Question

The molar heat of fusion of sodium metal is $2.60\mathrm{kJ}/\mathrm{mol}$, whereas its heat of vaporization is $97.0\mathrm{kJ}/\mathrm{mol}$. a. Why is the heat of vaporization so much larger than the heat of fusion? b. What quantity of heat would be needed to melt $1.00\mathrm{g}$ sodium at its normal melting point? c. What quantity of heat would be needed to vaporize $1.00\mathrm{g}$ sodium at its normal boiling point? d. What quantity of heat would be evolved if $1.00\mathrm{g}$ sodium vapor condensed at its normal boiling point?

Short answer

a. The heat of vaporization is larger than the heat of fusion because breaking the bonds between particles in a liquid to form a gas requires more energy than weakening the bonds in a solid to form a liquid. b. The heat needed to melt 1.00 g of sodium is 0.113 kJ. c. The heat needed to vaporize 1.00 g of sodium is 4.219 kJ. d. The heat evolved when 1.00 g of sodium vapor condenses is -4.219 kJ.

Step-by-step solution

Part a: Heat of Vaporization vs. Heat of Fusion

The heat of fusion is the amount of heat required to change a substance from a solid to a liquid, while the heat of vaporization is the amount of heat required to change a substance from a liquid to a gas. For most substances, including sodium, the heat of vaporization is significantly larger than the heat of fusion. This is because when the substance transforms from solid to liquid, the bonds between the particles are weakened, allowing them to move more freely. However, when the substance vaporizes (transforms from liquid to gas), the bonds must be completely broken, which requires more energy. In this case, sodium's heat of vaporization is about 37 times higher than its heat of fusion, which indicates that it takes a lot more heat to convert sodium from a liquid to a gas than from a solid to a liquid.

Part b: Heat needed to melt 1.00 g of sodium

To calculate the heat required to melt 1.00 g of sodium at its normal melting point, we'll use the molar heat of fusion and perform the following steps: 1. Find the moles (n) of sodium: $n={\displaystyle \frac{mass}{molarmass}}$, where the molar mass of sodium is 22.9897 g/mol. 2. Calculate the heat required: $q=n\ast \mathrm{\Delta }{H}_{fusion}$, where $\mathrm{\Delta }{H}_{fusion}$ is the molar heat of fusion (2.60 kJ/mol). Applying these steps, we get: $n={\displaystyle \frac{1.00}{22.9897}}=0.0435mol$ $q=0.0435\ast 2.60=0.113kJ$ Therefore, the heat required to melt 1.00 g of sodium at its normal melting point is 0.113 kJ.

Part c: Heat needed to vaporize 1.00 g of sodium

To calculate the heat required to vaporize 1.00 g of sodium at its normal boiling point, we'll use the molar heat of vaporization and perform the following steps: 1. Use the moles (n) of sodium that we calculated in part b. 2. Calculate the heat required: $q=n\ast \mathrm{\Delta }{H}_{vaporization}$, where $\mathrm{\Delta }{H}_{vaporization}$ is the molar heat of vaporization (97.0 kJ/mol). Applying these steps, we get: $q=0.0435\ast 97.0=4.219kJ$ Therefore, the heat required to vaporize 1.00 g of sodium at its normal boiling point is 4.219 kJ.

Part d: Heat evolved when 1.00 g of sodium vapor condenses

The heat released during the condensation is equal in magnitude, but opposite in sign, to the heat required for vaporization. Therefore, the heat evolved when 1.00 g of sodium vapor condenses at its normal boiling point would be -4.219 kJ. In conclusion, we have explained why the heat of vaporization is larger than the heat of fusion and calculated the heat required for melting and vaporization of 1.00 g sodium, as well as the heat evolved during condensation.

Key concepts

Molar Heat of Fusion

The molar heat of fusion is a critical concept in understanding how substances transition from a solid to a liquid state. This quantity refers to the amount of energy required to melt 1 mole of a solid substance at its melting point.
In the case of sodium, the molar heat of fusion is a relatively small value, 2.60 kJ/mol. This means that it takes 2.60 kJ of energy to convert 1 mole of solid sodium into liquid sodium at its melting point.

The reason why the energy requirement is smaller for fusion than for vaporization is due to the nature of bonding changes. When sodium melts, the particles need energy primarily to overcome some of the intermolecular forces sufficient to allow them to flow past one another, transitioning into a liquid. However, these forces do not have to be entirely broken, unlike what occurs in vaporization.
Thus, the molar heat of fusion gives a clear insight into the energy changes required for melting processes and the nature of the interactions during phase transitions between solids and liquids.

Sodium Heat Calculations

Sodium heat calculations involve determining the amount of heat needed for different phase changes with 1.00 g of sodium. To perform these calculations, it's essential to know both the molar mass of sodium and its molar heats of fusion and vaporization.

The molar mass of sodium is 22.9897 g/mol. For the heat calculation task:

• First, calculate the number of moles of sodium using: $n=\frac{mass}{molarmass}$.
• For a 1.00 g sample, this yields $n\approx 0.0435mol$.

Using the molar heat of fusion (2.60 kJ/mol), the heat required to melt 1.00 g of sodium is:$$q=0.0435\times 2.60\approx 0.113kJ$$
For the heat required to vaporize the same sample, using the heat of vaporization (97.0 kJ/mol), it is:$$q=0.0435\times 97.0\approx 4.219kJ$$
Conducting these calculations helps in quantifying the energy involved in heating processes central to thermochemistry studies involving sodium.

Phase Change Energy

Phase change energy refers to the amount of heat required to change the phase of a given quantity of a substance from one state to another, such as from solid to liquid or liquid to gas. These changes require energy because of the breaking or loosening of intermolecular interactions.
There are two primary types of phase changes involved in this context:

• Fusion (Melting): This is the transition from a solid to a liquid.
  Energy needed to melt depends on the heat of fusion.
• Vaporization: This is the transition from liquid to gas.
  Energy needed to vaporize depends on the heat of vaporization.

In sodium's case, melting requires considerably less energy compared to vaporizing due to fewer changes in bonding states. The larger energy for vaporization stems from the complete separation of particles into a gaseous state.

Understanding phase change energies helps explain why different substances require different amounts of energy to undergo each of these processes, aiding in both chemical education and practical applications.

Thermochemistry Calculations

Thermochemistry calculations are essential for understanding how energy changes in chemical reactions and physical processes like phase transitions. These calculations provide a numerical comprehension of how much energy is absorbed or released when substances change states.

For sodium, specific heat calculations involve:

• Heat of Fusion: Calculating the heat needed to melt sodium using $q=n\times \mathrm{\Delta }{H}_{fusion}$
• Heat of Vaporization: Calculating the heat required to convert liquid sodium into sodium vapor using $q=n\times \mathrm{\Delta }{H}_{vaporization}$
• Condensation: The energy released when sodium vapor condenses is equal to the opposite of the vaporization energy, $q=-4.219kJ$.

Thermochemistry explores these energy balances by co-relating the energy involved with changes in the molecular level.
Such calculations are instrumental in fields ranging from industrial processes to environmental science, each requiring accurate thermal management and energy efficiency.