Which one of the following reactions is a redox reaction? d) BaCl2(aq) + MgSO4(aq) → MgCl2(aq) + BaSO4(s)

The given reaction is:

• In $\text{BaCl}_{2}$: $\text{Ba}$ is an alkaline earth metal, so its oxidation state is $+2$. $\text{Cl}$ is a halogen, typically $-1$.
• In $\text{MgSO}_{4}$: $\text{Mg}$ is an alkaline earth metal, so its oxidation state is $+2$. Oxygen is typically $-2$. For the sulfate ion ($\text{SO}_{4}^{2-}$), the overall charge is $-2$. Thus, $\text{S} + 4(-2) = -2$, which means $\text{S} - 8 = -2$, so $\text{S} = +6$.

• In $\text{MgCl}_{2}$: $\text{Mg}$ is $+2$. $\text{Cl}$ is $-1$.
• In $\text{BaSO}_{4}$: $\text{Ba}$ is $+2$. Oxygen is $-2$. For the sulfate ion ($\text{SO}_{4}^{2-}$), $\text{S}$ is $+6$.

• $\text{Ba}$: $+2$ (in $\text{BaCl}_{2}$) $\rightarrow +2$ (in $\text{BaSO}_{4}$) - No change.
• $\text{Cl}$: $-1$ (in $\text{BaCl}_{2}$) $\rightarrow -1$ (in $\text{MgCl}_{2}$) - No change.
• $\text{Mg}$: $+2$ (in $\text{MgSO}_{4}$) $\rightarrow +2$ (in $\text{MgCl}_{2}$) - No change.
• $\text{S}$: $+6$ (in $\text{MgSO}_{4}$) $\rightarrow +6$ (in $\text{BaSO}_{4}$) - No change.
• $\text{O}$: $-2$ (in $\text{MgSO}_{4}$) $\rightarrow -2$ (in $\text{BaSO}_{4}$) - No change.

Since the oxidation states of all elements remain unchanged throughout the reaction, reaction (d) is not a redox reaction. It is a double displacement precipitation reaction.