Write a balanced chemical equation for the reaction that occurs when (a) \(\mathrm{Mg}(s)\) reacts with \(\mathrm{Cl}_{2}(g) ;(\mathbf{b})\) barium carbonate decomposes into barium oxide and carbon dioxide gas when heated; \((\mathbf{c})\) the hydrocarbon styrene, \(\mathrm{C}_{8} \mathrm{H}_{8}(l),\) is combusted in air; \((\mathbf{d})\) dimethylether, $\mathrm{CH}_{3} \mathrm{OCH}_{3}(g),$ is combusted in air.

First, let's write the unbalanced chemical equation for the reaction between Magnesium (Mg) and Chlorine (Cl₂). In this reaction, Magnesium will react with Chlorine to form Magnesium Chloride (MgCl₂): Mg (s) + Cl₂ (g) → MgCl₂ (s) Now, let's balance the equation. We have one magnesium atom on both sides and two chlorine atoms on the left side with only one chlorine atom on the right side. To balance the number of chlorine atoms, we can add a coefficient of 2 to MgCl₂: Mg (s) + Cl₂ (g) → 1MgCl₂ (s) Now, the balanced chemical equation is: Mg (s) + Cl₂ (g) → MgCl₂ (s)

First, write the unbalanced chemical equation for the decomposition of Barium Carbonate (BaCO₃) into Barium Oxide (BaO) and Carbon Dioxide (CO₂) when heated: BaCO₃ (s) → BaO (s) + CO₂ (g) Next, balance the equation. The numbers of Barium, Carbon, and Oxygen atoms on both sides are already balanced. Therefore the balanced chemical equation is: BaCO₃ (s) → BaO (s) + CO₂ (g)

First, let's write the unbalanced chemical equation for the combustion of Styrene (\(C_8H_8\)) in air. In a combustion reaction, Styrene reacts with Oxygen (O₂) to produce Carbon Dioxide (CO₂) and Water (H₂O): C₈H₈ (l) + O₂ (g) → CO₂ (g) + H₂O (g) Next, balance the equation. There are 8 carbon atoms, 8 hydrogen atoms and 2 oxygen atoms in the unbalanced equation. To balance the carbon atoms, we need to add a coefficient of 8 to CO₂: C₈H₈ (l) + O₂ (g) → 8CO₂ (g) + H₂O (g) To balance the hydrogen atoms, we need to add a coefficient of 4 to H₂O: C₈H₈ (l) + O₂ (g) → 8CO₂ (g) + 4H₂O (g) Now, to balance the oxygen atoms, we need to add a coefficient of 11/2 to O₂: C₈H₈ (l) + 11/2O₂ (g) → 8CO₂ (g) + 4H₂O (g) The balanced chemical equation is: C₈H₈ (l) + 11/2O₂ (g) → 8CO₂ (g) + 4H₂O (g)

First, write the unbalanced chemical equation for the combustion of Dimethyl Ether (CH₃OCH₃) in air. In a combustion reaction, Dimethyl Ether reacts with Oxygen (O₂) to produce Carbon Dioxide (CO₂) and Water (H₂O): CH₃OCH₃ (g) + O₂ (g) → CO₂ (g) + H₂O (g) Now, balance the equation. There are 2 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom in the unbalanced equation. To balance the carbon atoms, add a coefficient of 2 to CO₂: CH₃OCH₃ (g) + O₂ (g) → 2CO₂ (g) + H₂O (g) To balance the hydrogen atoms, add a coefficient of 3 to H₂O: CH₃OCH₃ (g) + O₂ (g) → 2CO₂ (g) + 3H₂O (g) Finally, to balance the oxygen atoms, add a coefficient of 2 to O₂: CH₃OCH₃ (g) + 2O₂ (g) → 2CO₂ (g) + 3H₂O (g) The balanced chemical equation is: CH₃OCH₃ (g) + 2O₂ (g) → 2CO₂ (g) + 3H₂O (g)