Problem 35 - Chemistry and Chemical Reactivity

Question

Benzene, \(\mathrm{C}_{6} \mathrm{H}_{6},\) is an organic liquid that freezes at \(\left.5.5^{\circ} \mathrm{C} \text { (Figure } 11.1\right)\) to form beautiful, feather-like crystals. How much energy is evolved as heat when \(15.5 \mathrm{g}\) of benzene freezes at \(5.5^{\circ} \mathrm{C} ?\) (The enthalpy of fusion of benzene is \(9.95 \mathrm{kJ} / \mathrm{mol} .\) ) If the \(15.5-\mathrm{g}\) sample is remelted, again at \(5.5^{\circ} \mathrm{C},\) what quantity of energy is required to convert it to a liquid?

Step-by-Step Solution

Answer

The energy evolved when benzene freezes is approximately 1.976 kJ and the same amount is required to remelt it.

Step 1: Calculate Moles of Benzene

Determine the number of moles of benzene in 15.5 g. The molecular weight of benzene \( \mathrm{C}_6 \mathrm{H}_6 \) is calculated as follows:\[ \text{Molar Mass} = 6(12.01) + 6(1.01) = 78.12 \, \text{g/mol} \]Number of moles \( n \) is:\[ n = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} = \frac{15.5 \, \text{g}}{78.12 \, \text{g/mol}} \approx 0.1986 \, \text{mol} \]

Step 2: Calculate Energy Evolved During Freezing

Use the enthalpy of fusion \( \Delta H_f = 9.95 \, \text{kJ/mol} \) to determine the energy evolved:\[ \text{Energy evolved} = n \times \Delta H_f = 0.1986 \, \text{mol} \times 9.95 \, \text{kJ/mol} \approx 1.976 \, \text{kJ} \]

Step 3: Calculate Energy Required for Melting

The energy required to melt the benzene is the same as the energy evolved during freezing, due to the conservation of energy. Thus:\[ \text{Energy required} = 1.976 \, \text{kJ} \]

Key Concepts

Freezing Point

The concept of freezing point is pivotal in understanding phase transitions. The freezing point is the specific temperature at which a liquid turns into a solid. For benzene, this occurs at precisely \(5.5^{\circ} \text{C}\). At this temperature, the molecules of benzene lose the energy needed to keep them in a liquid state. Therefore, they arrange themselves into a structured solid form, known as a crystal.

Knowledge of freezing points helps us predict and understand when a substance changes its phase from liquid to solid. It's also fundamental in applications such as designing cryogenics, food preservation, and understanding atmospheric processes.

• Freezing points vary between substances.
• They help in identifying and characterizing chemicals.
• They can indicate purity levels of substances, since impurities generally lower the freezing point.

Molecular Weight

Molecular weight, also known as molar mass, is essential in calculating how much of a substance is involved in a chemical reaction, such as freezing. For benzene \( (\text{C}_6 \text{H}_6) \) the molecular weight is calculated by adding the atomic masses of its constituent atoms:

\[ \text{Molar Mass} = 6(12.01 \, \text{g/mol (carbon)}) + 6(1.01 \, \text{g/mol (hydrogen)}) = 78.12 \, \text{g/mol}\]

This means that every mole of benzene weighs 78.12 grams. Knowing the molecular weight allows you to convert a given mass of benzene to moles, a measurement that is more useful in chemical calculations:

• Calculate the number of moles by dividing the mass by the molecular weight.
• This conversion is crucial in determining how much heat is evolved or absorbed in a reaction.
• Molecular weight provides insight into the quantitative aspects of chemistry.

Energy Conservation

Energy conservation is a core principle in chemistry, shown clearly in the interactions between freezing and melting. When benzene at its freezing point becomes solid, the energy in the form of enthalpy of fusion is released as heat. This is the concept of energy conservation at work: the energy is neither created nor destroyed but merely changes form.

Similarly, to remelt the benzene, the same amount of energy needs to be absorbed back. In our benzene scenario, during its phase change at \(5.5^{\circ} \text{C}\), the energy evolved and energy required both equal approximately \(1.976 \text{kJ}\).

• Conservation of energy can predict energy needs in phase transitions.
• Ensures that calculations in chemical reactions adhere to nature's fundamental laws.
• Can be applied across various scientific disciplines to analyze energetic processes.

Organic Chemistry

Organic chemistry is the field addressing the structure, properties, composition, reactions, and preparation of carbon-containing compounds. Benzene \( \text{(C}_6 \text{H}_6) \) is a prominent example due to its simple aromatic structure.

Understanding benzene in terms of freezing and melting introduces students to how organic compounds behave in different physical states. It also shows the critical role that carbon structures play in determining chemical and physical properties.

• Benzene's structure contributes to its stability and reactivity.
• Offers insight into the development of synthetic substances.
• Forms the basis for studying more complex organic molecules.