To determine the mass of a sample of \( \text{NH}_3 \) containing \( 7.20 \times 10^{24} \) molecules, we'll follow a step-by-step process:
1. Identify Given Values:
- Number of \( \text{NH}_3 \) molecules: \( 7.20 \times 10^{24} \)
- Avogadro's number (number of molecules per mole): \( 6.022 \times 10^{23} \)
- Molar mass of \( \text{NH}_3 \): 17 grams per mole
2. Calculate the Number of Moles:
- Use Avogadro's number to convert the number of molecules to moles.
- The formula to calculate the number of moles is:
[tex]\[
\text{moles of } \text{NH}_3 = \frac{\text{number of molecules of } \text{NH}_3}{\text{Avogadro's number}}
\][/tex]
- Substituting the given values:
[tex]\[
\text{moles of } \text{NH}_3 = \frac{7.20 \times 10^{24}}{6.022 \times 10^{23}} \approx 11.956
\][/tex]
3. Calculate the Mass of \( \text{NH}_3 \):
- Use the number of moles and the molar mass to calculate the mass.
- The formula to calculate the mass is:
[tex]\[
\text{mass of } \text{NH}_3 = \text{moles of } \text{NH}_3 \times \text{molar mass of } \text{NH}_3
\][/tex]
- Substituting the values:
[tex]\[
\text{mass of } \text{NH}_3 = 11.956 \times 17 \approx 203.25
\][/tex]
4. Choose the Closest Answer:
- The calculated mass is approximately 203 grams. Looking at the given options:
- 161 grams
- 187 grams
- 203 grams
- 214 grams
- The closest and most accurate option is 203 grams.
Therefore, the mass of the sample of [tex]\( \text{NH}_3 \)[/tex] containing [tex]\( 7.20 \times 10^{24} \)[/tex] molecules of [tex]\( \text{NH}_3 \)[/tex] is 203 grams.
