One reaction of iron with hydrochloric acid is represented by the following thermochemical equation.
Fe(s) + 2HCl(aq) → FeCl2(aq) + H2(g); ΔH°= –87.9 kJ
How much heat is liberated at constant pressure if 0.416 g of iron reacts with 42.0 mL of 0.457 M HCl?
A. 87.9 kJ
B. 4.03 kJ
C. 0.844 kJ
D. 0.655 kJ
E. 36.6 kJ
Answered below at your other post.
To solve this thermochemical problem, we need to use the equation:
q = mcΔT
Where:
q = heat released or absorbed (in Joules or kilojoules)
m = mass of the substance (in grams)
c = specific heat capacity of the substance (in J/g·°C or J/g·K)
ΔT = change in temperature (in °C or Kelvin)
First, we need to find the moles of Fe(s) and HCl(aq) using their respective molar masses:
molar mass of Fe = 55.847 g/mol
molar mass of HCl = 36.461 g/mol
moles of Fe = mass of Fe / molar mass of Fe
= 0.416 g / 55.847 g/mol
moles of HCl = volume of HCl x molarity
= 42.0 mL x 0.457 mol/L
= 42.0 mL x 0.457 L/mol
Next, we use the stoichiometry of the balanced equation to determine the ratio of moles of Fe to moles of HCl and the amount of heat released:
From the balanced equation, 1 mole of Fe reacts with 2 moles of HCl.
moles of HCl / moles of Fe = (42.0 mL x 0.457 L/mol) / (0.416 g / 55.847 g/mol)
= (42.0 mL x 0.457 L/mol) / (0.416 g x 55.847 g/mol)
Now, we can calculate the amount of heat released using the thermochemical equation:
heat released = moles of Fe x ΔH°
= (moles of HCl x 2) x ΔH°
= (42.0 mL x 0.457 L/mol) / (0.416 g x 55.847 g/mol) x (-87.9 kJ)
Finally, we convert the heat released from kilojoules to joules by multiplying by 1000 to get the answer in kilojoules:
heat released in J = heat released in kJ x 1000
Now, let's plug in the values and calculate:
heat released in J = (42.0 mL x 0.457 L/mol) / (0.416 g x 55.847 g/mol) x (-87.9 kJ) x 1000
After performing the calculations, we find that the heat released is approximately -4.03 kJ.
Therefore, the correct answer is B. 4.03 kJ.
(Note: The negative sign indicates that the reaction is exothermic, meaning heat is released.)