To find the total number of molecules in 34.0 grams of ammonia ([tex]\(NH_3\)[/tex]), we will go through a series of steps involving finding the molar mass, calculating the number of moles, and then using Avogadro's number.
### Step 1: Determine the molar mass of [tex]\(NH_3\)[/tex]
The molar mass of a compound is the sum of the atomic masses of its constituent elements. For [tex]\(NH_3\)[/tex]:
- The atomic mass of nitrogen (N) is 14.01 g/mol.
- The atomic mass of hydrogen (H) is 1.008 g/mol.
Therefore, the molar mass of [tex]\(NH_3\)[/tex] is:
[tex]\[ \text{Molar mass of } NH_3 = 14.01 + (3 \times 1.008) = 17.034 \text{ g/mol} \][/tex]
### Step 2: Calculate the number of moles of [tex]\(NH_3\)[/tex]
To find the number of moles, we use the formula:
[tex]\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} \][/tex]
Given the mass of [tex]\(NH_3\)[/tex] is 34.0 grams, the number of moles is:
[tex]\[ \text{Number of moles of } NH_3 = \frac{34.0 \text{ g}}{17.034 \text{ g/mol}} \approx 1.996 \text{ moles} \][/tex]
### Step 3: Calculate the total number of molecules
Avogadro's number, [tex]\(6.02 \times 10^{23}\)[/tex], is the number of molecules in one mole of a substance. To find the total number of molecules, we multiply the number of moles by Avogadro's number:
[tex]\[ \text{Total number of molecules} = 1.996 \text{ moles} \times 6.02 \times 10^{23} \text{ molecules/mole} \approx 1.2015968 \times 10^{24} \text{ molecules} \][/tex]
### Conclusion
Considering the closest approximation to our calculated number of molecules, which is around [tex]\(1.20 \times 10^{24}\)[/tex] molecules, the correct answer among the given options is:
[tex]\[ \boxed{2.00\left(6.02 \times 10^{23}\right)} \][/tex]
