A chemistry student needs to determine the concentration of a copper sulfate solution by using mass balance calculations. The student knows that a 100 mL sample of the solution at an unknown concentration was diluted to 500 mL, and then 50 mL of the diluted solution was titrated with a standardized sodium thiosulfate solution. The titre value was 10.0 mL. The student needs to determine the concentration of the copper sulfate solution in terms of grams per liter (g/L).

Question

A chemistry student needs to determine the concentration of a copper sulfate solution by using mass balance calculations. The student knows that a 100 mL sample of the solution at an unknown concentration was diluted to 500 mL, and then 50 mL of the diluted solution was titrated with a standardized sodium thiosulfate so

Answer 1

To determine the concentration of the copper sulfate solution, we first need to find the moles of copper sulfate in the titrated sample. The balanced equation for the reaction between copper sulfate and sodium thiosulfate is:2CuSO4 + 5Na2S2O3  Cu2S2O3 + 5Na2SO4From the balanced equation, we can see that 2 moles of CuSO4 react with 5 moles of Na2S2O3.The student titrated 50 mL of the diluted solution with 10.0 mL of sodium thiosulfate. Let's assume the concentration of the standardized sodium thiosulfate solution is 'x' mol/L.Moles of Na2S2O3 = Volume  L   Concentration  mol/L Moles of Na2S2O3 = 0.010 L  x mol/L = 0.010x molesNow, using the stoichiometry from the balanced equation:Moles of CuSO4 =  2/5   Moles of Na2S2O3Moles of CuSO4 =  2/5   0.010x = 0.004x molesThis is the moles of CuSO4 in the 50 mL titrated sample. However, this was taken from the 500 mL diluted solution. To find the moles of CuSO4 in the 500 mL diluted solution, we can use the proportion:Moles of CuSO4 in 500 mL =  0.004x moles    500 mL / 50 mL  = 0.040x molesNow, we need to find the moles of CuSO4 in the original 100 mL solution before dilution. Since the mass of CuSO4 remains constant during dilution:Moles of CuSO4 in 100 mL = Moles of CuSO4 in 500 mLMoles of CuSO4 in 100 mL = 0.040x molesTo find the concentration of CuSO4 in the original 100 mL solution, we can use the formula:Concentration  mol/L  = Moles / Volume  L Concentration of CuSO4 =  0.040x moles  / 0.100 L = 0.40x mol/LFinally, to express the concentration in grams per liter  g/L , we need to multiply by the molar mass of CuSO4  159.61 g/mol :Concentration of CuSO4  g/L  =  0.40x mol/L    159.61 g/mol  = 63.84x g/LSo, the concentration of the copper sulfate solution in terms of grams per liter  g/L  is 63.84x g/L, where 'x' is the concentration of the standardized sodium thiosulfate solution in mol/L.