To calculate the number of atoms in 50 dm³ of nitrogen gas (N₂), we can follow these steps:
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Use the Ideal Gas Law: At standard temperature and pressure (STP), 1 mole of any ideal gas occupies approximately 22.4 dm³.
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Calculate the number of moles in 50 dm³ of N₂: \[ \text{Number of moles (n)} = \frac{\text{Volume (V)}}{\text{Molar volume at STP (M)}} = \frac{50 , \text{dm}³}{22.4 , \text{dm}³/\text{mol}} \approx 2.2321 , \text{mol} \]
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Calculate the number of N₂ molecules: Since 1 mole of gas contains Avogadro's number of molecules (approximately \(6.022 \times 10^{23}\) molecules/mol), \[ \text{Number of molecules} = \text{moles} \times N_A = 2.2321 , \text{mol} \times 6.022 \times 10^{23} , \text{molecules/mol} \approx 1.344 \times 10^{24} , \text{molecules} \]
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Calculate the number of nitrogen atoms: Since each nitrogen molecule (N₂) contains 2 nitrogen atoms, \[ \text{Number of atoms} = \text{Number of molecules} \times 2 \approx 1.344 \times 10^{24} , \text{molecules} \times 2 \approx 2.688 \times 10^{24} , \text{atoms} \]
Thus, there are approximately \(2.688 \times 10^{24}\) nitrogen atoms in 50 dm³ of nitrogen gas at STP.