Which substance has the higher entropy?
a.) a sample of pure silicon (to be used in a computer chip)or a piece of silicon containing a trace of another element such as boron or phosphorus
b.) O2(g) at 0 degrees C or O2(g) at -50 degrees C
c.) I2(s) or I2(g), both at room temperature
d.) one mole of O2(g) at 1 bar pressure or one mole of O2(g) at 0.01 bar pressure (both at 298 K)
To determine which substance has the higher entropy in each of the given scenarios, we need to understand the factors that affect entropy.
Entropy is a measure of the randomness or disorder of a system. In general, higher entropy is associated with greater disorder, whereas lower entropy suggests more order or organization.
Let's analyze each scenario one by one:
a.) Pure silicon or silicon with a trace of another element:
To assess the entropy, we can consider the arrangement of atoms. A pure silicon crystal has a highly ordered structure and low entropy. In contrast, when a trace of another element like boron or phosphorus is added, it disrupts the ordered silicon lattice, resulting in higher disorder and increased entropy. Therefore, the piece of silicon containing a trace of another element would have higher entropy.
b.) O2(g) at 0 degrees C or O2(g) at -50 degrees C:
Temperature plays a significant role in entropy. As temperature increases, molecules generally gain more energy, move more vigorously, and occupy larger volumes of space. In this case, O2(g) at 0 degrees C would have lower entropy than O2(g) at -50 degrees C, since lower temperature limits molecular motion and reduces the system's disorder.
c.) I2(s) or I2(g) at room temperature:
In general, solids have lower entropy than gases because the particles in a solid are more closely packed and have less freedom of movement. Therefore, I2(s) would have lower entropy compared to I2(g) at room temperature, where the gaseous iodine molecules have more freedom to move around and exhibit greater disorder.
d.) One mole of O2(g) at 1 bar pressure or one mole of O2(g) at 0.01 bar pressure (both at 298 K):
Pressure also influences entropy. When pressure decreases, the volume occupied by the gas molecules increases. An increase in volume leads to greater disorder and higher entropy. Thus, one mole of O2(g) at 0.01 bar pressure would have higher entropy compared to O2(g) at 1 bar pressure.
In summary, the substances with higher entropy in each scenario are:
a.) A piece of silicon containing a trace of another element.
b.) O2(g) at -50 degrees C.
c.) I2(g) at room temperature.
d.) One mole of O2(g) at 0.01 bar pressure.
What's the problem here. You know increased T ALWAYS gets higher S.
solid to gas ALWAYS increases S.
Etc, so what's to ask questions about?