When 0.627 g of Ca metal is added to 200.0 mL of 0.500 M HCl(aq), a temperature increase of 102C 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.
The molar heat of reaction, H rxn, for the reaction of
Ca(s) + 2H+(aq) Ca2+(aq) + H2(g)
is ____kJ/mol.
To find the molar heat of reaction (Hrxn), we can use the equation:
q = mcΔT
Where:
q represents the heat gained or lost by the system,
m is the mass of the solution,
c is the specific heat capacity of the solution,
and ΔT is the change in temperature.
First, we need to calculate the heat gained or lost by the system (q). Since the reaction is exothermic, the heat is released by the system. Therefore, q will be negative.
Next, we calculate the mass of the solution. The density of the solution is given as 1.00 g/mL, and the final volume is 200.0 mL. So the mass of the solution is:
mass = volume x density
mass = 200.0 mL x 1.00 g/mL
mass = 200.0 g
Now, using the given heat capacity of 4.184 J/g°C, we can calculate the heat gained or lost by the system:
q = -mcΔT
q = - 200.0 g x 4.184 J/g°C x 102°C
q = -872,064 J (note: the negative sign indicates heat released)
Finally, we can use the moles of calcium (Ca) in the reaction to calculate ΔHrxn. The chemical equation shows that 1 mole of Ca reacts with 2 moles of H+ ions. The moles of Ca can be calculated using its molar mass:
Molar mass of Ca = 40.08 g/mol
moles of Ca = mass of Ca / molar mass of Ca
moles of Ca = 0.627 g / 40.08 g/mol
moles of Ca = 0.0156 mol
Since 1 mole of Ca releases q amount of heat, we can calculate the molar heat of reaction (Hrxn) as:
Hrxn = q / moles of Ca
Hrxn = -872064 J / 0.0156 mol
Hrxn = -55,896,000 J/mol
However, the answer is requested in kJ/mol, so we divide by 1000:
Hrxn = -55,896,000 J/mol / 1000
Hrxn = -55,896 kJ/mol
Therefore, the molar heat of reaction (Hrxn) for the given reaction is approximately -55,896 kJ/mol.