Problem 99 - Chemistry

Question

The molar heat of fusion of sodium metal is 2.60 kJ/mol,whereas its heat of vaporization is 97.0 kJ/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 g sodium at its normal melting point? c. What quantity of heat would be needed to vaporize 1.00 g sodium at its normal boiling point? d. What quantity of heat would be evolved if 1.00 g sodium vapor condensed at its normal boiling point

Step-by-Step Solution

Answer

a. The heat of vaporization is larger than the heat of fusion because breaking intermolecular bonds in a liquid state requires more energy than in a solid state. b. 0.113 kJ of heat is needed to melt 1.00 g of sodium at its normal melting point. c. 4.22 kJ of heat is needed to vaporize 1.00 g of sodium at its normal boiling point. d. 4.22 kJ of heat would be evolved if 1.00 g of sodium vapor condensed at its normal boiling point.

Step 1: a. Comparing heat of fusion and heat of vaporization

Heat of fusion refers to the amount of heat needed to convert a substance from solid to liquid state without changing temperature. Heat of vaporization is the amount of heat required to convert a substance from liquid to gas state, also without changing temperature. The heat of vaporization is larger than the heat of fusion because breaking the intermolecular bonds in a liquid state requires more energy than breaking those in a solid state. In a liquid state, the particles have more freedom to move, so there are more bonds to break before they can become gas particles.

Step 2: b. Calculate the heat needed to melt 1.00 g sodium

To calculate the amount of heat needed, we'll use the formula: Heat (q) = n * ΔH_f, where n is the number of moles, and ΔH_f is the molar heat of fusion. First, we need to convert mass (1.00 g) into moles using the molar mass of sodium (Na) which is 22.99 g/mol: n = mass / molar_mass n = 1.00 g / 22.99 g/mol ≈ 0.0435 mol Now substitute the values into the formula: q = 0.0435 mol * 2.60 kJ/mol ≈ 0.113 kJ So, 0.113 kJ of heat is needed to melt 1.00 g of sodium at its normal melting point.

Step 3: c. Calculate the heat needed to vaporize 1.00 g sodium

Again, we'll use the formula Heat (q) = n * ΔH_v, where this time ΔH_v is the molar heat of vaporization. We have already calculated the number of moles, now substitute the values into the formula: q = 0.0435 mol * 97.0 kJ/mol ≈ 4.22 kJ So, 4.22 kJ of heat is needed to vaporize 1.00 g of sodium at its normal boiling point.

Step 4: d. Quantity of heat evolved during condensation

When sodium vapor condenses, it releases the same amount of heat as it takes to vaporize it. Therefore, the amount of heat evolved in this process is the same as the amount needed to vaporize 1.00 g of sodium at its normal boiling point. So, 4.22 kJ of heat would be evolved if 1.00 g of sodium vapor condensed at its normal boiling point.

Key Concepts

Heat of Fusion

The heat of fusion is the amount of energy required to change a substance from a solid to a liquid at its melting point. This process occurs without any change in temperature. When we provide heat to a solid like sodium to make it melt, we are breaking the bonds holding the atoms in a fixed position.

Why is it important?

• It is a crucial concept for understanding melting processes.
• It helps in calculating the energy required for phase transitions.

Imagine ice turning into water; the heat of fusion is the energy provided to overcome the molecular forces in solid ice. For sodium, this amount is 2.60 kJ/mol, which is relatively low because only slight energy is needed to change sodium from solid to liquid at its melting point.

Enthalpy Change

Enthalpy change (\( \Delta H \)) is a measure of heat change during a chemical reaction, occurring at constant pressure. It can either involve absorption or release of energy. During phase transitions, such as melting or vaporization, we often refer to specific enthalpies like heat of fusion or vaporization.

Types of enthalpy changes

• Exothermic: Releases heat to surroundings (e.g., condensation).
• Endothermic: Absorbs heat from surroundings (e.g., melting or vaporization).

In practical terms, by understanding enthalpy change, scientists can predict how much energy is needed or released when substances change state, like when sodium melts or vaporizes.

Molar Mass

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It is crucial for converting mass into moles, which is necessary to perform calculations involving energy changes for chemical reactions or phase transitions.

For sodium (Na), the molar mass is 22.99 g/mol. This is used to convert the mass of sodium into moles using the formula:

• Number of moles, \( n = \frac{\text{mass}}{\text{molar mass}} \)

Knowing the molar mass allows for precise calculations of energy changes (enthalpy changes) in reactions, such as the heat required to melt a given mass of sodium.

Phase Transition

A phase transition is a change from one state of matter to another, such as solid to liquid (melting), liquid to gas (vaporization), and vice versa. Each transition involves energy changes without altering the temperature of the substance.

Key aspects of phase transitions

• Latent Heat: The energy absorbed or released during a transition without temperature change. This includes heat of fusion and vaporization.
• Different transitions require different amounts of energy depending on molecular interactions.

For sodium, the heat of vaporization (97.0 kJ/mol) is much greater than the heat of fusion due to the greater energy required to break intermolecular forces during vaporization compared to melting. Understanding these concepts is fundamental to complex processes, from simple ice melting to industrial applications involving liquid and gas analogs.