Problem 60 - Chemistry and Chemical Reactivity

Question

An \(8.82-\mathrm{g}\) sample of \(\mathrm{Br}_{2}\) is placed in an evacuated 1.00 L flask and heated to \(58.8^{\circ} \mathrm{C},\) the normal boiling point of bromine. Describe the contents of the flask under these conditions.

Step-by-Step Solution

Answer

At 58.8°C, within an evacuated container, \(\mathrm{Br}_2\) is predominantly in the vapor phase, with possible liquid-vapor equilibrium.

Step 1: Determine the moles of Br2

First, calculate the number of moles of bromine (\(\mathrm{Br}_2\)) using its molecular weight. The molar mass of bromine (\(\mathrm{Br}_2\)) is approximately \(159.808 \, \text{g/mol}\). Therefore, the number of moles can be found with the formula \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\).\[\text{moles of } \mathrm{Br}_2 = \frac{8.82 \, \text{g}}{159.808 \, \text{g/mol}} \approx 0.0552 \, \text{mol}\]

Step 2: Use the Ideal Gas Law to determine conditions

Since the temperature is the boiling point of bromine, \(\mathrm{Br}_2\) is at its phase change in a gaseous state under these conditions. Apply the ideal gas law \(PV = nRT\). Use: - \(P\) as the pressure in atm- \(V = 1.00 \, \text{L}\)- \(n = 0.0552 \, \text{mol}\)- \(R = 0.0821 \, \text{L atm/mol K}\)- \(T = 331.95 \, K\) (converted from \(58.8^{\circ} \mathrm{C}\) using \(T(\mathrm{K}) = T(^{\circ}\mathrm{C}) + 273.15\))\[\begin{align*}P \times 1.00 \, \text{L} & = 0.0552 \, \text{mol} \times 0.0821 \, \text{L atm/mol K} \times 331.95 \, K \P & \approx 1.50 \, \text{atm}\end{align*}\]

Step 3: Determine the Phase of Bromine

At its boiling point, a substance can exist in both liquid and gas phases simultaneously while in equilibrium. Since the container is evacuated and the pressure from the ideal gas law calculates to around 1.50 atm, most of the \(\mathrm{Br}_2\) would have vaporized. However, equilibrium between liquid and vapor could potentially still exist.

Key Concepts

Moles calculation

In understanding the behaviors of gases and their transformations, **moles calculation** plays a crucial role. Moles allow chemists to quantify the amount of a substance. It represents the number of molecules or atoms present in a given mass. To calculate the number of moles of a substance, the formula used is:

• Moles = \( \frac{\text{mass}}{\text{molar mass}} \).

For the given sample of bromine (\( \mathrm{Br}_2 \)) weighing 8.82 grams, using its molar mass of approximately 159.808 g/mol, we calculate it has about **0.0552 moles**. This involves simply dividing the mass by the molar mass, facilitating the process of understanding and predicting the behavior of substances under various conditions like temperature and pressure.

Boiling point

The **boiling point** is a significant physical property of a substance where it transitions from a liquid to a gas. It is the temperature at which the vapor pressure of the liquid equals the external pressure. On reaching its boiling point, a liquid can begin to transform into a gaseous state as more molecules possess enough energy to break free from the liquid's surface tension.

• For bromine (\( \mathrm{Br}_2 \)), this occurs at 58.8°C.
• During this state, energy is primarily used for phase change rather than increasing temperature.

This transition is essential in processes like chemical reactions where temperature plays a major role. For bromine in our case, reaching this temperature in the flask causes it to start vaporizing, demonstrating the fascinating dynamics of phase change.

Equilibrium between phases

When a substance reaches its **equilibrium between phases**, the number of molecules transitioning from a liquid to a gas equals the number returning from gas to liquid. This balance is especially relevant at the boiling point of a substance where liquid and vapor are often present simultaneously.

• In our scenario, the flask containing bromine is at such an equilibrium at its boiling point of 58.8°C.
• The pressure inside calculated via the Ideal Gas Law was around 1.50 atm, indicating a significant portion of bromine in the gaseous phase.

While the gaseous state dominates in an evacuated flask, a small amount of liquid could still be present. This simultaneous existence of two phases under stable conditions explains some critical industrial operations' dynamics and is a vital concept in understanding mixtures and solutions.