Question

which has a higher lattic energy? mgo mgcl₂

Explanation:

Step1: Recall lattice - energy formula

Lattice energy is related to the charges of ions ($q_1$ and $q_2$) and the distance between them ($r$) by Coulomb's law. The formula for lattice energy $U=\frac{kq_1q_2}{r}$, where $k$ is a constant.

Step2: Analyze ion charges in MgO and MgCl₂

In MgO, $Mg^{2 +}$ and $O^{2-}$ have charges of + 2 and - 2 respectively. In $MgCl_2$, $Mg^{2+}$ has a charge of + 2 and $Cl^-$ has a charge of - 1. The product of charges $q_1q_2$ for MgO is $(+2)\times(-2)= - 4$, and for $MgCl_2$ is $(+2)\times(-1)\times2=-4$ (but considering one $Mg^{2+}$ and two $Cl^-$).

Step3: Analyze ion - size and distance

The size of $O^{2-}$ is smaller than that of $Cl^-$. Since $r$ (distance between ions) is smaller in MgO (because $O^{2-}$ is smaller than $Cl^-$), and $U=\frac{kq_1q_2}{r}$, with $q_1q_2$ being of the same magnitude in both cases, a smaller $r$ leads to a higher lattice energy.

Answer:

MgO