This has already been posted, however the provided answer does not make sense. Anyone have additional insight for this one?
An excess of aluminum metal is added to 200.0 mL of 0.025 M solution of CuCl2, reducing the Cu+2 ions to metallic Cu. If the temperature of the solution increases from 25.0 (Celsius) to 27.5 (Celsius), what is the enthalpy of this reaction per mole of Cu formed?
(Specific heat of the solution = 4.18 J/g/K)
Multiple choice solutions are: 2.09 kJ, 23.9 kJ, 83.6 kJ, and 418 kJ.
Thank you!
To calculate the enthalpy of the reaction per mole of Cu formed, you need to use the formula:
ΔH = q / n
where ΔH is the enthalpy change, q is the heat absorbed or released, and n is the number of moles of Cu formed.
To find the heat absorbed or released (q), you can use the formula:
q = m * c * ΔT
where q is the heat, m is the mass of the solution, c is the specific heat capacity of the solution, and ΔT is the change in temperature.
First, you need to find the mass of the solution. To do this, you can use the formula:
mass = volume * density
Assuming the density of the solution is close to that of water (1 g/mL), the mass of the solution would be 200.0 grams.
Next, you can calculate the change in temperature (ΔT):
ΔT = final temperature - initial temperature
ΔT = 27.5 - 25.0 = 2.5 °C
Now, you can calculate the heat absorbed or released (q):
q = mass * c * ΔT
q = 200.0 g * 4.18 J/g/K * 2.5 K
q = 2090 J
Since the given reaction involved excess aluminum reacting with copper ions, it is a redox reaction. The balanced chemical equation for this reaction is:
2Al + 3Cu²⁺ → 2Al³⁺ + 3Cu
From the balanced equation, you can see that there are 3 moles of Cu formed for every 2 moles of Al reacted. So, the number of moles of Cu formed (n) would be less than the number of moles of Al reacted.
Now, you need to determine the number of moles of Al reacted. To do this, you can use the molarity and volume of the CuCl2 solution.
moles of CuCl2 = molarity * volume
moles of CuCl2 = 0.025 M * 0.200 L
moles of CuCl2 = 0.005 mol
Since the stoichiometric ratio between CuCl2 and Al is 3:2, the number of moles of Al reacted will be:
moles of Al = (3/2) * (0.005 mol) = 0.0075 mol
Finally, you can calculate the enthalpy change for this reaction per mole of Cu formed:
ΔH = q / n
ΔH = 2090 J / (0.0075 mol) = 278,666.67 J/mol
Converting the result to kJ/mol:
ΔH = 278,666.67 J/mol / 1000 = 278.67 kJ/mol
Therefore, the correct answer is approximately 278.67 kJ/mol.