Which one of the following samples of gases contains the most particles?
All gases are at 0 °C and 1 atm pressure, when 1 mole of gas has a volume of 22.4 L.
[Relative atomic mass, A_r: H = 1, He = 4, C = 12, O = 16, Cl = 35.5]
A. 33.6 L of chlorine gas
B. 66.0 g of carbon dioxide gas
C. 22.4 L of hydrogen gas
D. 10.0 g of helium gas
E. 64.0 g of oxygen gas
Approach: We need to get all gases into the same unit, and then we need to find the number of particles from here.
Recall:
Number of particles = (Avogadro’s Number)(number of moles)
Avogadro’s number ~ $(6.02)(10)^{23}
For this question, we only need to compare the number of moles since, as you can see, more moles = more particles. You should memorize Avogadro’s regardless because it could be needed for other questions.
Let’s start by converting everything to moles:
Number of Moles = mass / molecular mass
N = m/M
A. 33.6 L of chlorine gas
We are told that 1 mole of gas = 22.4L
B. 66.0 g of carbon dioxide gas
CO_2
Molecular Formula (M): 12g/mol + 2(16g/mol)
M = 44g/mol
C. 22.4 L of hydrogen gas
D. 10.0 g of helium gas
M = 4g/mol
E. 64.0 g of oxygen gas
Remember the diatomic gases when determining molecular weight: HOFBrINCl
Since oxygen is diatomic, its molecular weight in the form of oxygen gas is:
M = (2)(16g/mol) = 32g/mol
As we can see, Helium has the most moles and therefore it has the most particles.
Hi! I understood your explanation, but carbon dioxide is made of 3 atoms (unlike the other gasses in the question) so in my calculation it appears that it has 4.5 moles of particles and therefore more than helium. Can you please explain why ‘particles’ don’t mean atoms in this question?
hi.
I don’t know if I can answer, but usually in chemistry, particle means molecule.
Perhaps the question of finding the number of elements will specify the word element precisely.