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When we react beryllium hydroxide with acid we have an acid base reaction resulting in a salt and a water molecule. Similarly when we react it with base it results in formation of a salt. Most sources cannot provide me with the actual reason but instead state its amphoteric because it tends to react with acids and bases both. thats not a satisfying answer.

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Beryllium ion in solution exist as $\ce{Be(H2O)4^2+}$. The small positively charged beryllium ion at the centre of the complex pulls electrons in the water molecules towards itself (strong polarizing effect on the water molecules).

Now, when we say "beryllium hydroxide", it is not structurally a cationic-anionic salt. It is actually a neutral complex which is covalently bonded. It is formulated as $\ce{Be(H2O)2(OH)2}$.

Adding sodium hydroxide initiates proton loss from the water molecules in the complex and you get the sodium salt product, sodium tetraberyllate.

$$\ce{Be(H2O)2(OH)2 + OH- -> [Be(OH)4]^2- + 2H2O}$$

Now, conversely when you add acid (say hydrogen chloride), you get a beryllium salt which contains the beryllium ion $\ce{Be(H2O)4^2+}$.

$$\ce{Be(H2O)2(OH)2 ->[H+] Be(H2O)4^2+}$$

This is how beryllium hydroxide exhibit amphoterism. Now the question arises, why can't other group 2 hydroxide exhibit amphoterism? The reason is that the other hydroxides are purely ionic and contains only hydroxide ions, $\ce{OH-}$. These react with hydrogen ions from an acid to form water and so the hydroxide reacts with acids. There isn't any equivalent to the neutral complex. Adding more hydroxide ions from a base has no effect because they haven't got anything to react with.

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    $\begingroup$ What you tell may be a convincing "lie for students" but $\ce{Be(OH)2}$ isn't an aquo complex or even hydrate and is almost insoluble in water. It has significant ionic component. In general it's not much different then Mg(OH)2. It's just that $\ce{[Be(OH)4]^2-}$ isn't basic enough to make its creation in aqueous base impossible. $\endgroup$
    – Mithoron
    Jul 17 '21 at 13:11
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Don't get hung up on the distinction between "basic" and "amphoteric" metal hydroxides. The difference between beryllium hydroxide and "basic" metal hydroxides like magnesium hydroxide is less than meets the eye; under the right conditions just about any metal hydroxide can act as as acid, even sodium hydroxide[1]:

Sodium amide, NaNH2, has recently been shown to be a useful catalyst to decompose NH3 into H2 and N2, however, sodium hydroxide is omnipresent and commercially available NaNH2 usually contains impurities of NaOH (<2%). The thermal decomposition of NaNH2 and NaNH2–NaOH composites is systematically investigated and discussed. ... We report that 0.36 mol of NH3 per mol of NaNH2 is released below 400 °C during heating in an argon atmosphere, initiated at its melting point, T = 200 °C, possibly due to the formation of the mixed sodium amide imide solid solution. Furthermore, NaOH reacts with NaNH2 at elevated temperatures and provides the release of additional NH3. [emphasis added]

Reference

1. Lars H. Jepsen, Peikun Wang, Guotao Wu, Zhitao Xiong, Flemming Besenbacher, Ping Chen and Torben R. Jense; "Thermal decomposition of sodium amide, NaNH2, and sodium amide hydroxide composites, NaNH2–NaOH", Phys. Chem. Chem. Phys., 2016, 18, 25257-25264. https://doi.org/10.1039/C6CP01604A

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