Question

b. converting number of particles to moles
n = n / nₐ (nₐ ≈ 6.02×10²³)
where:
n = number of moles (mol)
n = the number of particles
nₐ = avogadros constant (6.02×10²³ particles/mol)
example:
how many moles are in 1.204×10²⁴ argon atoms?
n =?
n = 1.204×10²⁴ atoms
nₐ = 6.02×10²³ atoms/mol
n = n / nₐ
n = (1.204×10²⁴ atoms) / (6.02×10²³ atoms/mol)
n = 1.999 mol
test yourself

1. how many moles are present in 5.83×10²⁴ molecules of co₂?
2. how many moles are present in 8.5×10²² formula units of magnesium sulfate?
3. a sample of bauxite ore (clay) contains 7.71×10²⁴ formula units of aluminum oxide, al₂o₃. how many moles of aluminum oxide are in the sample?

Explanation:

Step1: Identify the formula

Use the formula $n=\frac{N}{N_A}$, where $n$ is the number of moles, $N$ is the number of particles, and $N_A = 6.02\times10^{23}\text{ particles/mol}$.

Step2: Solve for sub - question 1

Given $N = 5.83\times 10^{24}$ molecules of $CO_2$.
$n=\frac{5.83\times 10^{24}\text{ molecules}}{6.02\times 10^{23}\text{ molecules/mol}}=\frac{5.83}{6.02}\times10^{24 - 23}\text{ mol}\approx0.97\times10^{1}\text{ mol}=9.7\text{ mol}$

Step3: Solve for sub - question 2

Given $N = 8.5\times 10^{22}$ formula units of magnesium sulfate.
$n=\frac{8.5\times 10^{22}\text{ formula units}}{6.02\times 10^{23}\text{ formula units/mol}}=\frac{8.5}{6.02}\times10^{22-23}\text{ mol}\approx1.41\times10^{-1}\text{ mol}=0.141\text{ mol}$

Step4: Solve for sub - question 3

Given $N = 7.71\times 10^{24}$ formula units of $Al_2O_3$.
$n=\frac{7.71\times 10^{24}\text{ formula units}}{6.02\times 10^{23}\text{ formula units/mol}}=\frac{7.71}{6.02}\times10^{24 - 23}\text{ mol}\approx1.28\times10^{1}\text{ mol}=12.8\text{ mol}$

Answer:

1. $9.7\text{ mol}$
2. $0.141\text{ mol}$
3. $12.8\text{ mol}$