To calculate the number of nucleons in 10 cm³ of fluorine gas, we follow these steps:
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Determine the molecular formula of fluorine: Fluorine exists as a diatomic molecule (F₂).
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Determine the molar mass of F₂: The atomic mass of fluorine (F) is approximately 19 grams/mol. Therefore, the molar mass of F₂ is: \[ \text{Molar mass of } F_2 = 2 \times 19 , \text{g/mol} = 38 , \text{g/mol} \]
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Use the ideal gas law to find the number of moles in 10 cm³ of fluorine gas at standard conditions:
Standard temperature and pressure (STP) are defined as 0 °C and 1 atm. At STP, 1 mole of any ideal gas occupies approximately 22.4 liters (or 22,400 cm³).
Now, convert the volume to liters: \[ 10 , \text{cm}^3 = 0.010 , \text{L} \]
The number of moles (\( n \)) in this volume can be calculated using the molar volume: \[ n = \frac{\text{Volume}}{\text{molar volume}} = \frac{0.010 , \text{L}}{22.4 , \text{L/mol}} \approx 4.464 \times 10^{-4} , \text{mol} \]
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Calculate the number of F₂ molecules: The number of molecules can be calculated using Avogadro's number (\( N_A \approx 6.022 \times 10^{23} \) molecules/mol): \[ \text{Number of molecules} = n \times N_A \approx 4.464 \times 10^{-4} , \text{mol} \times 6.022 \times 10^{23} , \text{molecules/mol} \approx 2.686 \times 10^{20} , \text{molecules} \]
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Calculate the number of nucleons per molecule: Each molecule of F₂ contains 2 fluorine atoms. Each fluorine atom has 10 nucleons (9 protons and 1 neutron). Therefore, each F₂ molecule contains: \[ 2 , \text{atoms/molecule} \times 10 , \text{nucleons/atom} = 20 , \text{nucleons/molecule} \]
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Calculate the total number of nucleons: \[ \text{Total nucleons} = \text{Number of molecules} \times \text{nucleons per molecule} \] \[ \text{Total nucleons} \approx 2.686 \times 10^{20} , \text{molecules} \times 20 , \text{nucleons/molecule} \approx 5.372 \times 10^{21} , \text{nucleons} \]
Therefore, there are approximately \( 5.372 \times 10^{21} \) nucleons in 10 cm³ of fluorine gas at standard conditions.