Question

Calculate the standard enthalpy change for the reaction where 250 mL of 2M HCl is mixed with 500 mL of 1M NaOH, assuming that the specific heat capacity of the resulting solution is 4.18 J/g°C and the density of the solution is 1.00 g/mL. (Hint: The balanced chemical equation for the reaction is HCl(aq) + NaOH(aq) → NaCl(aq) + H2O(l))

Answer 1

To calculate the standard enthalpy change for the reaction, we first need to determine the limiting reactant and the amount of heat released during the reaction. Then, we can use the heat released and the moles of the limiting reactant to calculate the standard enthalpy change.1. Determine the limiting reactant:HCl: 250 mL  2 mol/L = 0.5 molNaOH: 500 mL  1 mol/L = 0.5 molSince both HCl and NaOH have the same number of moles, neither is the limiting reactant, and the reaction will go to completion.2. Calculate the heat released during the reaction:The total volume of the solution is 250 mL + 500 mL = 750 mL. Since the density of the solution is 1.00 g/mL, the mass of the solution is 750 g.The heat released during the reaction can be calculated using the formula q = mcT, where q is the heat released, m is the mass of the solution, c is the specific heat capacity, and T is the change in temperature.We are not given the change in temperature  T  in the problem, so we cannot calculate the heat released  q  directly. However, we can still calculate the standard enthalpy change using the moles of the limiting reactant.3. Calculate the standard enthalpy change:Since the reaction goes to completion, 0.5 mol of HCl reacts with 0.5 mol of NaOH to produce 0.5 mol of NaCl and 0.5 mol of H2O. The standard enthalpy change for the reaction can be calculated using the formula H = q/n, where H is the standard enthalpy change, q is the heat released, and n is the moles of the limiting reactant.Again, we do not have the heat released  q  or the change in temperature  T  to calculate the standard enthalpy change directly. However, we can look up the standard enthalpy of formation for the reactants and products in a reference table and use Hess's Law to calculate the standard enthalpy change for the reaction.The standard enthalpy of formation  Hf  for the reactants and products are as follows:HCl aq : -167.2 kJ/molNaOH aq : -469.15 kJ/molNaCl aq : -407.27 kJ/molH2O l : -285.83 kJ/molUsing Hess's Law, the standard enthalpy change for the reaction is:H = [Hf NaCl  + Hf H2O ] - [Hf HCl  + Hf NaOH ]H = [ -407.27 kJ/mol  +  -285.83 kJ/mol ] - [ -167.2 kJ/mol  +  -469.15 kJ/mol ]H = -693.1 kJ/mol + 636.35 kJ/molH = -56.75 kJ/molThe standard enthalpy change for the reaction is -56.75 kJ/mol.