A Coordination compound is represented by the formula $[\mathrm{CoBr}_3(e n) x]$. This compound required one mole of $\mathrm{AgNO}_3$ to form a pale yellow precipitate of $\mathrm{AgBr}$. What is the value of $\mathrm{x}$ in the compound?

The coordination compound is given as $[CoBr_3(en)x]$. The reaction with $AgNO_3$ produces a pale yellow precipitate of $AgBr$, which indicates that one bromide ion is present outside the coordination sphere as a counter ion.

The reaction can be represented as $[CoBr_2(en)x]Br + AgNO_3 \rightarrow [CoBr_2(en)x]NO_3 + AgBr(s)$.

The coordination number of Cobalt(III) in such complexes is typically 6. The ethylenediamine (en) ligand is bidentate, occupying 2 coordination sites. Let the number of bromide ions inside the coordination sphere be $y$. Then the total coordination number is $2(en) + y(Br) = 6$.

Since there are 3 bromide ions in total and 1 is outside, $y = 2$. Thus, $2(en) + 2(Br) = 6$, which implies $2(2) + 2 = 6$. This is consistent with the coordination number of 6.

The formula is $[CoBr_2(en)x]Br$. Comparing this with the given formula $[CoBr_3(en)x]$, we see that $x$ represents the number of ethylenediamine ligands. Since $2(en)$ is required to satisfy the coordination number, $x = 2$.

Answer: 2