20% surface sites have absorbed N2. On heating N2 gas is evolved from ...
No. of surface sites = 6.023*10^14 * 1000
occupied sites = 20/100 * 6.023 * 10^14 * 1000 = 6.022/5*10^17
no. of moles of N2 = 0.001 * 0.00246 / 0.0821 * 298 = 10^-7
no. of molecules = 10^-7 * 6.022*10^23 = 6.022 * 10^16
so no. of surface sites per molecule of N2 = (6.022*10^17/5)/(6.022*10^16) = 2
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20% surface sites have absorbed N2. On heating N2 gas is evolved from ...
Surface Sites and N2 Absorption
In this problem, we are given information about the absorption and desorption of N2 gas on surface sites. We need to determine the number of surface sites occupied per molecule of N2.
Given Data:
- Percentage of surface sites that have absorbed N2: 20%
- Pressure of the collected N2 gas: 0.001 atm
- Temperature of the collected N2 gas: 298 K
- Volume of the container: 2.46 cm3
- Density of surface sites: 6.023 × 10^14 cm2
- Surface area: 1000 cm2
Calculating the Number of Moles of N2:
First, we need to calculate the number of moles of N2 gas collected in the container using the ideal gas law equation: PV = nRT.
Given:
- Pressure (P) = 0.001 atm
- Volume (V) = 2.46 cm3 (convert to liters by dividing by 1000)
- Temperature (T) = 298 K
- Gas constant (R) = 0.0821 L.atm/mol.K
Rearranging the equation and solving for n:
n = PV / RT
Substituting the values:
n = (0.001 atm) * (2.46 cm3 / 1000) / (0.0821 L.atm/mol.K * 298 K)
Calculating the value of n, we find that it is approximately 1.02 × 10^-8 mol.
Calculating the Number of Molecules of N2:
To calculate the number of molecules of N2, we need to use Avogadro's number, which states that 1 mole of any substance contains 6.023 × 10^23 entities (atoms, molecules, etc.).
Given:
- Number of moles of N2 (n) = 1.02 × 10^-8 mol
Calculating the number of molecules of N2:
Number of molecules = (Number of moles) * (Avogadro's number)
Substituting the values:
Number of molecules = (1.02 × 10^-8 mol) * (6.023 × 10^23 molecules/mol)
Calculating the value, we find that it is approximately 6.14 molecules.
Calculating the Number of Surface Sites Occupied per Molecule of N2:
To find the number of surface sites occupied per molecule of N2, we need to divide the total number of surface sites by the number of molecules of N2.
Given:
- Total number of surface sites = 6.023 × 10^14 cm2
Calculating the number of surface sites occupied per molecule of N2:
Number of surface sites per molecule = (Total number of surface sites) / (Number of molecules)
Substituting the values:
Number of surface sites per molecule = (6.023 × 10^14 cm2) / (6.14 molecules)
Calculating the value, we find that it is approximately 9.81 × 10^13 cm2/molecule.
Conclusion:
The number of surface sites occupied per molecule of N2 is approximately 9.81 × 10^13 cm2/molecule. However,