To calculate the number of atoms in 85 g of ammonia gas (NH₃), we first need to determine the number of moles of NH₃ in that mass, and then we can find the total number of atoms.
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Calculate the molar mass of NH₃:
- Nitrogen (N): 14.01 g/mol
- Hydrogen (H): 1.01 g/mol (there are 3 hydrogen atoms in NH₃)
The molar mass of NH₃ is calculated as: \[ \text{Molar mass of NH₃} = 14.01 , \text{g/mol} + (3 \times 1.01 , \text{g/mol}) = 14.01 , \text{g/mol} + 3.03 , \text{g/mol} = 17.04 , \text{g/mol} \]
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Calculate the number of moles of NH₃ in 85 g: \[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{85 , \text{g}}{17.04 , \text{g/mol}} \approx 4.99 , \text{mol} \]
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Calculate the total number of molecules in 4.99 moles of NH₃: Using Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol): \[ \text{Number of molecules} = 4.99 , \text{mol} \times 6.022 \times 10^{23} , \text{molecules/mol} \approx 3.00 \times 10^{24} , \text{molecules} \]
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Calculate the total number of atoms in the ammonia molecules: Each molecule of NH₃ contains 4 atoms (1 nitrogen atom and 3 hydrogen atoms). \[ \text{Total number of atoms} = \text{Number of molecules} \times \text{atoms per molecule} \] \[ \text{Total number of atoms} = 3.00 \times 10^{24} , \text{molecules} \times 4 , \text{atoms/molecule} \approx 1.20 \times 10^{25} , \text{atoms} \]
So, there are approximately \(1.20 \times 10^{25}\) atoms in 85 g of ammonia gas.