In a constant-pressure calorimeter, 60.0 mL of 0.300 M Ba(OH)2 was added to 60.0 mL of 0.600 M HCl. The reaction caused the temperature of the solution to rise from 21.75 °C to 25.84 °C. If the solution has the same density and specific heat as water (1.00 g/mL and 4.184 J/g·°C, respectively), what is ΔH for this reaction (per mole of H2O produced)? Assume that the total volume is the sum of the individual volumes.
To find ΔH for the reaction, we can use the equation:
ΔH = q / n
where ΔH is the enthalpy change of the reaction, q is the heat generated or absorbed by the reaction, and n is the number of moles of the substance involved in the reaction.
First, let's find the heat generated or absorbed by the reaction (q). For a constant-pressure calorimeter, the heat absorbed or released by the reaction is equal to the heat absorbed or released by the surroundings, given by:
q = C × m × ΔT
where C is the specific heat capacity of the solution (which is assumed to be the same as water, 4.184 J/g·°C), m is the mass of the solution, and ΔT is the change in temperature.
To calculate the mass of the solution, we need to take into account the density of the solution, which is 1.00 g/mL. Since we have 60.0 mL of Ba(OH)2 solution and 60.0 mL of HCl solution, the total volume is 120.0 mL.
Mass of the solution = volume × density = 120.0 g
Now, we can calculate q:
q = 4.184 J/g·°C × 120.0 g × (25.84 °C - 21.75 °C)
Next, we need to find the number of moles of water (H2O) in the reaction. From the balanced equation:
Ba(OH)2(aq) + 2 HCl(aq) → BaCl2(aq) + 2 H2O(l)
we can see that for every 2 moles of HCl, 2 moles of water are produced. Since the initial volume of HCl is 60.0 mL and the concentration is 0.600 M, we can calculate the number of moles of HCl:
moles HCl = volume (L) × concentration (M) = 0.060 L × 0.600 mol/L
To get the number of moles of H2O, we divide the moles of HCl by 2:
moles H2O = moles HCl / 2
Finally, we can calculate ΔH:
ΔH = q / n
where n is the number of moles of water (H2O) produced.
Plug in the values for q and n to find ΔH. The units for ΔH will be in joules per mole (J/mol).
..Ba(OH)2 + 2HCl ==> BaCl2 + 2HCl
mols Ba(OH)2 = 0.060 x 0.300 = 0.18
mols HCl = 0.060 x 0.600 = 0.036
mols Ba(OH)2 left = 0
mols HCl left = 0
mols H2O formed = 0.036
q = dH = mass H2O x specific heat H2O x (Tfinal-Tinitial)
Then convert J to kJ. That is ? kJ for 0.036. To find per mol it is
dH/0.036 = ? kJ/mol. Approx 57 kJ/mol.