Question

how many atoms of n are in 137.0 grams of n₂o₃?
a. 1.085×10²³
b. 1.802×10²³
c. 5.985×10²³
d. 2.171×10²⁴
e. 3.604×10²⁴

Explanation:

Step1: Calculate molar mass of N₂O₃

The molar mass of N is 14.01 g/mol and of O is 16.00 g/mol. For N₂O₃, molar mass $M=(2\times14.01 + 3\times16.00)$ g/mol$= 76.02$ g/mol.

Step2: Calculate moles of N₂O₃

Number of moles of N₂O₃, $n=\frac{m}{M}$, where $m = 137.0$ g. So $n=\frac{137.0}{76.02}$ mol$\approx1.802$ mol.

Step3: Calculate moles of N

In one - mole of N₂O₃, there are 2 moles of N. So moles of N in 1.802 mol of N₂O₃ is $n_N=2\times1.802$ mol = 3.604 mol.

Step4: Calculate number of N atoms

Using Avogadro's number $N_A = 6.022\times10^{23}$ atoms/mol. The number of N atoms, $N=n_N\times N_A=3.604\times6.022\times10^{23}$ atoms$\approx2.171\times 10^{24}$ atoms.

Answer:

D. $2.171\times 10^{24}$