(a) What sign for ΔS do you expect when the volume of 0.200 mol of an ideal gas at 27 °C is increased isothermally from an initial volume of 10.0 L? (b) If the final volume is 18.5 L, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change?

Verified step by step guidance

1. Step 1: Understand the concept of entropy (ΔS). Entropy is a measure of the disorder or randomness in a system. For an ideal gas, when the volume increases, the disorder increases, leading to a positive change in entropy (ΔS > 0).
2. Step 2: Use the formula for the entropy change of an ideal gas during an isothermal expansion: ΔS = nR ln(V_f/V_i), where n is the number of moles, R is the ideal gas constant (8.314 J/mol·K), V_f is the final volume, and V_i is the initial volume.
3. Step 3: Substitute the given values into the formula: n = 0.200 mol, V_i = 10.0 L, and V_f = 18.5 L. Calculate the natural logarithm of the volume ratio (V_f/V_i).
4. Step 4: Multiply the result from Step 3 by the number of moles (n) and the ideal gas constant (R) to find the entropy change ΔS.
5. Step 5: Address the question about temperature. For an isothermal process, the temperature remains constant, so you do not need to specify the temperature to calculate the entropy change, as it does not appear in the formula for ΔS.

Key Concepts

Entropy (ΔS)

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, an increase in volume for an ideal gas at constant temperature typically leads to an increase in entropy, as the gas molecules have more space to occupy, resulting in greater disorder.

Isothermal Process

An isothermal process occurs at a constant temperature. For an ideal gas, this means that any change in volume will not affect the temperature, allowing us to use the ideal gas law and the formula for entropy change without needing to account for temperature variations.

Entropy Change Calculation

The change in entropy (ΔS) for an ideal gas during an isothermal expansion can be calculated using the formula ΔS = nR ln(Vf/Vi), where n is the number of moles, R is the ideal gas constant, Vf is the final volume, and Vi is the initial volume. This calculation shows how the entropy change is dependent on the ratio of the final and initial volumes.