When 0.752 g of Ca metal is added to 200.0 mL of 0.500 M HCl(aq), a temperature increase of 12.2C 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)
? is kJ/mol.
q = massH2O*sp.h.*delta T
mass H2O is 200 grams (200 mL and density is 1.00 g/mL).
specific heat H2O is 4.184 from the problem.
delta T is 12.2o C from the problem.
This is the q obtained by reacting 0.725 g Ca. Convert to a mol Ca (about 40 g but look up the atomic mass Ca on the periodic table). That will be the Joules of heat/ mol for the reaction.
Post your work if you get stuck.
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To calculate the molar heat of reaction (Hrxn) for the given reaction, we need to follow a few steps.
Step 1: Calculate the heat gained or lost by the solution using the formula:
q = mass H2O × specific heat H2O × delta T
Here,
- mass H2O is the mass of water in the solution. Since the volume is given as 200.0 mL and density is 1.00 g/mL, the mass H2O is 200.0 grams.
- specific heat H2O is given as 4.184 J/gC.
- delta T is the change in temperature, which is given as 12.2C.
Plugging in the values:
q = 200.0 g × 4.184 J/gC × 12.2C
q = 10,250.24 J
Step 2: Calculate the moles of calcium (Ca) reacted.
Given that 0.752 g of Ca reacted, we need to convert this mass to moles. The molar mass of Ca is approximately 40 g/mol (you can verify this on the periodic table).
moles Ca = mass Ca / molar mass Ca
moles Ca = 0.752 g / 40 g/mol
moles Ca ≈ 0.0188 mol
Step 3: Calculate the molar heat of reaction (Hrxn) by dividing the heat gained or lost by the moles of reactant (Ca).
Hrxn = q / moles Ca
Hrxn = 10,250.24 J / 0.0188 mol
Remember to convert the answer to kilojoules by dividing by 1000:
Hrxn ≈ 545,645 J/mol ≈ 545.65 kJ/mol
Therefore, the molar heat of reaction (Hrxn) for the given reaction is approximately 545.65 kJ/mol.