Calculate the heat (in kJ) required to transform 58.60 g of dinitrogen tetraoxide from a solid at a

temperature of -9.3 °C to a gas at 47 °C. Report your answer to one decimal place. Data:
Molar mass of dinitrogen tetraoxide, N2O4
= 92.011 g/mol
Melting point = -9.3 °C Boiling point = 21°C.
Enthalpy of fusion = 14.65 kJ/mol
Enthalpy of vaporization = 38.12 kJ/mol.
Molar heat capacity of the liquid phase = 142.7 J/mol•K
Molar heat capacity of the gas phase= 77.3 J/mol•K

Here is how you do it.

For temperature changes in the same phase( all solid, all liquid, all gas),
q = mass x specific heat in that phase x (Tfinal-Tinitial).

For changing phases (from solid to liquid of liquid to gas),
q = mass x heat fusion (at melting point)
q = mass x heat vaporization (at boiling point)

Then add each q together to arrive at the total Q from the starting point to the ending point.

To calculate the heat required to transform the dinitrogen tetraoxide from a solid to a gas, we need to consider the different energy changes that occur during the process.

First, we need to calculate the heat required to raise the solid dinitrogen tetraoxide from its initial temperature of -9.3 °C to its melting point of -9.3 °C. This can be calculated using the formula:

q1 = mass * specific heat capacity * change in temperature

The specific heat capacity in this case is the molar heat capacity of the solid phase, which we do not have in the given data. We need to assume that it is the same as the molar heat capacity of the liquid phase.

Given:
mass = 58.60 g
change in temperature = (melting point - initial temperature) = (-9.3 °C - (-9.3 °C)) = 0 °C

Next, we need to calculate the heat required to melt the dinitrogen tetraoxide at its melting point. This can be calculated using the formula:

q2 = moles * enthalpy of fusion

To calculate the moles, we use the molar mass of dinitrogen tetraoxide:

moles = mass / molar mass

Given:
mass = 58.60 g
molar mass = 92.011 g/mol

Next, we need to calculate the heat required to raise the liquid dinitrogen tetraoxide from its melting point to its boiling point. This can be calculated using the formula:

q3 = moles * specific heat capacity * change in temperature

Given:
moles (from previous calculation)
specific heat capacity = 142.7 J/mol•K
change in temperature = (boiling point - melting point) = (21 °C - (-9.3 °C)) = 30.3 °C

Finally, we need to calculate the heat required to vaporize the dinitrogen tetraoxide at its boiling point. This can be calculated using the formula:

q4 = moles * enthalpy of vaporization

Given:
moles (from previous calculation)
enthalpy of vaporization = 38.12 kJ/mol

To find the total heat (q), we sum up all the calculated heats:

q = q1 + q2 + q3 + q4

Make sure to convert the units appropriately to get the final answer in kJ.