(a) What sign for Δ𝑆 do you expect when the pressure on 0.600...

Question

(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) Which of the following statements about this process are true? (i) The entropy change you calculated will be the same for at any other constant temperature. (ii) The value of Δ𝑆 you calculated is valid only if the compression is done irreversibly. (iii) If the number of moles of gas being compressed were decreased by a factor of three, the entropy change would increase by a factor of three.

Accepted Answer

(a) Sign of ΔS: When the pressure on a gas is increased isothermally, the volume decreases. Since entropy (ΔS) is related to the disorder or randomness of a system, a decrease in volume at constant temperature typically leads to a decrease in entropy. Therefore, we expect ΔS to be negative.. (b) Calculating ΔS: Use the formula for entropy change for an ideal gas under isothermal conditions: $$ \Delta S = nR \ln \left( \frac{P_1}{P_2} \right) $$, where $$ n  is $$the number of moles, $$ R  is $$the ideal gas constant (8.314 J/mol·K), $$ P_1  is $$the initial pressure, and $$ P_2  is $$the final pressure. Substitute the given values: $$ n = 0.600 $$ mol, $$ P_1 = 0.750 $$ atm, $$ P_2 = 1.20 $$ atm.. (c) Evaluating statements: (i) True, because entropy change for an isothermal process depends only on the initial and final states, not on the path or specific temperature, as long as the temperature is constant. (ii) False, the calculated ΔS is valid for a reversible process; for an irreversible process, the entropy change would be different. (iii) False, if the number of moles is decreased by a factor of three, the entropy change would decrease by a factor of three, not increase.. Additional Consideration: Remember that the natural logarithm function $$ \ln $$ will yield a negative value when the argument is less than 1, which aligns with our expectation of a negative ΔS for compression.. Final Thought: Always check the units and ensure consistency, especially when using the ideal gas constant $$ R . $$Here, we used $$ R = 8.314  J/$$mol·K, which is appropriate for calculations involving entropy in joules.\u003e

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Entropy (ΔS)

Ideal Gas Law

Isothermal Process