which of the following samples has the greatest number of atoms
20 million O2 molecules
0.1 mole of Fe
2.0 mole of Ar
100 g of Pb
5 g of He
2.0 mole of Ar
20 million O2 has 40 million O atoms.
0.1 mole Fe has 0.1 x 6.022E23 atoms.
2.0 moles Ar has 2.0 x 6.022E23
etc.
Hint:I would convert 100 g Pb and 5g He to moles and compare with the other moles.
Well, let's break down the options.
First, we have 20 million O2 molecules. Now, each O2 molecule consists of two oxygen atoms, so we would have a total of 40 million oxygen atoms.
Next, we have 0.1 mole of Fe. Since each mole of any substance contains Avogadro's number of particles (which is around 6.022 x 10^23), we can assume that 0.1 mole of Fe would contain approximately 6.022 x 10^22 iron atoms.
Now, we have 2.0 moles of Ar. Similar to the previous example, we can calculate that 2.0 moles of Ar would contain approximately 1.2044 x 10^24 argon atoms.
Moving on, we have 100 g of Pb. To calculate the number of atoms in this sample, we need to determine how many moles of Pb are present. Using the molar mass of lead (207.2 g/mol), we find that 100 g of Pb is approximately 0.482 moles. Therefore, we would have about 2.994 x 10^23 lead atoms.
Lastly, we have 5 g of He. Using the molar mass of helium (4.0026 g/mol), we find that 5 g of He is approximately 1.249 moles. Thus, we would have roughly 7.53 x 10^23 helium atoms.
Therefore, the sample with the greatest number of atoms would be the one with 2.0 mole of Ar, containing approximately 1.2044 x 10^24 argon atoms. That's quite a bunch!
To determine which sample has the greatest number of atoms, we need to calculate the number of atoms in each sample.
1. 20 million O2 molecules:
To calculate the number of atoms in this sample, we first need to find the number of moles of O2 molecules:
Number of moles = Number of molecules / Avogadro's number.
Avogadro's number is approximately 6.02 x 10^23.
Number of moles of O2 = 20,000,000 / (6.02 x 10^23 molecules)
Number of moles of O2 ≈ 3.32 x 10^-14 mole.
Since 1 mole of O2 contains 2 moles of oxygen atoms (O), we can multiply the number of moles of O2 by 2 to find the number of atoms:
Number of atoms = Number of moles x Avogadro's number
Number of atoms of O2 = (3.32 x 10^-14 mole) x (6.02 x 10^23 atoms/mole)
Number of atoms of O2 ≈ 1.99 x 10^10 atoms.
2. 0.1 mole of Fe:
In this case, the number of atoms is given directly since 0.1 mole of Fe contains 0.1 x Avogadro's number atoms:
Number of atoms of Fe = 0.1 x 6.02 x 10^23 atoms
Number of atoms of Fe ≈ 6.02 x 10^22 atoms.
3. 2.0 mole of Ar:
Similar to the previous case, we can calculate the number of atoms:
Number of atoms of Ar = 2.0 x Avogadro's number
Number of atoms of Ar ≈ 2.0 x 6.02 x 10^23 atoms
Number of atoms of Ar ≈ 1.20 x 10^24 atoms.
4. 100 g of Pb:
To calculate the number of atoms in this sample, we need to convert the mass of Pb to moles first using its molar mass. The molar mass of Pb is approximately 207.2 g/mole.
Number of moles of Pb = Mass of Pb / Molar mass
Number of moles of Pb = 100 g / 207.2 g/mole
Number of moles of Pb ≈ 0.482 mole.
Number of atoms of Pb = Number of moles x Avogadro's number
Number of atoms of Pb = 0.482 mole x 6.02 x 10^23 atoms/mole
Number of atoms of Pb ≈ 2.90 x 10^23 atoms.
5. 5 g of He:
Similarly, we need to convert the mass of He to moles using its molar mass. The molar mass of He is approximately 4.0026 g/mole.
Number of moles of He = Mass of He / Molar mass
Number of moles of He = 5 g / 4.0026 g/mole
Number of moles of He ≈ 1.25 mole.
Number of atoms of He = Number of moles x Avogadro's number
Number of atoms of He = 1.25 mole x 6.02 x 10^23 atoms/mole
Number of atoms of He ≈ 7.52 x 10^23 atoms.
Now, let's compare the number of atoms in each sample:
- 1.99 x 10^10 atoms (O2 molecules)
- 6.02 x 10^22 atoms (Fe)
- 1.20 x 10^24 atoms (Ar)
- 2.90 x 10^23 atoms (Pb)
- 7.52 x 10^23 atoms (He)
From the calculations, we can see that the sample with the greatest number of atoms is 1.20 x 10^24 atoms of Ar.