Problem 109 - Chemistry The Molecular Science

Question

The normal boiling point of \(\mathrm{SO}_{2}\) is \(263.1 \mathrm{~K}\) and that of \(\mathrm{NH}_{3}\) is \(239.7 \mathrm{~K}\). At \(-40^{\circ} \mathrm{C}\), would you predict that ammonia has a vapor pressure greater than, less than, or equal to that of sulfur dioxide? Explain.

Step-by-Step Solution

Answer

At \(-40^{\circ} \mathrm{C}\), ammonia has a higher vapor pressure than sulfur dioxide.

Step 1: Convert Temperature

The given temperature is \(-40^{\circ} \mathrm{C}\). First, we need to convert this Celsius temperature to Kelvin. The conversion formula is: \(T_{\text{K}} = T_{\text{C}} + 273.15\). Therefore, \(-40^{\circ} \mathrm{C} = -40 + 273.15 = 233.15 \mathrm{~K}\).

Step 2: Compare Boiling Points and Temperature

Compare the converted temperature (233.15 K) to the normal boiling points of \(\mathrm{SO}_{2}\) (263.1 K) and \(\mathrm{NH}_{3}\) (239.7 K). At 233.15 K, we see that this temperature is below both the boiling points of \(\mathrm{SO}_{2}\) and \(\mathrm{NH}_{3}\).

Step 3: Analyze Vapor Pressure Tendency

The general rule is that substances with higher boiling points tend to have lower vapor pressures at a given temperature below their boiling point. Since ammonia's boiling point (239.7 K) is lower than sulfur dioxide's (263.1 K), it means \(\mathrm{NH}_{3}\) will have a higher vapor pressure compared to \(\mathrm{SO}_{2}\) at 233.15 K.

Key Concepts

Boiling Point

The boiling point of a substance is the temperature at which its vapor pressure equals the external pressure surrounding the liquid. This is the temperature at which the liquid transforms into a gas. Understanding boiling points can help us predict how substances behave under certain temperatures.
For example, in a scenario where we are comparing sulfur dioxide (SO₂) and ammonia (NH₃), butane’s boiling point is lower, we can conclude some aspects of their vapor pressures at given temperatures.
Here are the boiling points:

• The normal boiling point of SO₂ is 263.1 K.
• The normal boiling point of NH₃ is 239.7 K.

Due to their boiling points, if the temperature falls below these points, like at 233.15 K, both substances remain in liquid form. However, NH₃ reaches its boiling point first, showcasing its tendency to move to a gaseous state more readily.

Temperature Conversion

To solve problems involving boiling points and vapor pressures, especially when temperatures are given in Celsius, it's crucial to convert those to Kelvin. Kelvin is preferred in scientific contexts because it begins from absolute zero, a baseline where no molecular motion occurs.
To convert Celsius to Kelvin, use the formula: \[ T_{\text{K}} = T_{\text{C}} + 273.15 \] Applying this formula,

• Given: \(-40^{\circ} \text{C}\)
• Conversion: \[ -40 + 273.15 = 233.15 \text{ K} \]

This conversion is important to understand the behavior of substances like NH₃ and SO₂ at low temperatures in Kelvin scales, making comparisons straightforward.

Vapor Pressure Tendencies

Vapor pressure is the force exerted by a vapor in equilibrium with its liquid at a particular temperature. As temperature increases, so does vapor pressure. To predict vapor pressure tendencies at a specific temperature, it is essential to analyze boiling points.
Here are some key points:

• Substances with higher boiling points generally have lower vapor pressures at temperatures below their boiling points.
• Conversely, substances with lower boiling points tend to have higher vapor pressures at these temperatures.

In our comparison, ammonia (NH₃) has a lower boiling point than sulfur dioxide (SO₂). Therefore, at a temperature of 233.15 K, below both their boiling points, NH₃ demonstrates a higher vapor pressure than SO₂. This is because NH₃ is closer to its boiling temperature, making it easier for its molecules to escape into vapor form.