Difference between revisions of "Boiling-point elevation"
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==Description== | ==Description== | ||
| − | The boiling-point elevation Δ''T''<sub>b</sub> is proportional to the [[molality]] of the solution ''m'': the proportionality constant is called the '''ebullioscopic constant''' ''K''<sub> | + | {| class="wikitable" align=right |
| − | :Δ''T''<sub>b</sub> = ''K''<sub> | + | |- |
| + | ! Solvent | ||
| + | ! ''K''<sub>b</sub><br/>{{overline|K kg mol<sup>−1</sup>}} | ||
| + | |- | ||
| + | | [[Acetic acid]] || align=center | 3.07 | ||
| + | |- | ||
| + | | [[Acetone]] || align=center | 1.71 | ||
| + | |- | ||
| + | | [[Aniline]] || align=center | 3.22 | ||
| + | |- | ||
| + | | [[Benzene]] || align=center | 2.53 | ||
| + | |- | ||
| + | | [[Carbon disulfide]] || align=center | 2.37 | ||
| + | |- | ||
| + | | [[Chloroform]] || align=center | 3.66 | ||
| + | |- | ||
| + | | [[Cyclohexane]] || align=center | 2.79 | ||
| + | |- | ||
| + | | [[Diethyl ether]] || align=center | 1.82 | ||
| + | |- | ||
| + | | [[Nitrobenzene]] || align=center | 5.26 | ||
| + | |- | ||
| + | | [[Tetrachloromethane]] || align=center | 4.95 | ||
| + | |- | ||
| + | | [[Water]] || align=center | 0.51 | ||
| + | |- | ||
| + | |} | ||
| + | The boiling-point elevation Δ''T''<sub>b</sub> is proportional to the [[molality]] of the solution ''m'': the proportionality constant is called the '''ebullioscopic constant''' ''K''<sub>b</sub>. | ||
| + | :Δ''T''<sub>b</sub> = ''K''<sub>b</sub>''m'' | ||
The molality of the solution is the amount of solute divided by the mass of solvent. For dilute solutions, where the mass of the solution can be approximated by the mass of solvent, the molality is equal to the [[mass fraction]] ''w'' of solute divided by its [[molar mass]] ''M''.<ref group="Note">In formal terms, ''w'' = ''m''<sub>2</sub>/(''m''<sub>1</sub>+''m''<sub>2</sub>) ≈ ''m''<sub>2</sub>/''m''<sub>1</sub> if ''m''<sub>2</sub> ≪ ''m''<sub>1</sub> (here, ''m''<sub>2</sub> is the mass of solute and ''m''<sub>1</sub> is the mass of solvent).</ref> Hence, the molar mass of a solute can be calculated from the boiling-point elevation by | The molality of the solution is the amount of solute divided by the mass of solvent. For dilute solutions, where the mass of the solution can be approximated by the mass of solvent, the molality is equal to the [[mass fraction]] ''w'' of solute divided by its [[molar mass]] ''M''.<ref group="Note">In formal terms, ''w'' = ''m''<sub>2</sub>/(''m''<sub>1</sub>+''m''<sub>2</sub>) ≈ ''m''<sub>2</sub>/''m''<sub>1</sub> if ''m''<sub>2</sub> ≪ ''m''<sub>1</sub> (here, ''m''<sub>2</sub> is the mass of solute and ''m''<sub>1</sub> is the mass of solvent).</ref> Hence, the molar mass of a solute can be calculated from the boiling-point elevation by | ||
| − | :''M'' = ''K''<sub> | + | :''M'' = ''K''<sub>b</sub>''w''/Δ''T''<sub>b</sub> |
The same phenomenon can be described in terms of [[vapour pressure]] for any given temperature. If ''p''<sub>0</sub> is the vapour pressure of the pure solvent and ''p'' is the vapour pressure of the solution: | The same phenomenon can be described in terms of [[vapour pressure]] for any given temperature. If ''p''<sub>0</sub> is the vapour pressure of the pure solvent and ''p'' is the vapour pressure of the solution: | ||
Revision as of 11:27, 27 March 2011
Boiling-point elevation is the increase in temperature of the boiling point of a liquid that contains non-volatile solute. It is a colligative property: for dilute solutions of non-electrolytes, the difference in boiling point from that of the pure solvent is proportional to the amount of solute.
Ebullioscopy is the experimental technique that uses boiling-point elevation to measure the molecular weight of compounds. Tonometry is a related technique that directly measures the reduction in vapour pressure of the solution compared to that of the pure solvent. Both techniques are of historical interest only, although their development led to the formulation of Raoult's law.
Description
| Solvent | Kb K kg mol−1 |
|---|---|
| Acetic acid | 3.07 |
| Acetone | 1.71 |
| Aniline | 3.22 |
| Benzene | 2.53 |
| Carbon disulfide | 2.37 |
| Chloroform | 3.66 |
| Cyclohexane | 2.79 |
| Diethyl ether | 1.82 |
| Nitrobenzene | 5.26 |
| Tetrachloromethane | 4.95 |
| Water | 0.51 |
The boiling-point elevation ΔTb is proportional to the molality of the solution m: the proportionality constant is called the ebullioscopic constant Kb.
- ΔTb = Kbm
The molality of the solution is the amount of solute divided by the mass of solvent. For dilute solutions, where the mass of the solution can be approximated by the mass of solvent, the molality is equal to the mass fraction w of solute divided by its molar mass M.[Note 1] Hence, the molar mass of a solute can be calculated from the boiling-point elevation by
- M = Kbw/ΔTb
The same phenomenon can be described in terms of vapour pressure for any given temperature. If p0 is the vapour pressure of the pure solvent and p is the vapour pressure of the solution:
- (p0 − p)/p0 = K′Rm
where K′R is a constant that is specific for each solvent and m is the molality of the solution. French physical chemist François-Marie Raoult (1830–1901) investigated this relation in the 1880s, and found in 1887[1] that a single constant (KR) for all solvents could be obtained by replacing the molality with the amount fraction of solute x, that is by dividing the molality by the molar mass of the solvent:[Note 2]
- (p0 − p)/p0 = KRx
where KR ≈ 1 (Raoult found a value of 1.05).
Both of these descriptions only apply for dilute solutions. They also break down if the solute dissociates (e.g. electrolytes) or associates (e.g. acetic acid in non-polar solvents) in solution.
Derivation
See also
Notes and references
Notes
References
- ↑ Raoult, F.-M. Loi générale des tensions de vapeur des dissolvants. C. R. Hebd. Seances Acad. Sci. 1887, 104, 1430–33, <http://gallica.bnf.fr/ark:/12148/bpt6k30607.image.f1429.langEN>. English translation
External links
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See also the corresponding article on Wikipedia. |
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