When 0.969 g of CaO is added to 200.0 mL of 0.500 M HCl(aq), a temperature increase of 397C 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.
Delta Hrxn, for the reaction of
CaO(s) + 2H+(aq) Ca2+(aq) + H2O(l)
is ________________ kJ/mol.
To calculate the enthalpy change (ΔHrxn) for the given reaction in kJ/mol, we need to follow these steps:
1. Convert the mass of CaO to moles.
2. Determine the amount of HCl reacting in moles.
3. Calculate the heat absorbed by the solution using the formula:
q = mcΔT, where q is heat absorbed, m is mass, c is specific heat capacity, and ΔT is temperature change.
4. Use the equation q = ΔHrxn × moles to find ΔHrxn.
5. Convert ΔHrxn from J/mol to kJ/mol.
Let's go through each step:
Step 1: Convert the mass of CaO to moles.
Given:
Mass of CaO = 0.969 g
Molar mass of CaO = 56.08 g/mol
To find moles, divide the mass by the molar mass:
moles of CaO = 0.969 g / 56.08 g/mol
Step 2: Determine the amount of HCl reacting in moles.
Given:
Volume of HCl = 200.0 mL
Molarity of HCl = 0.500 M
To find moles, use the formula:
moles = volume (L) × concentration (mol/L)
moles of HCl = 0.200 L × 0.500 mol/L
Step 3: Calculate the heat absorbed by the solution (q).
Given:
Temperature change (ΔT) = 397°C
Density of the solution = 1.00 g/mL
Heat capacity (c) = 4.184 J/g°C
First, calculate the mass of the solution:
Mass of the solution = volume × density
Mass of the solution = 200.0 mL × 1.00 g/mL
Next, calculate the heat absorbed:
q = mass × c × ΔT
Step 4: Calculate ΔHrxn.
We'll use the equation:
q = ΔHrxn × moles
Rearrange the equation to solve for ΔHrxn:
ΔHrxn = q / moles
Step 5: Convert ΔHrxn from J/mol to kJ/mol.
Divide ΔHrxn by 1000 to convert J to kJ:
ΔHrxn = ΔHrxn / 1000
Now, let's substitute the values into the equations and calculate ΔHrxn:
Step 1:
moles of CaO = 0.969 g / 56.08 g/mol
Step 2:
moles of HCl = 0.200 L × 0.500 mol/L
Step 3:
Mass of the solution = 200.0 mL × 1.00 g/mL
q = mass × c × ΔT
Step 4:
ΔHrxn = q / moles
Step 5:
ΔHrxn = ΔHrxn / 1000
By following these steps and performing the necessary calculations, you should be able to determine ΔHrxn in kJ/mol.