When 0.671 g of Ca metal is added to 200.0 mL of 0.500 M HCl(aq), a temperature increase of 109C is observed.
Assume the solution's final volume is 200.0 mL, the density is 1.00 g/mL, and the heat capacity is 4.184 J/gC.
(Note: Pay attention to significant figures. Do not round until the final answer.)
The molar heat of reaction, H rxn, for the reaction of
Ca(s) + 2H+(aq) Ca2+(aq) + H2(g)
To calculate the molar heat of reaction (Hrxn) for the given reaction, we can use the equation:
q = (m)(C)(ΔT)
where:
q = heat exchanged during the reaction
m = mass of the substance (in grams)
C = heat capacity of the substance (in J/g°C)
ΔT = change in temperature (in °C)
First, let's calculate the heat exchanged during the reaction. We can use the equation:
q = mH2O × C × ΔT
where:
mH2O = mass of water (in grams)
Given that the density is 1.00 g/mL and the final volume is 200.0 mL, we can calculate the mass of water as follows:
mH2O = (density)(volume) = (1.00 g/mL)(200.0 mL) = 200.0 g
Next, we need to find the change in temperature (ΔT). The temperature increased by 109°C, so:
ΔT = 109°C
Now, we have all the necessary values to calculate the heat exchanged during the reaction:
q = (200.0 g)(4.184 J/g°C)(109°C)
Calculating this gives us:
q = 92,591.2 J
Note: Since the units for heat capacity and change in temperature are in J/g°C, the unit for mass must be in grams to ensure proper calculation.
Now, let's calculate the number of moles of HCl that reacted. The balanced equation tells us that the stoichiometric ratio between Ca and HCl is 1:2. Therefore, the moles of HCl is:
moles of HCl = (moles of Ca) × 2
The molar mass of Ca is 40.08 g/mol. Using the given mass of Ca (0.671 g), we can calculate the moles of Ca as follows:
moles of Ca = (mass of Ca)/(molar mass of Ca)
= (0.671 g)/(40.08 g/mol)
Calculating this gives us:
moles of Ca = 0.0167 mol
Now, let's calculate the moles of HCl:
moles of HCl = (0.0167 mol) × 2
Calculating this gives us:
moles of HCl = 0.0334 mol
Finally, we can calculate the molar heat of reaction (Hrxn) using the equation:
Hrxn = q / (moles of HCl)
Hrxn = 92,591.2 J / (0.0334 mol)
Calculating this gives us the answer for the molar heat of reaction (Hrxn) for the given reaction.