Question

put the following compounds in order of decreasing expected lattice energy. ga2s3, cas, alp, cacl2

Explanation:

Step1: Recall lattice - energy formula and factors

Lattice energy ($U$) is given by $U=\frac{kQ_1Q_2}{r}$, where $k$ is a constant, $Q_1$ and $Q_2$ are the charges of the ions, and $r$ is the distance between the ions. Lattice energy is directly proportional to the product of ion - charges and inversely proportional to the ionic radius.

Step2: Determine ion - charges of each compound

• In $Ga_2S_3$, $Ga^{3 +}$ and $S^{2-}$, so $Q_1Q_2=(3)\times(2) = 6$.
• In $CaS$, $Ca^{2+}$ and $S^{2-}$, so $Q_1Q_2=(2)\times(2)=4$.
• In $AlP$, $Al^{3+}$ and $P^{3 -}$, so $Q_1Q_2=(3)\times(3)=9$.
• In $CaCl_2$, $Ca^{2+}$ and $Cl^{-}$, so $Q_1Q_2=(2)\times(1)=2$.

Step3: Consider ionic radii

For ions with the same charge, the ionic radius affects the lattice energy. But the effect of ion - charge product is more significant in this case.

Step4: Rank the compounds

Based on the ion - charge product, the order of decreasing lattice energy is: $AlP>Ga_2S_3>CaS>CaCl_2$.

Answer:

1. $AlP$
2. $Ga_2S_3$
3. $CaS$
4. $CaCl_2$