A student determines the heat of dissolution of solid potassium perchlorate using a coffee-cup calorimeter of negligible heat capacity.
When 2.13 g of KClO4(s) is dissolved in 106.00 g of water, the temperature of the solution drops from 25.00 to 23.17 °C. Based on the student's observation, calculate the enthalpy of dissolution of KClO4(s) in kJ/mol. Assume the specific heat of the solution is 4.184 J/g°C.
q = mass H2O x specific heat H2O x (Tfinal-Tinitial)
That's q = delta H in J for 2.13 g.
Then (delta H/2.13)*molar mass KClO4 = dH in J/mol. Convert to kJ/mol.
To calculate the enthalpy of dissolution of KClO4(s), we need to use the formula:
q = m x c x ΔT
where:
q is the heat gained or lost by the solution (in this case, it is the heat of dissolution)
m is the mass of the solution
c is the specific heat capacity of the solution (given as 4.184 J/g°C)
ΔT is the change in temperature of the solution
Step 1: Calculate the heat lost by the solution (q)
q = m x c x ΔT
First, calculate the mass of the solution:
mass of solution = mass of KClO4 + mass of water
mass of solution = 2.13 g + 106.00 g
mass of solution = 108.13 g
Next, calculate the change in temperature:
ΔT = final temperature - initial temperature
ΔT = 23.17 °C - 25.00 °C
ΔT = -1.83 °C
Now, substitute the values into the formula:
q = (108.13 g)(4.184 J/g°C)(-1.83 °C)
q = -844.66 J
Step 2: Convert the heat of dissolution from J to kJ and calculate the enthalpy change per mole of KClO4.
To convert from J to kJ, divide the heat value by 1000:
q = -844.66 J / 1000
q = -0.845 kJ
To find the enthalpy change per mole of KClO4, divide the heat by the number of moles of KClO4 used.
Step 3: Calculate the number of moles of KClO4 used:
moles of KClO4 = mass of KClO4 / molar mass of KClO4
The molar mass of KClO4 is:
K (39.10 g/mol) + Cl (35.45 g/mol) + 4O (16.00 g/mol)
molar mass of KClO4 = 39.10 g/mol + 35.45 g/mol + (4 * 16.00 g/mol)
molar mass of KClO4 = 39.10 g/mol + 35.45 g/mol + 64.00 g/mol
molar mass of KClO4 = 138.55 g/mol
moles of KClO4 = 2.13 g / 138.55 g/mol
moles of KClO4 = 0.01536 mol
Step 4: Calculate the enthalpy change per mole of KClO4:
enthalpy change per mole of KClO4 = q / moles of KClO4
enthalpy change per mole of KClO4 = -0.845 kJ / 0.01536 mol
enthalpy change per mole of KClO4 = -55.0 kJ/mol
Therefore, the enthalpy of dissolution of KClO4(s) is -55.0 kJ/mol.
To calculate the enthalpy of dissolution of KClO4(s), you need to use the equation:
q = m * c * ΔT
Where:
q = heat transferred (in joules)
m = mass of the solution (in grams)
c = specific heat capacity of the solution (in J/g°C)
ΔT = change in temperature (in °C)
First, calculate the heat transferred by the solution using the given values:
m = 106.00 g (mass of water)
c = 4.184 J/g°C (specific heat of the solution)
ΔT = 23.17 °C - 25.00 °C = -1.83 °C
q = m * c * ΔT
q = 106.00 g * 4.184 J/g°C * (-1.83 °C)
q = -802.40 J
Next, convert the heat transferred to kilojoules:
1 kJ = 1000 J
q = -802.40 J / 1000
q = -0.8024 kJ
Now, calculate the moles of KClO4(s) that were dissolved:
molar mass of KClO4 = 39.10 g/mol (K) + 35.45 g/mol (Cl) + 4 * 16.00 g/mol (4 O)
molar mass of KClO4 = 138.55 g/mol
moles of KClO4 = mass / molar mass
moles of KClO4 = 2.13 g / 138.55 g/mol
moles of KClO4 = 0.01536 mol
Finally, calculate the enthalpy of dissolution per mole of KClO4(s):
enthalpy = q / moles of KClO4
enthalpy = -0.8024 kJ / 0.01536 mol
enthalpy = -52.17 kJ/mol
Therefore, the enthalpy of dissolution of KClO4(s) is -52.17 kJ/mol.