Question

which of the following correctly shows the relationship, in terms of number of particles, of the three substances?
1 mole of aluminum < 1 mole helium > 1 mole of water
1 mole of water = 1 mole of helium = 1 mole of aluminum
1 mole of aluminum < 1 mole of helium < 1 mole of water
1 mole of water <1 mole of helium < 1 mole of aluminum

Explanation:

Step1: Recall Avogadro's Number

Avogadro's number ($N_A$) is the number of particles (atoms, molecules, ions, etc.) in one mole of a substance, and it is approximately $6.022\times10^{23}$ particles per mole.

Step2: Analyze Each Substance

• For 1 mole of aluminum: Aluminum is an element, and 1 mole of aluminum contains $6.022\times10^{23}$ aluminum atoms.
• For 1 mole of helium: Helium is a noble gas (element), and 1 mole of helium contains $6.022\times10^{23}$ helium atoms.
• For 1 mole of water ($H_2O$): Water is a compound, and 1 mole of water contains $6.022\times10^{23}$ water molecules.

In terms of the number of particles (atoms for elements, molecules for compounds), 1 mole of any substance contains the same number of particles (Avogadro's number of particles). So, 1 mole of water, 1 mole of helium, and 1 mole of aluminum all have the same number of particles.

Answer:

1 mole of water = 1 mole of helium = 1 mole of aluminum