Questions: How many molecules of ammonia are present in 3.0 g of ammonia (Formula = NH3)?
1.1 x 10^23
1.8 x 10^1
3.6 x 10^23
1.2 x 10^24
2.9 x 10^-25
Transcript text: 6. How many molecules of ammonia are present in 3.0 g of ammonia (Formula $=\mathrm{NH}_{3}$ )?
$1.1 \times 10^{23}$
$1.8 \times 10^{1}$
$3.6 \times 10^{23}$
$1.2 \times 10^{24}$
$2.9 \times 10^{-25}$
Solution
Solution Steps
Step 1: Calculate the Molar Mass of Ammonia
The chemical formula for ammonia is \(\mathrm{NH}_3\). To find the molar mass, we sum the atomic masses of nitrogen and hydrogen:
Nitrogen (N): \(14.01 \, \text{g/mol}\)
Hydrogen (H): \(1.008 \, \text{g/mol}\)
The molar mass of \(\mathrm{NH}_3\) is:
\[
14.01 + 3 \times 1.008 = 17.034 \, \text{g/mol}
\]
Step 2: Calculate the Number of Moles of Ammonia
To find the number of moles in 3.0 g of ammonia, use the formula:
\[
\text{moles of } \mathrm{NH}_3 = \frac{\text{mass}}{\text{molar mass}} = \frac{3.0 \, \text{g}}{17.034 \, \text{g/mol}}
\]
Calculating this gives:
\[
\text{moles of } \mathrm{NH}_3 = 0.1761 \, \text{mol}
\]
Step 3: Calculate the Number of Molecules
Using Avogadro's number (\(6.022 \times 10^{23} \, \text{molecules/mol}\)), calculate the number of molecules:
\[
\text{molecules of } \mathrm{NH}_3 = 0.1761 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol}
\]
Calculating this gives:
\[
\text{molecules of } \mathrm{NH}_3 = 1.060 \times 10^{23}
\]
Final Answer
The closest option to our calculated value is \(1.1 \times 10^{23}\). Therefore, the number of molecules of ammonia in 3.0 g is: