Question

The following data have been collected for substance X. Construct a heating curve for substance X. (The drawing does not need to be absolutely to scale, but it should clearly show relative differences.) normal melting point molar heat of fusion normal boiling point molar heat of vaporization \(-15^{\circ} \mathrm{C}\) \(2.5 \mathrm{kJ} / \mathrm{mol}\) \(134^{\circ} \mathrm{C}\) \(55.3 \mathrm{kJ} / \mathrm{mol}\)

Short answer

To construct a heating curve for substance X using the given data: 1. Use the normal melting point (-15°C) and boiling point (134°C) to determine the temperature range for the y-axis. 2. Divide the x-axis into 5 segments representing the distinct phases and phase transitions of substance X. 3. Plot the solid phase as a horizontal line at -15°C. 4. Plot the phase transition from solid to liquid as a diagonal line with a slope determined by the molar heat of fusion (2.5 kJ/mol). 5. Plot the liquid phase as a horizontal line at -15°C. 6. Plot the phase transition from liquid to gas as a diagonal line with a slope determined by the molar heat of vaporization (55.3 kJ/mol). 7. Plot the gas phase as a horizontal line at 134°C.

Step-by-step solution

Determine the y-axis dimensions

The y-axis of the heating curve will represent temperature. Given the normal melting point and boiling point, we know our y-axis should have a range that includes -15°C to 134°C. Choose an appropriate scale for the y-axis, e.g., -20°C to 140°C, with an increment of 20°C. Step 2: Plan the heating curve

Determine the x-axis dimensions

The x-axis will represent the amount of heat energy added to the substance. We do not have exact values for the x-axis, so we will represent it as a relative scale. Divide the x-axis into 5 segments representing the 5 distinct parts of the heating curve. Step 3: Draw the curve

Plot the solid phase

Start at an arbitrary point on the x-axis and draw a horizontal line at -15°C, representing the temperature of substance X in its solid phase. This line will extend until the heat energy required for fusion is reached. Step 4: Draw the curve

Plot the phase transition from solid to liquid

Once the heat energy required for fusion is reached, begin the phase transition by drawing a diagonal line extending upward until it reaches a temperature of -15°C, representing the normal melting point. The slope of this line is determined by the molar heat of fusion (2.5 kJ/mol). Step 5: Draw the curve

Plot the liquid phase

Starting from the end of the diagonal line, draw a horizontal line at -15°C until the heating curve reaches the heat energy required for the substance to reach its normal boiling point (134°C). Step 6: Draw the curve

Plot the phase transition from liquid to gas

When the necessary heat energy is reached, begin the phase transition from liquid to gas by drawing a diagonal line extending upward until it reaches a temperature of 134°C, representing the normal boiling point. The slope of this line is determined by the molar heat of vaporization (55.3 kJ/mol). Step 7: Draw the curve

Plot the gas phase

From the end of the diagonal line representing vaporization, continue the curve horizontally at 134°C. This represents the heating of substance X in its gaseous state. Review the constructed heating curve, which should depict the solid, liquid, and gaseous states of substance X and the phase transitions between them. The curve will not be to an absolute scale but should still clearly represent the relative differences in the data provided.

Key concepts

Phase Transition

Phase transitions are fascinating moments on the heating curve where a substance changes its state, such as from solid to liquid or from liquid to gas. These transitions occur without changing the temperature of the substance even though heat energy is added. During these periods, all the added heat is used to change the state of the substance rather than to increase its temperature.
This is why, on a heating curve, you observe flat, horizontal lines at the melting and boiling points. For Substance X, these horizontal lines appear at its normal melting point of -15°C and its normal boiling point of 134°C. These plateaus indicate the phase transitions, where the substance is absorbing heat but not increasing in temperature.

Molar Heat of Fusion

The molar heat of fusion is the amount of energy needed to convert a mole of a solid into a liquid at its melting point. It is an essential concept in understanding phase transitions, as it helps quantify the energy required to overcome the forces holding the solid structure together.
For substance X, the molar heat of fusion is given as 2.5 kJ/mol. This means that 2.5 kJ of energy is required to melt one mole of substance X at its normal melting point of -15°C. On a heating curve, this requirement is represented by a flat or horizontal line extending at the melting point, indicating that the energy is being used for the phase change from solid to liquid.

Molar Heat of Vaporization

The molar heat of vaporization is crucial for understanding the heating curve as it describes the energy needed to convert a mole of a liquid into a gas at its boiling point. This energy is required to break the intermolecular forces holding liquid molecules close together.
For substance X, the molar heat of vaporization is a significant 55.3 kJ/mol. Such a high energy requirement is common for phase transitions from liquid to gas, as intermolecular forces in a liquid are stronger than in solids. This energy absorption is shown on the heating curve as a horizontal line at the boiling point (134°C), marking the transition from liquid to vapor.

Temperature Change

Temperature change on a heating curve reflects periods where added heat energy results in an increase in the kinetic energy of particles, thereby raising the temperature. Unlike the flat phases, during these periods, the curve trends upward.
For substance X, the curve will angle upwards between melting and boiling points as it exists in liquid form, and again after complete vaporization. The slope of these lines indicates the specific heat capacities of the substance in each phase. The steeper the slope, the less heat is needed to change the temperature, as compared with a flatter slope which indicates more heat is needed.

Heat Energy

Heat energy is the driving force behind the heating curve and all state changes it demonstrates. As heat energy is added to a substance, its temperature can change, or a phase transition can occur. Both processes require energy, and both are visualized in different ways on a heating curve.
In constructing the heating curve for substance X, each segment of the curve represents energy's influence: heating the solid, melting it, heating the liquid, boiling it, and heating the gas. The relative length of each segment corresponds to the relative energy needed — shorter segments mean less energy is required, while longer segments require more.