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Answer :
Sure, let's solve the problem step-by-step.
### Step 1: Understand the given data
We need to find the mass in grams of [tex]\( 1.70 \times 10^{24} \)[/tex] molecules of Silver azide ([tex]\( AgN_3 \)[/tex]).
### Step 2: Use Avogadro's number
Avogadro's number is [tex]\( 6.022 \times 10^{23} \)[/tex], which tells us the number of molecules in one mole of a substance.
### Step 3: Calculate the molar mass of Silver azide ([tex]\( AgN_3 \)[/tex])
To find the molar mass, we need to add up the atomic masses of all atoms in one molecule of [tex]\( AgN_3 \)[/tex].
- Atomic mass of Silver (Ag): [tex]\( 107.8682 \)[/tex] g/mol
- Atomic mass of Nitrogen (N): [tex]\( 14.0067 \)[/tex] g/mol
Since there are three nitrogen atoms in one molecule:
[tex]\[ \text{Molar mass of } AgN_3 = 107.8682 + 3 \times 14.0067 \][/tex]
[tex]\[ \text{Molar mass of } AgN_3 = 107.8682 + 42.0201 \][/tex]
[tex]\[ \text{Molar mass of } AgN_3 = 149.8883 \, \text{g/mol} \][/tex]
### Step 4: Calculate the number of moles of [tex]\( AgN_3 \)[/tex]
To find the number of moles, we divide the given number of molecules by Avogadro's number.
[tex]\[ \text{Number of moles} = \frac{1.70 \times 10^{24}}{6.022 \times 10^{23}} = 2.82298239787446 \, \text{moles} \][/tex]
### Step 5: Calculate the mass in grams
Finally, to find the mass in grams, we multiply the number of moles by the molar mass.
[tex]\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \][/tex]
[tex]\[ \text{Mass} = 2.82298239787446 \times 149.8883 \][/tex]
[tex]\[ \text{Mass} = 423.1320325473265 \, \text{grams} \][/tex]
### Conclusion
The mass of [tex]\( 1.70 \times 10^{24} \)[/tex] molecules of Silver azide ([tex]\( AgN_3 \)[/tex]) is approximately [tex]\( 423.13 \)[/tex] grams.
### Step 1: Understand the given data
We need to find the mass in grams of [tex]\( 1.70 \times 10^{24} \)[/tex] molecules of Silver azide ([tex]\( AgN_3 \)[/tex]).
### Step 2: Use Avogadro's number
Avogadro's number is [tex]\( 6.022 \times 10^{23} \)[/tex], which tells us the number of molecules in one mole of a substance.
### Step 3: Calculate the molar mass of Silver azide ([tex]\( AgN_3 \)[/tex])
To find the molar mass, we need to add up the atomic masses of all atoms in one molecule of [tex]\( AgN_3 \)[/tex].
- Atomic mass of Silver (Ag): [tex]\( 107.8682 \)[/tex] g/mol
- Atomic mass of Nitrogen (N): [tex]\( 14.0067 \)[/tex] g/mol
Since there are three nitrogen atoms in one molecule:
[tex]\[ \text{Molar mass of } AgN_3 = 107.8682 + 3 \times 14.0067 \][/tex]
[tex]\[ \text{Molar mass of } AgN_3 = 107.8682 + 42.0201 \][/tex]
[tex]\[ \text{Molar mass of } AgN_3 = 149.8883 \, \text{g/mol} \][/tex]
### Step 4: Calculate the number of moles of [tex]\( AgN_3 \)[/tex]
To find the number of moles, we divide the given number of molecules by Avogadro's number.
[tex]\[ \text{Number of moles} = \frac{1.70 \times 10^{24}}{6.022 \times 10^{23}} = 2.82298239787446 \, \text{moles} \][/tex]
### Step 5: Calculate the mass in grams
Finally, to find the mass in grams, we multiply the number of moles by the molar mass.
[tex]\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \][/tex]
[tex]\[ \text{Mass} = 2.82298239787446 \times 149.8883 \][/tex]
[tex]\[ \text{Mass} = 423.1320325473265 \, \text{grams} \][/tex]
### Conclusion
The mass of [tex]\( 1.70 \times 10^{24} \)[/tex] molecules of Silver azide ([tex]\( AgN_3 \)[/tex]) is approximately [tex]\( 423.13 \)[/tex] grams.
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