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My textbook represents the copper ion as "tetraaminecopper(II) sulfate-1-water", so I assumed that this complex ion has only 1 water of crystallization.
Then, in the Wikipedia article, they represent the ion as $\ce{[Cu(NH3)4(H2O)_n]SO4}$. The same formula is used but the number of water of crystallization is variable, denoted by $n$. So $n$ must have a range of values.
My question is what determines the value of $n$? What condition would cause $n$ to be larger or lower?
Tetraamminecopper(II) Sulfate or cuprammonium sulfate can be synthesized as its monohydrate (Ref.1):
A solution of $\pu{50 g}$ of finely divided $\ce{CuSO4 . 5 H2O}$ in $\pu{75 mL}$ of conc. ammonia and $\pu{50 mL}$ of water is filtered and precipitated by slow addition of $\pu{75 mL}$ of alcohol. After standing for several hours in the cold, the crystals are filtered on a Büchner funnel, washed with a mixture of alcohol and conc. ammonia (1:1) and then with alcohol and ether, and dried by suction.
$$\ce{CuSO4.5H2O + 4NH3 -> [Cu(NH3)4]SO4.H2O + 4H2O}$$
The properties of tetraamminecopper(II) Sulfate monohydrate is listed as follows (Ref.1):
Deep blue crystals, $\mathrm{d}^{20}_4$: 1.81. Solubility ($\pu{21.5 ^{\circ}C}$): $\pu{18.5 g} / \pu{100 g}\: \ce{H2O}$. Decomposes in air. Loses $\ce{H2O}$ and $\ce{2NH3}$ on heating to $\pu{120 ^{\circ}C}$; the remaining ammonia is evolved at $\pu{160 ^{\circ}C}$.
The crystallographic study of tetraamminecopper(II) Sulfate monohydrate was done several times, and most recently by Mazzi (Ref.2). In the abstract of Ref.1, the author states that:
$\ce{Cu(NH3)4SO4.H2O}$ is orthorhombie, $Pmcn-D^{16}_{2h}$, with four molecules in the unit cell. The determination of the structure was carried out by means of Patterson and Fourier projections on $(001)$ and $(100)$. The structure consists in layers parallel to $(010)$ formed by $\ce{Cu(NH3)4}$ squares and $\ce{SO4}$ tetrahedra held together by $\ce{H2O}$ molecules. Copper atoms, which lie on symmetry planes, have four nearest $\ce{NH3}$ neighbours ($\ce{Cu-N} = \pu{2.04-2.06 Å}$) and two more $\ce{H2O}$ neighbours ($\ce{Cu-O} = \pu{2.59-3.37 Å}$), which complete the distorted octahedral co-ordination group. Each $\ce{SO4}$ tetrahedron ($\ce{S-O} = \pu{1.40-1.43-1.46 Å}$) has two oxygen atoms linked with hydrogen bonds to adjacent $\ce{H2O}$ molecules ($\ce{OH...O} = \pu{2.67 Å}$).
All of these data directed to the comment of @andselisk who states that tetraamminecopper(II) sulfate is a monohydrate but, Probably why Wikipeda article suggesting it as $\ce{[Cu(NH3)4(H2O)n]SO4}$ that this compound may be hygroscopic, and thus, its water content may deviate (or vary). The crystal structure has confirmed it is a monohydrate.
References:
