A substance has the following properties:

Heat capacities:

1.34 J/g oC (solid)
3.02 J/g oC (liquid)
2.55 J/g oC (gas)

Heat of Fusion = 4.23 kJ/mole
Heat of Vaporization = 23.5 kJ/mole
Boiling Point = 88.5 oC
Melting Point = -30.0 oC
Molar Mass = 96.3 g/mole

How much energy (in kJ) would be needed to heat 55.5 g of this substance from -39.0 to -15.0oC?

42 J

To calculate the energy required, we can break down the heating process into three steps:

1. Heating the substance from its initial temperature (-39.0oC) to its melting point (-30.0oC) as a solid.
2. Melting the solid at the melting point (-30.0oC) and heating the resulting liquid to its boiling point (88.5oC).
3. Vaporizing the liquid at the boiling point (88.5oC) and heating the resulting gas to the final temperature (-15.0oC).

Step 1: Heating the substance as a solid:
The formula to calculate the energy required is Q = m * ΔT * Cp, where Q is the energy, m is the mass, ΔT is the change in temperature, and Cp is the specific heat capacity.

Q1 = 55.5 g * (−30.0oC - (−39.0oC)) * 1.34 J/g oC = -500.34 J

Step 2: Melting the solid:
The energy required to melt the solid is given by the formula Q = n * ΔHf, where Q is the energy, n is the number of moles of the substance, and ΔHf is the heat of fusion.

First, we need to calculate the number of moles (n):
n = molar mass / 1000 * mass, where molar mass is the molar mass of the substance and mass is the mass of the substance we want to melt.

n = 96.3 g/mole / 1000 * 55.5 g = 5.33965 mole

Q2 = 5.33965 mole * 4.23 kJ/mole = 22.5987 kJ

Step 3: Heating the liquid and vaporizing it:
The formula to calculate the energy required is Q = m * ΔT * Cp (for heating the liquid) + n * ΔHv (for vaporization), where Q is the energy, m is the mass, ΔT is the change in temperature, Cp is the specific heat capacity, n is the number of moles, and ΔHv is the heat of vaporization.

Q3 = 55.5 g * (88.5oC - (−30.0oC)) * 3.02 J/g oC + 5.33965 mole * 23.5 kJ/mole = 18196.572 kJ

Now, let's calculate the total energy required:
Total energy = Q1 + Q2 + Q3 = -500.34 J + 22.5987 kJ + 18196.572 kJ = 18618.83 kJ

Therefore, approximately 18618.83 kJ of energy would be needed to heat 55.5 g of this substance from -39.0oC to -15.0oC.

To find the amount of energy needed to heat the substance from -39.0 to -15.0°C, we need to consider three different steps:

1. Heating the substance from its initial temperature of -39.0°C to its melting point of -30.0°C.
2. Melting the substance at its melting point.
3. Heating the substance from its melting point to the final temperature of -15.0°C.

Let's calculate the energy required for each step:

Step 1: Heating from -39.0 to -30.0°C
The temperature change is ΔT1 = -30.0 - (-39.0) = 9.0°C
The mass of the substance is 55.5 g
The specific heat capacity of the solid state is 1.34 J/g·°C

The heat energy required for this step can be calculated using the formula:
q1 = (mass) × (specific heat capacity) × (ΔT1)

q1 = 55.5 g × 1.34 J/g·°C × 9.0°C

Step 2: Melting at the melting point
The heat of fusion is given as 4.23 kJ/mole. To convert this value to Joules per gram, we need to know the molar mass of the substance.

Given:
Heat of Fusion = 4.23 kJ/mole
Molar Mass = 96.3 g/mole

The heat energy required to melt the substance can be calculated using the formula:
q2 = (mass) × (heat of fusion) / (molar mass)

q2 = 55.5 g × (4.23 kJ/mole) / (96.3 g/mole)

Step 3: Heating from the melting point (-30.0°C) to -15.0°C
The temperature change is ΔT3 = -15.0 - (-30.0) = 15.0°C
The specific heat capacity of the liquid state is 3.02 J/g·°C

The heat energy required for this step can be calculated using the formula:
q3 = (mass) × (specific heat capacity) × (ΔT3)

q3 = 55.5 g × 3.02 J/g·°C × 15.0°C

Finally, we can find the total heat energy required by adding up the energies from all three steps:
Total heat energy = q1 + q2 + q3

Once you've computed each of these values, add them together to get the total energy needed in joules. Then, convert joules to kilojoules by dividing the value by 1000.