Question

theobromine
molar mass
in this problem, we want to eventually determine the number of
atoms of nitrogen present in a 250.0 g sample of theobromine.
we will follow the pathway below:

g c₇h₈n₄o₂ → mol c₇h₈n₄o₂ → mol n → atoms n

the first step is to convert from grams to moles, so we need the
molar mass of theobromine.

g c₇h₈n₄o₂ → mol c₇h₈n₄o₂ → mol n → atoms n

Explanation:

Step1: Calculate molar mass of \( C_7H_8N_4O_2 \)

Molar mass = \( (7\times12.01) + (8\times1.008) + (4\times14.01) + (2\times16.00) \)
\( = 84.07 + 8.064 + 56.04 + 32.00 = 180.174 \, g/mol \)

Step2: Convert grams to moles of \( C_7H_8N_4O_2 \)

Moles = \( \frac{mass}{molar\ mass} = \frac{250.0\ g}{180.174\ g/mol} \approx 1.3876\ mol \)

Step3: Moles of N from moles of \( C_7H_8N_4O_2 \)

1 mole \( C_7H_8N_4O_2 \) has 4 moles N, so moles N = \( 1.3876\ mol \times 4 = 5.5504\ mol \)

Step4: Convert moles N to atoms N

Atoms = \( moles \times Avogadro's\ number = 5.5504\ mol \times 6.022\times10^{23}\ atoms/mol \approx 3.343\times10^{24}\ atoms \)

Answer:

The number of nitrogen atoms is approximately \( \boldsymbol{3.34\times10^{24}} \) (or more precise \( 3.343\times10^{24} \))