In a coffee-cup calorimeter, 1.50 g of NH4NO3 is mixed with 72.0 g of water at an initial temperature of 25.00°C. After dissolution of the salt, the final temperature of the calorimeter contents is 23.65°C. Assuming the solution has a heat capacity of 4.18 J/°C·g and assuming no heat loss to the calorimeter, calculate the enthalpy change for the dissolution of NH4NO3 in units of kJ/mol.
q extracted from the water is
q = mass H2O x specific heat H2O x (Tfinal-Tinitial)
That gives you q for 1.50g sample. The 1.5g sample is how many mols? That's 1.5/molar mass NH4NO3.
Then q from above/#mols = q in J/mol. Convert to kJ/mol.
59kg
To calculate the enthalpy change for the dissolution of NH4NO3 in units of kJ/mol, we can use the equation:
ΔH = q / n
where ΔH is the enthalpy change, q is the heat absorbed or released, and n is the number of moles of NH4NO3.
First, we need to calculate the heat (q). The heat absorbed or released can be calculated using the equation:
q = m * c * ΔT
where q is the heat, m is the mass of the solution, c is the heat capacity, and ΔT is the change in temperature.
Given values:
Mass of NH4NO3 = 1.50 g
Mass of water = 72.0 g
Initial temperature = 25.00°C
Final temperature = 23.65°C
Heat capacity (c) = 4.18 J/°C·g
Step 1: Calculate the mass of the solution.
Mass of the solution = Mass of NH4NO3 + Mass of water
Mass of the solution = 1.50 g + 72.0 g = 73.5 g
Step 2: Calculate the change in temperature.
ΔT = Final temperature - Initial temperature
ΔT = 23.65°C - 25.00°C = -1.35°C
Note: The negative sign indicates a decrease in temperature.
Step 3: Calculate the heat (q).
q = m * c * ΔT
q = 73.5 g * 4.18 J/°C·g * -1.35°C
q = -425.00 J (rounded to the nearest whole number)
Step 4: Calculate the number of moles of NH4NO3.
The molar mass of NH4NO3 is needed to calculate the number of moles.
Molar mass of NH4NO3 = 14.01 g/mol (N) + 4 * 1.01 g/mol (H) + 3 * 16.00 g/mol (O)
Molar mass of NH4NO3 = 80.05 g/mol
Number of moles of NH4NO3 = Mass of NH4NO3 / Molar mass of NH4NO3
Number of moles of NH4NO3 = 1.50 g / 80.05 g/mol
Number of moles of NH4NO3 = 0.01875 mol
Step 5: Calculate the enthalpy change (ΔH).
ΔH = q / n
ΔH = -425.00 J / 0.01875 mol
ΔH = -22,666.67 J/mol (rounding to the nearest whole number)
Finally, to convert the enthalpy change to kJ/mol, we divide the result by 1000:
ΔH = -22,666.67 J/mol / 1000
ΔH = -22.67 kJ/mol
So, the enthalpy change for the dissolution of NH4NO3 is -22.67 kJ/mol.