0.949 g of CaO is added to 200.0 mL of 0.500 M HCl(aq), a temperature increase of 389C 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.
And the question is?
To calculate the heat released during this reaction, we can use the formula:
q = m × C × ΔT
where q is the heat released, m is the mass of the solution, C is the heat capacity, and ΔT is the change in temperature.
First, let's calculate the mass of the solution. Since the density is given as 1.00 g/mL, the mass of the solution is equal to its volume:
mass = volume × density = 200.0 mL × 1.00 g/mL = 200.0 g
Next, we need to calculate the change in temperature (ΔT) by subtracting the initial temperature from the final temperature:
ΔT = final temperature - initial temperature = 389°C - initial temperature
Now, let's calculate the heat released (q):
q = 200.0 g × 4.184 J/g°C × (389°C - initial temperature)
Remember that HCl is a strong acid and completely ionizes in water, so we can consider it to be a 0.500 M solution of H+ ions reacting with CaO. The balanced equation for this reaction is:
CaO + 2HCl --> CaCl2 + H2O
Since the reaction is 1:2 between CaO and HCl, we need to find out the number of moles of CaO. We can use the formula:
moles of CaO = mass of CaO / molar mass of CaO
The molar mass of CaO is calculated by adding the atomic masses of calcium (Ca) and oxygen (O):
molar mass of CaO = atomic mass of Ca + atomic mass of O = 40.08 g/mol + 16.00 g/mol = 56.08 g/mol
Now, we can calculate the moles of CaO using the mass of CaO given:
moles of CaO = 0.949 g / 56.08 g/mol
With the moles of CaO, we can determine the moles of HCl that reacted:
moles of HCl = 2 × moles of CaO
Finally, we can use the molarity of HCl to find the volume of HCl solution that reacted with CaO. The formula for this is:
volume of HCl solution = moles of HCl / molarity of HCl
volume of HCl solution = moles of HCl / 0.500 mol/L (since M and L denote molarity and volume in liters)
Remember that the initial volume of the solution is given as 200.0 mL. To find the final volume, we need to calculate the volume of water produced in the reaction:
volume of water = moles of HCl × (2 mol of H2O / 2 mol of HCl) × (1 L / 1000 mL)
Finally, the final volume of the solution is the sum of the initial volume and the volume of water produced:
final volume of the solution = 200.0 mL + volume of water
Now that we have the final volume of the solution, we can proceed to calculate the concentration of HCl in the solution:
molarity of HCl = moles of HCl / final volume of the solution
With the concentration of HCl and the molar mass of HCl (H = 1.01 g/mol, Cl = 35.45 g/mol), we can calculate the mass of HCl in the solution:
mass of HCl = molarity of HCl × final volume of the solution × molar mass of HCl
After calculating the mass of HCl, we can use it to determine the heat released (q) using the formula mentioned earlier:
q = mass of HCl × heat capacity × ΔT
where ΔT is the change in temperature (389°C - initial temperature).