Calculating Molar Heat Of Fusion For Substance X A Step-by-Step Guide
In the realm of thermodynamics, understanding phase transitions and their associated energy changes is crucial. The molar heat of fusion is a key concept in this area, representing the amount of heat required to melt one mole of a substance at its melting point. This article delves into the calculation of the molar heat of fusion, using a sample problem as an example. We'll explore the underlying principles, the formula involved, and a step-by-step solution to enhance your understanding of this important thermochemical property.
The molar heat of fusion, often denoted as ΔHfus, is an intensive property that quantifies the energy needed to convert one mole of a substance from its solid state to its liquid state at its melting point temperature and constant pressure. This energy is used to overcome the intermolecular forces holding the solid structure together, allowing the molecules to move more freely in the liquid phase. The molar heat of fusion is typically expressed in units of Joules per mole (J/mol) or Kilojoules per mole (kJ/mol). When a substance freezes, it releases the same amount of energy as it absorbs when melting, but in the form of heat, the heat released during freezing is known as the molar heat of solidification, and it has the same magnitude but opposite sign as the molar heat of fusion.
The magnitude of the molar heat of fusion depends on the strength of the intermolecular forces within the substance. Substances with strong intermolecular forces, such as ionic compounds or those with extensive hydrogen bonding, tend to have higher molar heats of fusion compared to substances with weaker intermolecular forces, such as nonpolar molecules. This is because more energy is required to break these stronger interactions and allow the substance to transition into the liquid phase.
The fundamental equation used to calculate the heat involved in a phase transition is:
q = nΔH
Where:
- q represents the heat absorbed or released during the phase transition (in Joules or Kilojoules).
- n is the number of moles of the substance undergoing the phase transition.
- ΔH is the molar heat of fusion (or molar heat of vaporization, sublimation, etc., depending on the phase transition) in Joules per mole (J/mol) or Kilojoules per mole (kJ/mol).
This equation highlights the direct relationship between the heat transfer, the number of moles involved, and the molar heat of the phase transition. By rearranging this equation, we can solve for the molar heat of fusion (ΔH) if we know the heat transfer (q) and the number of moles (n):
ΔH = q / n
Let's tackle a practical problem to illustrate the calculation of the molar heat of fusion. Consider the following scenario:
A sample of substance X with a mass of 326.0 g releases 4325.8 calories when it freezes at its freezing point. If substance X has a molar mass of 58.45 g/mol, what is the molar heat of fusion for substance X?
To solve this problem, we'll follow a structured approach, breaking down the calculation into manageable steps.
Step 1: Convert Heat from Calories to Joules
The heat released is given in calories, but the standard unit for energy in thermochemistry is Joules. We'll use the conversion factor 1 calorie (cal) = 4.184 Joules (J) to convert the heat from calories to Joules:
q (in Joules) = q (in calories) × Conversion factor
q (in Joules) = 4325.8 cal × 4.184 J/cal
q (in Joules) = 18099.7 J
Since the substance is releasing heat, this is an exothermic process, and the value of q is negative:
q = -18099.7 J
Step 2: Calculate the Number of Moles of Substance X
To use the formula q = nΔH, we need to determine the number of moles (n) of substance X in the sample. We can calculate this using the mass of the sample and the molar mass of substance X:
n = mass / molar mass
n = 326.0 g / 58.45 g/mol
n = 5.577 moles
Step 3: Apply the Formula to Calculate Molar Heat of Fusion
Now that we have the heat (q) in Joules and the number of moles (n), we can use the formula ΔH = q / n to calculate the molar heat of fusion (ΔH). Remember that since the substance is freezing, we are actually calculating the molar heat of solidification, which is the negative of the molar heat of fusion.
ΔH = q / n
ΔH = -18099.7 J / 5.577 moles
ΔH = -3245.4 J/mol
Since we are looking for the molar heat of fusion, we take the absolute value of the result:
Molar heat of fusion = |−3245.4 J/mol| = 3245.4 J/mol
Step 4: Convert Molar Heat of Fusion to Kilojoules per Mole (kJ/mol)
It's often convenient to express molar heats in kJ/mol. To do this, we divide the value in J/mol by 1000:
Molar heat of fusion (in kJ/mol) = 3245.4 J/mol / 1000 J/kJ
Molar heat of fusion (in kJ/mol) = 3.2454 kJ/mol
Therefore, the molar heat of fusion for substance X is approximately 3.2454 kJ/mol. This means that it requires 3.2454 kJ of energy to melt one mole of substance X at its melting point.
The molar heat of fusion is a valuable property that provides insights into the nature of the substance and its intermolecular forces. It helps in:
- Identifying substances: Different substances have unique molar heats of fusion, making it a useful property for identification.
- Understanding intermolecular forces: A high molar heat of fusion indicates strong intermolecular forces, while a low value suggests weaker interactions.
- Predicting behavior during phase transitions: Knowing the molar heat of fusion allows us to predict how much energy is required or released during melting or freezing processes.
- Applications in various fields: The molar heat of fusion is important in various fields such as chemistry, materials science, and engineering, where phase transitions play a critical role.
The molar heat of fusion is a fundamental thermochemical property that reflects the energy changes associated with phase transitions. By understanding the formula q = nΔH and applying it systematically, we can calculate the molar heat of fusion for various substances. This knowledge is essential for comprehending the behavior of matter and its interactions at the molecular level. The sample problem we worked through provides a clear illustration of the calculation process, and the broader discussion highlights the significance of molar heat of fusion in diverse scientific and engineering applications.
In summary, the molar heat of fusion is an indispensable tool for scientists and engineers working with materials and their transformations, offering valuable insights into the energetic aspects of phase changes. Understanding this concept is crucial for accurately predicting and controlling the behavior of substances in various chemical and physical processes.
