Verified Answer :

  • Identify the reactants \(BaCl_2\) and \(MgSO_4\) as ionic compounds undergoing a double displacement reaction.
  • Determine the resulting ions: \(Ba^{2+}\), \(Cl^-\), \(Mg^{2+}\), and \(SO_4^{2-}\).
  • Pair the cations and anions to form the products: Barium sulfate (\(BaSO_4\)) and Magnesium chloride (\(MgCl_2\)).
  • Select the balanced reaction: \(BaCl_2 + MgSO_4 \rightarrow BaSO_4(s) + MgCl_2\).
  • Final Answer: \(\boxed{BaSO_4(s) + MgCl_2}\)

Explanation

  1. Identifying the Reaction Type

This chemical reaction involves two ionic compounds, Barium chloride (\(BaCl_2\)) and Magnesium sulfate (\(MgSO_4\)), reacting in an aqueous solution. This is a classic example of a double displacement (or metathesis) reaction. In such reactions, the cations and anions of the two reactants exchange partners to form new products. Specifically, the cation of the first reactant pairs with the anion of the second, and the cation of the second reactant pairs with the anion of the first.

  1. Determining the Ion Exchange

The reactants are composed of the following ions:

  • Barium chloride (\(BaCl_2\)) contains \(Ba^{2+}\) and \(Cl^-\) ions.
  • Magnesium sulfate (\(MgSO_4\)) contains \(Mg^{2+}\) and \(SO_4^{2-}\) ions.

According to the rules of double displacement, we exchange the cations:

  • The Barium ion (\(Ba^{2+}\)) will now pair with the Sulfate ion (\(SO_4^{2-}\)).
  • The Magnesium ion (\(Mg^{2+}\)) will now pair with the Chloride ion (\(Cl^-\)).
  1. Forming the Products and Balancing the Equation

Now, we form the new chemical compounds by combining the ions, ensuring the resulting compounds are electrically neutral:

  • Pairing \(Ba^{2+}\) with \(SO_4^{2-}\) gives Barium sulfate, with the chemical formula \(BaSO_4\). In aqueous reactions, this compound typically forms an insoluble solid, which we denote as \(BaSO_4(s)\).
  • Pairing \(Mg^{2+}\) with \(Cl^-\) gives Magnesium chloride. Since the Magnesium ion has a charge of \(2+\) and the Chloride ion has a charge of \(1-\), we need two chloride ions for every magnesium ion, resulting in the formula \(MgCl_2\).

Putting these together, the equation becomes:
\[BaCl_2 + MgSO_4 \rightarrow BaSO_4(s) + MgCl_2\]

  1. Conclusion

Finally, we check the balance of the equation:

  • Left side: 1 Ba, 2 Cl, 1 Mg, 1 \(SO_4\).
  • Right side: 1 Ba, 1 \(SO_4\), 1 Mg, 2 Cl.

Since the number of atoms for every element is equal on both sides, the equation is already balanced. Comparing this to the given options, the correct product is \(BaSO_4(s) + MgCl_2\).

Examples

Double displacement reactions are fundamental in water treatment processes. For instance, when treating hard water, chemicals are added to precipitate out unwanted ions like calcium or magnesium. Similarly, in analytical chemistry, scientists often use precipitation reactions—where one of the products is an insoluble solid—to isolate specific ions from a solution for measurement or removal. Understanding how these reactions work helps in designing effective filtration and purification systems.

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