please help its due at 5
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 ,in KJ/mol for the reaction of
Ca(s) + 2H+(aq) Ca2+(aq) + H2(g)
To find the molar heat of reaction (Hrxn) for the given reaction, we can use the formula:
Hrxn = q / (n * ΔT)
Where:
- q is the heat absorbed or released by the reaction
- n is the number of moles of the limiting reactant
- ΔT is the change in temperature
First, let's find the heat absorbed or released by the reaction (q). We can use the formula:
q = msΔT
Where:
- m is the mass of the solution
- s is the specific heat capacity of the solution
- ΔT is the change in temperature
Given:
- m = volume x density = 200.0 mL x 1.00 g/mL = 200.0 g
- s = specific heat capacity = 4.184 J/g°C
- ΔT = 109°C
Using the formula, we can calculate q:
q = 200.0 g x 4.184 J/g°C x 109°C = 915,296 J
Now, let's calculate the number of moles of the limiting reactant (n). From the balanced equation, we can see that the stoichiometric ratio between Ca and HCl is 1:2. Therefore, for every 1 mole of Ca reacted, we have 2 moles of HCl. We need to calculate the moles of Ca.
Given:
- molar mass of Ca = 40.08 g/mol
- mass of Ca = 0.671 g
Using the formula, we can calculate n:
n = mass / molar mass = 0.671 g / 40.08 g/mol = 0.0167 mol
Finally, we can calculate Hrxn using the formula:
Hrxn = q / (n * ΔT) = 915,296 J / (0.0167 mol x 109°C)
Converting the temperature to Kelvin: ΔT = 109°C + 273.15 = 382.15 K
Hrxn = 915,296 J / (0.0167 mol x 382.15 K) = 85,373 J/mol or 85.4 kJ/mol
Therefore, the molar heat of reaction (Hrxn) for the given reaction is 85.4 kJ/mol.