Solution Stoichiometry

58) (a) [HCl]₁ = 0.100 M          [HCl]₂ = 0.500 M

           V_HCl1 = 20.0 mL           V_HCl2 = 10.0 mL

           HCl(aq) H⁺(aq) + Cl^-(aq)

           [HCl]₁ = n₁/V_HCl1

           n₁ = [HCl]₁ x V_HCl1 = 0.100 mol HCl/L x 20.0 mL x 1 L/10³ mL = 2.00 x 10^-3 mol HCl

           n₂ = [HCl]₂ x V_HCl2 = 0.500 mol HCl/L x 10.0 mL x 1 L/10³ mL = 5.00 x 10^-3 mol HCl

           [HCl] = n_T/V_T = (2.00 x 10^-3 mol HCl + 5.00 x 10^-3 mol HCl)/((20.0 mL + 10.0 mL) x 1 L/10³ mL) = 0.233 M

           [H⁺] = 0.233 mol HCl/L x 1 mol H⁺/1 mol HCl = 0.233 M

           [Cl ^-] = 0.233 mol HCl/L x 1 mol Cl ^-/1 mol HCl = 0.233 M

      (b) [Na₂SO₄] = 0.300 M          [KCl] = 0.200 M

           V_Na2SO4 = 15.0 mL            V_KCl = 10.0 mL

           Na₂SO₄(aq) 2Na⁺(aq) + SO₄^2-(aq)

           KCl(aq) K⁺(aq) + Cl^-(aq)

           [Na₂SO₄] = n/V

           n_Na2SO4 = [Na₂SO₄] x V = 0.300 mol Na₂SO₄/L x 15.0 mL x 1 L/10³ mL = 4.50 x 10^-3 mol Na₂SO₄

           n_KCl = [KCl] x V = 0.200 mol KCl/L x 10.0 mL x 1 L/10³ mL = 2.00 x 10^-3 mol KCl

           [Na₂SO₄] = n_T/V_T = 4.50 x 10^-3 mol Na₂SO₄/(25.0 mL x 1 L/10³ mL) = 0.180 M Na₂SO₄

           [KCl] = 2.00 x 10^-3 mol KCl/(25.0 mL x 1 L/10³ mL) = 0.0800 M KCl

           [Na⁺] = 0.180 mol Na₂SO₄/L x 2 mol Na⁺/1 mol Na₂SO₄ = 0.360 M

           [SO₄^2-] = 0.180 mol Na₂SO₄/L x 1 mol SO₄^2-/1 mol Na₂SO₄ = 0.180 M

           [K⁺] = 0.0800 mol KCl /L x 1 mol K⁺/1 mol KCl = 0.0800 M

           [Cl^-] = 0.0800 mol KCl /L x 1 mol Cl^-/1 mol KCl = 0.0800 M

      (c) m = 3.50 g NaCl          [CaCl₂] = 0.500 M          V = 50.0 mL

           NaCl(aq) Na⁺(aq) + Cl^-(aq)

           CaCl₂(aq) Ca²⁺(aq) + 2Cl^-(aq)

           n_NaCl = 3.50 g NaCl x 1 mol NaCl/58.44 g NaCl = 0.0599 mol NaCl

           n_CaCl2  = 0.500 mol CaCl₂/L x 50.0 mL x 1 L/10³ mL = 0.0250 mol CaCl₂

           [Na⁺] = n/V_T = 0.0599 mol NaCl/(50.0 ml x 1 L/10³ mL) = 1.20 M

           [Cl^-] = (0.0599 mol Cl^- + 2 x 0.0250 mol Cl^- )/(50.0 ml x 1 L/10³ mL) = 2.20 M

           [Ca²⁺] = 0.0250 mol CaCl₂/(50.0 ml x 1 L/10³ mL) x 1 mol Ca²⁺/ 1 mol CaCl₂ = 0.500 M