Which of these samples contains the fewest molecules? A) 1.0L of H2 at STP (0°C and 1 atm), B) 1.0L of N2 at STP, C) 1.0L of H2 at 20°C and 760 torr, D) 1.0L of N2 at 0°C and 800 torr, or E) 1.0L of He at STP.

The correct answer is:

D) 1.0L of N2 at 0°C and 800 torr, as it is under a higher pressure and will contain the fewest molecules in a fixed volume of 1.0L when compared to the other samples at (or equivalent to) STP.

To determine which sample contains the fewest molecules, we use Avogadro's principle, which states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. Therefore, we can compare the number of molecules in each container by looking at their conditions.

At standard temperature and pressure (STP), which is defined as 0°C (273.15 K) and 1 atm pressure, one mole of any gas occupies 22.4 liters. Since all options except C and D are at STP, we can initially say that samples A, B, and E have the same number of molecules, assuming the volumes are equal and the gases behave ideally, which would be one mole or 6.022 x 10^23 molecules (Avogadro's number).

For sample C: The temperature is increased to 20°C (293.15 K), which means, according to Charles's Law (V1/T1 = V2/T2), that this sample would expand if the pressure remained constant. However, since we are comparing 1.0L samples at different temperatures, a 1.0L sample of H2 at 20°C (and pressure adjusted to 760 torr or 1 atm) would contain the same number of molecules as a 1.0L sample at STP. This is assuming ideal gas behavior, so sample C also contains one mole of H2 molecules.

For sample D: The pressure is increased to 800 torr from 760 torr. According to Boyle's Law (P1V1 = P2V2), if temperature remains constant, increasing pressure would result in a decrease in volume. Here, since we are considering a fixed volume of 1.0L under a higher pressure, the sample will contain more molecules than it would under standard pressure (1 atm or 760 torr). Therefore, sample D would have slightly more molecules than in samples A, B, C, and E at STP.

Taking into account the temperature and pressure conditions for each of these samples and Avogadro's principle, we can conclude that samples A, B, C, and E (all at STP or equivalent conditions for a fixed volume of 1.0L) contain more molecules than sample D.