Question

which of these is the correct balanced chemical equation, including states of matter, for the reaction of aqueous sodium sulfate and aqueous calcium chloride? na₂so₄(aq) + cacl₂(aq) → 2nacl(aq) + caso₄(s) na₂so₄(aq) + 2cacl₂(aq) → nacl(aq) + caso₄(s) na₂so₄(aq) + 2cacl₂(aq) → 2nacl(aq) + 2caso₄(s) 2na₂so₄(aq) + 2cacl₂(aq) → 4nacl(aq) + caso₄(s)

Explanation:

Step1: Analyze reactants and products

Reactants: Aqueous sodium sulfate ($\ce{Na2SO4(aq)}$) and aqueous calcium chloride ($\ce{CaCl2(aq)}$). Products: Sodium chloride ($\ce{NaCl}$) and calcium sulfate ($\ce{CaSO4}$). Calcium sulfate is insoluble, so state is (s); sodium chloride is soluble, state (aq).

Step2: Balance atoms

• Na atoms: Reactant has 2 (in $\ce{Na2SO4}$), product needs 2. So $\ce{NaCl}$ coefficient 2.
• Ca atoms: Reactant has 1 (in $\ce{CaCl2}$), product has 1 (in $\ce{CaSO4}$) – balanced.
• S atoms: Reactant has 1 (in $\ce{Na2SO4}$), product has 1 (in $\ce{CaSO4}$) – balanced.
• Cl atoms: Reactant has 2 (in $\ce{CaCl2}$), product has 2 (in $2\ce{NaCl}$) – balanced.
• O atoms: Reactant has 4 (in $\ce{Na2SO4}$), product has 4 (in $\ce{CaSO4}$) – balanced.

Check each option:

1. $\ce{Na2SO4(aq) + CaCl2(aq) -> 2NaCl(aq) + CaSO4(s)}$: Atoms balanced (2 Na, 1 Ca, 1 S, 2 Cl, 4 O).
2. $\ce{Na2SO4(aq) + 2CaCl2(aq) -> NaCl(aq) + CaSO4(s)}$: Na unbalanced (2 vs 1), Ca unbalanced (2 vs 1) – wrong.
3. $\ce{Na2SO4(aq) + 2CaCl2(aq) -> 2NaCl(aq) + 2CaSO4(s)}$: Ca unbalanced (2 vs 2? No, reactant Ca: 2, product Ca: 2? Wait, no – original reactant $\ce{CaCl2}$ with coefficient 2 gives 2 Ca, but product $\ce{CaSO4}$ with 2 gives 2 Ca. But S: reactant 1, product 2 – unbalanced. Wrong.
4. $\ce{2Na2SO4(aq) + 2CaCl2(aq) -> 4NaCl(aq) + CaSO4(s)}$: S unbalanced (2 vs 1), Ca unbalanced (2 vs 1) – wrong.

Answer:

$\ce{Na2SO4(aq) + CaCl2(aq) -> 2NaCl(aq) + CaSO4(s)}$ (the first option: $\boldsymbol{\ce{Na2SO4(aq) + CaCl2(aq) -> 2NaCl(aq) + CaSO4(s)}}$)