What is the entropy change when the volume of 1.6 g of O2 increases from 2.5 L to 3.5 L at a constant temperature of 75 °C? Assume that O2 behaves as an ideal gas.

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Convert the mass of O_2 to moles using the molar mass of O_2 (32.00 g/mol).

Use the ideal gas law to find the initial number of moles of O_2, if needed, using PV = nRT, where R is the ideal gas constant.

Apply the formula for entropy change for an ideal gas during a volume change at constant temperature: \( \Delta S = nR \ln \left( \frac{V_f}{V_i} \right) \), where \( V_f \) and \( V_i \) are the final and initial volumes, respectively.

Substitute the values for n (moles of O_2), R (ideal gas constant), \( V_f \) (3.5 L), and \( V_i \) (2.5 L) into the entropy change formula.

Calculate the natural logarithm and multiply by the other terms to find the entropy change, \( \Delta S \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the amount of energy in a physical system that is not available to do work. An increase in volume at constant temperature typically leads to an increase in entropy, as the gas molecules have more space to occupy, resulting in greater disorder.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to predict how gases will behave under various conditions, including changes in volume.

Change in Entropy for an Ideal Gas

The change in entropy (ΔS) for an ideal gas can be calculated using the formula ΔS = nR ln(Vf/Vi), where Vf is the final volume, Vi is the initial volume, n is the number of moles, and R is the ideal gas constant. This equation shows that entropy increases as the volume of the gas increases, reflecting the greater number of accessible microstates available to the gas molecules.

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