Question

Mercury has \(\mathrm{mp}=-38.8^{\circ} \mathrm{C}\) and \(\mathrm{bp}=356.6^{\circ} \mathrm{C}\). What, if any, phase changes take place under the following conditions at \(1.0\) atm pressure? (a) The temperature of a sample is raised from \(-30^{\circ} \mathrm{C}\) to \(365^{\circ} \mathrm{C}\). (b) The temperature of a sample is lowered from \(291 \mathrm{~K}\) to \(238 \mathrm{~K}\). (c) The temperature of a sample is lowered from \(638 \mathrm{~K}\) to \(231 \mathrm{~K}\).

Short answer

(a) Liquid to gas, (b) Liquid to solid, (c) Gas to liquid to solid.

Step-by-step solution

Understand Mercury's Phase Changes

Mercury transitions from solid to liquid at the melting point (mp) of \(-38.8°C\) and from liquid to gas at the boiling point (bp) of \(356.6°C\). These are the critical temperatures to determine phase changes.

Analyze Condition (a)

The sample's temperature changes from \(-30^{\circ} \mathrm{C}\) to \(365^{\circ} \mathrm{C}\). Since \(-30^{\circ} \mathrm{C}\) is above the melting point, it starts as liquid. At \(356.6^{\circ} \mathrm{C}\), it boils and changes from liquid to gas. Therefore, during this range, mercury changes state from liquid to gas.

Analyze Condition (b)

Convert temperatures from Kelvin to Celsius:\(291\, \mathrm{K} = 291 - 273.15 = 17.85^{\circ} \mathrm{C}\)\(238\, \mathrm{K} = 238 - 273.15 = -35.15^{\circ} \mathrm{C}\)The temperature changes from \(17.85^{\circ} \mathrm{C}\) (liquid) to \(-35.15^{\circ} \mathrm{C}\) (solid, as \(-35.15^{\circ} \mathrm{C}\) is below mp). Hence, the phase change is from liquid to solid, or freezing occurs.

Analyze Condition (c)

Convert temperatures from Kelvin to Celsius:\(638\, \mathrm{K} = 638 - 273.15 = 364.85^{\circ} \mathrm{C}\)\(231\, \mathrm{K} = 231 - 273.15 = -42.15^{\circ} \mathrm{C}\)The sample's temperature changes from \(364.85^{\circ} \mathrm{C}\) (which is a gas temperature, as it is higher than bp) to \(-42.15^{\circ} \mathrm{C}\) (solid, as it is below mp). First, it condenses from gas to liquid as temperature falls past \(356.6^{\circ} \mathrm{C}\), and then it freezes from liquid to solid as temperature falls past \(-38.8^{\circ} \mathrm{C}\).

Key concepts

Mercury Phase Transitions

Understanding the phase transitions of mercury is essential to grasp how changes in temperature affect its state. Mercury, like many elements, can exist in three primary states: solid, liquid, and gas. These transitions occur at specific temperatures known as the melting point and boiling point.

The melting point of mercury is \(-38.8^{\circ}C\), where it transitions from solid to liquid. Conversely, its boiling point is \(356.6^{\circ}C\), where it changes from liquid to gas. These values are crucial because they determine how mercury behaves under varying temperature conditions. For example:

• Above \(356.6^{\circ}C\), mercury becomes a gas.
• Between \(-38.8^{\circ}C\) and \(356.6^{\circ}C\), it remains a liquid.
• Below \(-38.8^{\circ}C\), it solidifies.

Recognizing these transitions helps predict how mercury will respond to changes, crucial for both practical applications and theoretical understanding.

Melting Point

The melting point of a substance is a key concept in understanding phase changes. For mercury, this is the temperature where it changes from a solid to a liquid, which is \(-38.8^{\circ}C\). This point can be thought of as the threshold temperature. Any rise above this will cause the solid mercury to melt and become liquid.

In context, if a sample of mercury is at a temperature below \(-38.8^{\circ}C\), it remains solid. As soon as the temperature crosses this threshold, mercury begins to transition to a liquid state. This knowledge is critical when handling mercury at varying temperatures, ensuring that you know when it might become liquid and behave differently in its container or system.

Boiling Point

Boiling points indicate the temperature at which a liquid becomes a gas. For mercury, this point is \(356.6^{\circ}C\). At temperatures above this, mercury will be in a gaseous state. Thus, this number is invaluable for industrial processes and safety protocols involving mercury.

When mercury is at temperatures between its melting point and boiling point, it is in liquid form. Upon reaching \(356.6^{\circ}C\), mercury undergoes a phase transition from liquid to gas. Understanding when and how these transitions occur is important for effectively managing mercury in various scientific and industrial settings, even preventing unintended gas release that could be hazardous.

Kelvin to Celsius Conversion

Often temperatures are given in Kelvin in scientific contexts, requiring conversion to Celsius for clarity regarding mercury's phase changes. The conversion from Kelvin to Celsius involves a straightforward calculation: You subtract 273.15 from the Kelvin temperature.

For instance, to convert \(291 \text{ K}\) to Celsius, you do:

• \(291 \text{ K} - 273.15 = 17.85^{\circ}C\)

This places mercury in a liquid state as it is above its melting point. Similarly, \(238 \text{ K}\) becomes:

• \(238 \text{ K} - 273.15 = -35.15^{\circ}C\)

This value falls below the melting point, indicating a solid state.

These conversions help predict and understand the phase of mercury according to the given temperature, facilitating better control and application in lab work and theoretical predictions.