Consider the following reaction.
2 HCl(aq) + Ba(OH)2(aq) BaCl2(aq) + 2 H2O(l) ΔH = -118 kJ
Calculate the heat when 103.6 mL of 0.500 M HCl is mixed with 300.0 mL of 0.550 M Ba(OH)2. Assuming that the temperature of both solutions was initially 25.0°C and that the final mixture has a mass of 403.6 g and a specific heat capacity of 4.18 J/°C·g, calculate the final temperature of the mixture.
To calculate the final temperature of the mixture, we can use the principle of energy conservation. The heat released by the reaction will be equal to the heat absorbed by the final mixture.
First, let's calculate the heat released by the reaction using the given enthalpy change:
ΔH = -118 kJ/mol (given in the question)
Next, let's calculate the moles of the limiting reactant (the one that will be fully consumed) in the reaction. In this case, it is HCl.
Moles of HCl = volume of HCl solution (in liters) x molarity of HCl
The volume of the HCl solution is given as 103.6 mL, so we need to convert it to liters:
Volume of HCl = 103.6 mL ÷ 1000 mL/L = 0.1036 L
Moles of HCl = 0.1036 L x 0.500 mol/L = 0.0518 mol
Since the stoichiometric ratio between HCl and BaCl2 is 2:1, the moles of BaCl2 formed will be half the moles of HCl:
Moles of BaCl2 = 0.0518 mol ÷ 2 = 0.0259 mol
Now, let's calculate the heat released by the reaction:
Heat released = moles of HCl x ΔH
Heat released = 0.0518 mol x -118 kJ/mol = -6.1084 kJ
Since energy is conserved, the heat released by the reaction will be absorbed by the final mixture:
Heat absorbed by the mixture = -6.1084 kJ
To calculate the change in temperature of the mixture, we can use the formula:
Heat absorbed = mass of the mixture x specific heat capacity x change in temperature
Rearranging the formula, we can solve for the change in temperature:
Change in temperature = Heat absorbed / (mass of the mixture x specific heat capacity)
Plugging in the given values:
Change in temperature = -6.1084 kJ / (403.6 g x 4.18 J/°C·g) ≈ -0.036 °C
Finally, to calculate the final temperature of the mixture, we need to add the change in temperature to the initial temperature:
Final temperature = 25.0°C + (-0.036 °C) ≈ 24.964 °C
Therefore, the final temperature of the mixture is approximately 24.964 °C.