Problem 46
Question
What is the entropy change (in \(\mathrm{JK}^{-1} \mathrm{~mol}^{-1}\) ) when \(1 \mathrm{~mol}\) of ice is converted into water at \(0^{\circ} \mathrm{C}\) ? (The enthalpy change for the conversion of ice to liquid water is \(6.0\) \(\mathrm{kJ} \mathrm{mol}^{-1}\) at \(\left.0^{\circ} \mathrm{C}\right)\) (a) \(2.198\) (b) \(21.98\) (c) \(20.13\) (d) \(2.013\)
Step-by-Step Solution
Verified Answer
The entropy change is \(21.98 \text{ J/K/mol}\).
1Step 1: Understand the problem
We need to find the entropy change when 1 mole of ice is converted to water at 0°C. We know the enthalpy change for this process is 6.0 kJ/mol. Entropy change can be calculated using the formula \( \Delta S = \frac{\Delta H}{T} \).
2Step 2: Convert units
Convert the enthalpy change from kJ/mol to J/mol, since we want the entropy change in J/K/mol.\[ \Delta H = 6.0 \text{ kJ/mol} = 6000 \text{ J/mol} \]
3Step 3: Use the entropy formula
We need to calculate the entropy change using the formula \( \Delta S = \frac{\Delta H}{T} \). First, convert the temperature from Celsius to Kelvin (0°C = 273.15 K). Then plug the values into the formula:\[ \Delta S = \frac{6000 \text{ J/mol}}{273.15 \text{ K}} \]
4Step 4: Calculate the entropy change
Perform the division to find the entropy change:\[ \Delta S = \frac{6000}{273.15} \approx 21.98 \text{ J/K/mol} \]
5Step 5: Choose the correct answer
From options (a) to (d), identify which value matches our calculated entropy change of \(21.98 \text{ J/K/mol}\). The correct option is (b).
Key Concepts
Enthalpy ChangePhase TransitionThermodynamicsTemperature Conversion
Enthalpy Change
Enthalpy change is a crucial concept in thermodynamics. It refers to the heat absorbed or released during a chemical or physical process at constant pressure. For phase transitions, such as converting ice to water, it specifically describes the energy required to change the physical state, without altering temperature. Here, the enthalpy change for the ice-to-water transition is given as 6.0 kJ/mol.
To proceed with calculations like entropy change involving this concept, ensure to always match units. Often we need enthalpy in units compatible with other variables, like entropy, often resulting in necessary conversions such as from kJ/mol to J/mol.
Understanding enthalpy change helps us grasp the energy dynamics within reactions and phase changes, emphasizing how energy is conserved and transformed within systems.
To proceed with calculations like entropy change involving this concept, ensure to always match units. Often we need enthalpy in units compatible with other variables, like entropy, often resulting in necessary conversions such as from kJ/mol to J/mol.
Understanding enthalpy change helps us grasp the energy dynamics within reactions and phase changes, emphasizing how energy is conserved and transformed within systems.
Phase Transition
Phase transition involves a material changing its state, such as from solid to liquid. In our exercise, this is the conversion of ice, a solid, to liquid water. These transitions occur at specific temperatures and pressures, and require or release energy, known as the latent heat, which is closely associated with enthalpy change.
During a phase transition like melting, the temperature remains constant while the substance absorbs heat. This is because the energy absorbed goes into changing the state, not the temperature. Understanding these ideas is essential for calculating the entropy change during such processes, as seen in the given solution, where no temperature change occurs until the phase transition is complete.
Key properties that impact phase transitions include:
During a phase transition like melting, the temperature remains constant while the substance absorbs heat. This is because the energy absorbed goes into changing the state, not the temperature. Understanding these ideas is essential for calculating the entropy change during such processes, as seen in the given solution, where no temperature change occurs until the phase transition is complete.
Key properties that impact phase transitions include:
- Temperature
- Pressure
- The amount of substance
Thermodynamics
Thermodynamics is the study of energy, heat, work, and how they interrelate. It provides the principles underpinning the exercise on entropy change. By applying the first law of thermodynamics, we account for energy conservation. The second law introduces entropy, a measure of disorder or randomness in systems.
In our exercise, understanding entropy through thermodynamics tells us about the degree of increase in disorder when ice turns into water. This process exemplifies thermodynamics in action, as we calculate entropy change using the enthalpy change and temperature, representing a core application of the laws governing energy exchange processes.
Important components of thermodynamics comprise:
In our exercise, understanding entropy through thermodynamics tells us about the degree of increase in disorder when ice turns into water. This process exemplifies thermodynamics in action, as we calculate entropy change using the enthalpy change and temperature, representing a core application of the laws governing energy exchange processes.
Important components of thermodynamics comprise:
- Energy conservation (First Law)
- Entropy and spontaneous processes (Second Law)
- Thermal equilibrium and temperature
Temperature Conversion
Temperature conversion is crucial, especially in thermodynamics where calculations often require temperature in Kelvin. This ensures consistency in using the absolute scale required for most thermodynamic formulas, including entropy calculations.
As seen in the exercise, converting from Celsius to Kelvin ensures all variables align correctly for using formulas like entropy change ( \( \Delta S = \frac{\Delta H}{T} \) ). Here 0°C converts to 273.15 K, ensuring accurate application of the entropy formula. This conversion prevents calculation errors that could lead to incorrect results.
Steps for temperature conversion include:
As seen in the exercise, converting from Celsius to Kelvin ensures all variables align correctly for using formulas like entropy change ( \( \Delta S = \frac{\Delta H}{T} \) ). Here 0°C converts to 273.15 K, ensuring accurate application of the entropy formula. This conversion prevents calculation errors that could lead to incorrect results.
Steps for temperature conversion include:
- Add 273.15 to convert Celsius to Kelvin
- Subtract 273.15 to convert Kelvin to Celsius
Other exercises in this chapter
Problem 44
Standard enthalpy and standard entropy changes for the oxidation of ammonia at \(298 \mathrm{~K}\) are \(-382.64 \mathrm{~kJ}\) \(\mathrm{mol}^{-1}\) and \(-145
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For the reaction, \(\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 3 \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{H}_{2} \ma
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2 mole of an ideal gas at \(27^{\circ} \mathrm{C}\) temperature is expanded reversibly from \(2 \mathrm{~L}\) to \(20 \mathrm{~L}\). Find entropy change in cal.
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