Textbook Question
(b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of ΔSsurr?
Ch.19 - Chemical Thermodynamics
Chapter 19, Problem 28
(a) What sign for ΔS do you expect when the pressure on 0.600 mol of an ideal gas at 350 K is increased isothermally from an initial pressure of 0.750 atm? (b) If the final pressure on the gas is 1.20 atm, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change?
Verified step by step guidance1
Identify the nature of the process: Isothermal compression of an ideal gas, where the temperature remains constant while the pressure increases.
Understand the concept of entropy (ΔS) in relation to the volume and pressure of a gas. For an ideal gas undergoing isothermal compression, the volume decreases as the pressure increases, leading to a decrease in the randomness or disorder of the gas particles, which suggests a negative ΔS.
Use the formula for the entropy change of an ideal gas during an isothermal process: ΔS = nR \ln\left(\frac{V_f}{V_i}\right), where n is the number of moles of the gas, R is the gas constant, and V_f and V_i are the final and initial volumes, respectively. Alternatively, since P_iV_i = P_fV_f for an isothermal process (from the ideal gas law), the formula can be rewritten using pressures as ΔS = nR \ln\left(\frac{P_i}{P_f}\right).
Substitute the given values into the entropy change formula: n = 0.600 mol, R = 8.314 J/(mol·K), P_i = 0.750 atm, and P_f = 1.20 atm. Calculate the natural logarithm of the ratio of the initial to final pressures.
Confirm that specifying the temperature is necessary for the calculation, as it ensures the process is isothermal and validates the use of the ideal gas law in its standard form.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Entropy (ΔS)
Entropy is a measure of the disorder or randomness in a system. In thermodynamics, a positive change in entropy (ΔS > 0) indicates an increase in disorder, while a negative change (ΔS < 0) suggests a decrease in disorder. For an ideal gas, increasing pressure typically leads to a decrease in volume, which can affect the entropy of the system.
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Isothermal Process
An isothermal process occurs at a constant temperature, meaning that any heat added to the system is used to do work rather than change the internal energy. For an ideal gas undergoing an isothermal compression or expansion, the relationship between pressure, volume, and temperature is described by the ideal gas law, and the entropy change can be calculated using specific formulas that account for these conditions.
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Entropy Change Calculation
The entropy change (ΔS) for an ideal gas can be calculated using the formula ΔS = nR ln(P2/P1), where n is the number of moles, R is the ideal gas constant, and P2 and P1 are the final and initial pressures, respectively. While the temperature remains constant in this scenario, it is essential to know the temperature to use the ideal gas law and to understand the context of the entropy change, as it influences the absolute values of entropy.
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Related Practice
Textbook Question
(c) During a certain reversible process, the surroundings undergo an entropy change, ΔSsurr = -78 J/K. What is the entropy change of the system for this process?
Textbook Question
For the isothermal expansion of a gas into a vacuum, ΔE = 0, q = 0, and w = 0. (b) Explain why no work is done by the system during this process.
Textbook Question
(a) What is the difference between a state and a microstate of a system?