In a coffee-cup calorimeter, 1.70 g of NH4NO3 is mixed with 76.0 g of water at an initial temperature of 25.00°C. After dissolution of the salt, the final temperature of the calorimeter contents is 23.71°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.

Question

In a coffee-cup calorimeter, 1.70 g of NH4NO3 is mixed with 76.0 g of water at an initial temperature of 25.00°C. After dissolution of the salt, the final temperature of the calorimeter contents is 23.71°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.

Answer 1

heat lost = mass H2O x specific heat H2O x (Tfinal-Tinitial) = q

delta H NH4NO3 = q/1.70 for delta H/g. Multiply by molar mass NH4NO3 to convert to delta H/mol. Convert from J to kJ.

Answer 2

To calculate the enthalpy change for the dissolution of NH4NO3 in units of kJ/mol, we need to use the equation:

ΔH = q / n

Where:
- ΔH is the enthalpy change (in kJ/mol)
- q is the heat absorbed or released (in Joules)
- n is the number of moles of the substance involved in the reaction

First, let's calculate the heat absorbed or released by the water using the equation:

q_water = m_water * C_water * ΔT

Where:
- q_water is the heat absorbed or released by water (in Joules)
- m_water is the mass of water (in grams)
- C_water is the specific heat capacity of water (4.18 J/°C · g)
- ΔT is the change in temperature (in °C)

Given data:
- Mass of water, m_water = 76.0 g
- Specific heat capacity of water, C_water = 4.18 J/°C · g
- Change in temperature, ΔT = (final temperature - initial temperature) = 23.71°C - 25.00°C

Let's calculate q_water:

q_water = 76.0 g * 4.18 J/°C · g * (23.71°C - 25.00°C)

Next, we need to calculate the number of moles of NH4NO3 dissolved. To do this, we use the equation:

n = m / M

Where:
- n is the number of moles
- m is the mass (in grams)
- M is the molar mass (in g/mol)

Given data:
- Mass of NH4NO3, m = 1.70 g
- Molar mass of NH4NO3 = 80.05 g/mol

Let's calculate n:

n = 1.70 g / 80.05 g/mol

Now we can calculate the enthalpy change:

ΔH = q_water / n

Finally, convert the units to kJ/mol:

ΔH = ΔH / 1000

Now, let's plug in the values and calculate:

Step 1: Calculate q_water
q_water = 76.0 g * 4.18 J/°C · g * (23.71°C - 25.00°C)

Step 2: Calculate n
n = 1.70 g / 80.05 g/mol

Step 3: Calculate ΔH
ΔH = q_water / n

Step 4: Convert to kJ/mol
ΔH = ΔH / 1000

By following these steps and plugging in the values, you can calculate the enthalpy change for the dissolution of NH4NO3 in units of kJ/mol.