Which of the following transformations represent an increase in the entropy of the system. choose all that apply
a. 2 mol he (1.42 atm, 470k)2 mol he (1.42 atm, 235k)
b. 4 mol co2 (5.28 l, 205k)4 mol co2 (10.6 l, 205k)
c. 26 g c6h6 (liquid, 353k)26 g c6h6 (gas, 353k)
d. 40 g cu (liquid, 1.356×103k)40 g cu (solid, 1.356×103k)
e. 26 g c6h6 (liquid, 284k)26 g c6h6 (liquid, 348k)

The entropy will increase for option B, C and E

B. 4 mol CO2 (5.28 L, 205K)4 mol CO2 (10.6 L, 205K) (increase volume)

C 26 g C6H6 (liquid, 353K)26 g C6H6 (gas, 353K) (change from liquid to gasphase

E. 26 g C6H6 (liquid, 284K)26 g C6H6 (liquid, 348K)  (increase in temperature)

Explanation:

An increase in entropy means more disorder, or more microstates.  

Going from solid to liquid, or liquid to gas will be an increase in entropy because in each case, the molecules become MORE disordered.  

If no phase change, then an increase in temperature will increase entropy because ∆S = q/T

A. 2 mol He (1.42 atm, 470K)2 mol He (1.42 atm, 235K)

⇒ Here we see a decrease of the temperature. Number of moles and pressure is constant. if temperature decreses randomness disorder between particles will decrease as well.

This means there will be a decrease of entropy

B. 4 mol CO2 (5.28 L, 205K)4 mol CO2 (10.6 L, 205K)

⇒ Here we see, the number of moles and temperature is constant. There is an increase in volume.

When the volume increases, there is more space for the gas molecules to move. More space to move means more disorder. The entropy will increase.

C. 26 g C6H6 (liquid, 353K)26 g C6H6 (gas, 353K)

⇒ Here we see a change from liquid to gas phase.

The particles are no longer locked in place. Because they are now free to move, they can distribute themselves in more ways. This means more disorder. The entropy will increase.

D. 40 g Cu (liquid, 1.356×103K)40 g Cu (solid, 1.356×103K)

⇒ Here we see a change from liquid to solid phase. A solid is more ordered than a liquid. This means the particles are in a place with less disorder. The entropy will decrease.

E. 26 g C6H6 (liquid, 284K)26 g C6H6 (liquid, 348K)

⇒ Here we see an increase in temperature: More energy put into a system excites the molecules and the amount of random activity. This will give more disorder. The entropy increases.