentage\; protonated\; =\; \{molarity\; of\; HB^+\; over\; initial\; molarity\; of\; B\}\; times\; 100\%\; =\; \{[\{HB\}^+]over\; [B]\_\{initial\}\}\; \{times\; 100\%\}$

In this formula, [B]_{initial} is the initial molar concentration of the base, assuming that no protonation has occurred.

Calculate the pH and percentage protonation of a .20 M aqueous solution of pyridine, C_{5}H_{5}N. The K_{b} for C_{5}H_{5}N is 1.8 x 10^{-9}.

First, write the proton transfer equilibrium:

- $mathrm\{H\_2O(l)\; +\; C\_5H\_5N(aq)\; leftrightarrow\; C\_5H\_5NH^+\; (aq)\; +\; OH^-\; (aq)\}$

- $K\_b=mathrm\{[C\_5H\_5NH^+][OH^-]over\; [C\_5H\_5N]\}$

The equilibrium table, with all concentrations in moles per liter, is

C_{5}H_{5}N
| C_{5}H_{6}N^{+}
| OH^{-} | |
---|---|---|---|

initial normality | .20 | 0 | 0 |

change in normality | -x | +x | +x |

equilibrium normality | .20 -x | x | x |

Substitute the equilibrium molarities into the basicity constant | $K\_b=mathrm\; \{1.8\; times\; 10^\{-9\}\}\; =\; \{x\; times\; x\; over\; .20-x\}$ |

We can assume that x is so small that it will be meaningless by the time we use significant figures. | $mathrm\; \{1.8\; times\; 10^\{-9\}\}\; approx\; \{x^2\; over\; .20\}$ |

Solve for x. | $mathrm\; x\; approx\; sqrt\{.20\; times\; (1.8\; times\; 10^\{-9\})\}\; =\; 1.9\; times\; 10^\{-5\}$ |

Check the assumption that x << .20 | $mathrm\; 1.9\; times\; 10^\{-5\}\; ll\; .20$; so the approximation is valid |

Find pOH from pOH = -log [OH^{-}] with [OH^{-}]=x
| $mathrm\; pOH\; approx\; -log(1.9\; times\; 10^\{-5\})\; =\; 4.7$ |

From pH = pK_{w} - pOH,
| $mathrm\; pH\; approx\; 14.00\; -\; 4.7\; =\; 9.3$ |

From the equation for percentage protonated with [HB^{+}] = x and [B]_{initial} = .20,
| $mathrm\; percentage\; protonated\; =\; \{1.9\; times\; 10^\{-5\}\; over\; .20\}\; times\; 100\%\; =\; .0095\%$ |

This means .0095% of the pyridine is in the protonated form of C_{5}H_{6}N^{+}.

- Alanine, C
_{3}H_{5}O_{2}NH_{2} - Ammonia, NH
_{3} - Methylamine, CH
_{3}NH_{2} - Pyridine, C
_{5}H_{5}N

Other weak bases are essentially any bases not on the list of strong bases.

- Atkins, Peter, and Loretta Jones. Chemical Principles: The Quest for Insight, 3rd Ed., New York: W.H. Freeman, 2005.

- http://wine1.sb.fsu.edu/chm1046/notes/AcidBase/WeakBase/WeakBase.htm
- http://www.chemguide.co.uk/physical/acidbaseeqia/bases.html
- http://bouman.chem.georgetown.edu/S02/lect16/lect16.htm
- http://www.intute.ac.uk/sciences/reference/plambeck/chem1/p01154.htm

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Last updated on Thursday May 15, 2008 at 22:01:17 PDT (GMT -0700)

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