Final answer:
To find the entropy of 0.5 mole of helium gas at room temperature and atmospheric pressure, the standard molar entropy from a reference table should be halved to account for the reduced amount of substance, and then expressed in J/K to one decimal place.
Step-by-step explanation:
The Sackur-Tetrode equation is a formula used to calculate the entropy of an ideal monatomic gas. To calculate the entropy of 0.5 mole of helium gas at room temperature (298 K) and atmospheric pressure (1 atm), we first need to determine the standard molar entropy of helium at this condition using entropy values provided in standard tables (since the Sackur-Tetrode equation itself isn't provided).
One mole of helium has a standard molar entropy at these conditions. Using that standard molar entropy, the entropy for 0.5 mole of helium can be calculated by simply dividing the molar entropy by two (since the amount of substance is half a mole).
Assuming that the standard molar entropy of helium gas at 298 K and 1 atm is given by a value S, the entropy of the 0.5 mole of helium gas can be calculated as 0.5 × S. The result should be expressed in units of J/K and rounded to one decimal place.