is [Ag(NH3)2]+

[Mn(CN)6]3-
[CrCl3(H2O)3]

are any of these colorless?

See below.

To determine whether any of these complexes are colorless, we need to consider the central metal ion and the ligands surrounding it. The color of a coordination complex depends on various factors such as the electronic structure of the metal ion and the nature of ligands.

Let's analyze each complex:

1. [Ag(NH3)2]+ (silver diammine ion):
The central metal ion is Ag+, which typically forms complexes that are colorless. In this case, the ligands are ammonia (NH3), which are also colorless. So, [Ag(NH3)2]+ is likely to be colorless.

2. [Mn(CN)6]3- (hexacyanomanganate):
The central metal ion is Mn^3+, which has an electronic configuration that can absorb light in the visible region of the electromagnetic spectrum. Hence, complexes with Mn^3+ ions often exhibit color. In this case, the ligands are cyanide ions (CN-), which are generally colorless. However, due to the presence of the Mn^3+ ion, [Mn(CN)6]3- is expected to have a color.

3. [CrCl3(H2O)3] (trichloroaquachromium):
The central metal ion is Cr^3+, which also has an electronic structure capable of absorbing light in the visible region. Therefore, complexes with Cr^3+ ions usually show color. The ligands in this compound include chloride ions (Cl-) and water molecules (H2O), which are both colorless. However, the presence of Cr^3+ suggests that [CrCl3(H2O)3] is likely to be colored.

In summary, based on the electronic structure of the central metal ions and the ligands involved, it is expected that [Ag(NH3)2]+ is colorless, while [Mn(CN)6]3- and [CrCl3(H2O)3] are likely colored.