Answer :
Let's solve this step-by-step:
1. Determine the molar mass of ammonia (NH₃):
The molar mass of ammonia is calculated by adding the atomic masses of its constituent atoms:
- Nitrogen (N) has an atomic mass of 14 g/mol.
- Hydrogen (H) has an atomic mass of 1 g/mol, and there are 3 hydrogen atoms in ammonia.
Therefore, the molar mass of NH₃ is:
[tex]\[ 14 + (3 \times 1) = 14 + 3 = 17 \text{ g/mol} \][/tex]
2. Calculate the number of moles of ammonia in 17 grams:
The number of moles ([tex]\(n\)[/tex]) is given by the formula:
[tex]\[ n = \frac{\text{mass}}{\text{molar mass}} \][/tex]
Given the mass of ammonia is 17 grams and the molar mass is 17 g/mol, the number of moles is:
[tex]\[ n = \frac{17 \text{ g}}{17 \text{ g/mol}} = 1 \text{ mole} \][/tex]
3. Determine the number of molecules in 1 mole of ammonia using Avogadro's number:
Avogadro's number ([tex]\(N_A\)[/tex]) is [tex]\(6.023 \times 10^{23}\)[/tex], which is the number of molecules in one mole of a substance.
Since we have 1 mole of ammonia:
[tex]\[ \text{Number of molecules} = 1 \text{ mole} \times 6.023 \times 10^{23} \text{ molecules/mole} = 6.023 \times 10^{23} \text{ molecules} \][/tex]
4. Compare the calculated result with the options:
- Option a: [tex]\(6.023 \times 10^{23}\)[/tex] molecules
- Option b: [tex]\(602.3 \times 10^{23}\)[/tex] molecules
- Option c: [tex]\(\frac{1}{2} \times 6.023 \times 10^{23}\)[/tex] molecules
- Option d: All of the above
From the calculation, we see that 17 grams of ammonia contains [tex]\(6.023 \times 10^{23}\)[/tex] molecules. This matches option a. Options b and c do not match the computed value, and option d cannot be correct because not all the provided options are true.
Thus, the correct answer is:
a. [tex]\(6.023 \times 10^{23}\)[/tex] molecules
1. Determine the molar mass of ammonia (NH₃):
The molar mass of ammonia is calculated by adding the atomic masses of its constituent atoms:
- Nitrogen (N) has an atomic mass of 14 g/mol.
- Hydrogen (H) has an atomic mass of 1 g/mol, and there are 3 hydrogen atoms in ammonia.
Therefore, the molar mass of NH₃ is:
[tex]\[ 14 + (3 \times 1) = 14 + 3 = 17 \text{ g/mol} \][/tex]
2. Calculate the number of moles of ammonia in 17 grams:
The number of moles ([tex]\(n\)[/tex]) is given by the formula:
[tex]\[ n = \frac{\text{mass}}{\text{molar mass}} \][/tex]
Given the mass of ammonia is 17 grams and the molar mass is 17 g/mol, the number of moles is:
[tex]\[ n = \frac{17 \text{ g}}{17 \text{ g/mol}} = 1 \text{ mole} \][/tex]
3. Determine the number of molecules in 1 mole of ammonia using Avogadro's number:
Avogadro's number ([tex]\(N_A\)[/tex]) is [tex]\(6.023 \times 10^{23}\)[/tex], which is the number of molecules in one mole of a substance.
Since we have 1 mole of ammonia:
[tex]\[ \text{Number of molecules} = 1 \text{ mole} \times 6.023 \times 10^{23} \text{ molecules/mole} = 6.023 \times 10^{23} \text{ molecules} \][/tex]
4. Compare the calculated result with the options:
- Option a: [tex]\(6.023 \times 10^{23}\)[/tex] molecules
- Option b: [tex]\(602.3 \times 10^{23}\)[/tex] molecules
- Option c: [tex]\(\frac{1}{2} \times 6.023 \times 10^{23}\)[/tex] molecules
- Option d: All of the above
From the calculation, we see that 17 grams of ammonia contains [tex]\(6.023 \times 10^{23}\)[/tex] molecules. This matches option a. Options b and c do not match the computed value, and option d cannot be correct because not all the provided options are true.
Thus, the correct answer is:
a. [tex]\(6.023 \times 10^{23}\)[/tex] molecules
