Question

1. how many moles of magnesium is 3.01 x 10²² atoms of magnesium?
2. how many molecules are in 2.50 moles of o₂?
3. how many moles are in 2.40 x 10⁴ molecules of tin?
4. how many atoms are in 0.850 moles of pb?
5. how many moles are in 2.91 x 10²² atoms of he?
6. how many moles are in 1.23 x 10⁵⁰ molecules of h₂?

Explanation:

Step1: Use Avogadro's number ($N_A = 6.022\times10^{23}$)

The formula to convert number of particles ($N$) to moles ($n$) is $n=\frac{N}{N_A}$, and to convert moles to number of particles is $N = n\times N_A$.

Step2: Solve each problem

Problem 1

Given $N = 3.01\times10^{22}$ atoms of $Mg$.
$n=\frac{3.01\times 10^{22}}{6.022\times10^{23}}=\frac{3.01}{6.022}\times10^{- 1}\approx0.05$ mol

Problem 2

Given $n = 2.50$ moles of $O_2$.
$N=2.50\times6.022\times 10^{23}=1.5055\times10^{24}$ molecules

Problem 3

Given $N = 2.40\times10^{4}$ molecules of $Sn$.
$n=\frac{2.40\times10^{4}}{6.022\times10^{23}}=\frac{2.40}{6.022}\times10^{-19}\approx3.99\times10^{-20}$ mol

Problem 4

Given $n = 0.850$ moles of $Pb$.
$N=0.850\times6.022\times10^{23}=5.1187\times10^{23}$ atoms

Problem 5

Given $N = 2.91\times10^{22}$ atoms of $He$.
$n=\frac{2.91\times10^{22}}{6.022\times10^{23}}=\frac{2.91}{6.022}\times10^{-1}\approx0.0483$ mol

Problem 6

Given $N = 1.23\times10^{50}$ molecules of $H_2$.
$n=\frac{1.23\times10^{50}}{6.022\times10^{23}}=\frac{1.23}{6.022}\times10^{27}\approx2.04\times10^{26}$ mol

Answer:

1. Approximately $0.05$ mol
2. $1.5055\times10^{24}$ molecules
3. Approximately $3.99\times10^{-20}$ mol
4. $5.1187\times10^{23}$ atoms
5. Approximately $0.0483$ mol
6. Approximately $2.04\times10^{26}$ mol