Calculate the number of atoms in 50dm³ nitrogen gas
To calculate the number of atoms in 50 dm³ of nitrogen gas (N₂), we need to use Avogadro's number and the molar volume of a gas at standard temperature and pressure (STP).
1. Convert 50 dm³ to liters:
50 dm³ = 50 liters
2. Determine the molar volume at STP:
At STP, 1 mole of any gas occupies 22.4 liters.
3. Calculate the number of moles of nitrogen gas:
50 liters / 22.4 liters/mol = 2.23 moles
4. Use Avogadro's number to calculate the number of atoms:
1 mole of any substance contains 6.022 x 10²³ entities (atoms, molecules, etc.).
2.23 moles x (6.022 x 10²³ atoms/mole) = 1.3443 x 10²⁴ atoms
Therefore, there are approximately 1.3443 x 10²⁴ atoms in 50 dm³ of nitrogen gas.
To calculate the number of atoms in a given amount of gas, we first need to determine the number of moles of the gas using the ideal gas equation:
PV = nRT
Where:
P = pressure (in Pascals)
V = volume (in cubic meters)
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
Given:
Volume (V) = 50 dm³ = 0.05 m³
Since the volume is given in dm³, we need to convert it to cubic meters by dividing it by 1000 (since 1 dm³ = 0.001 m³).
V = 0.05 m³
Now, we need to determine the number of moles (n) of nitrogen gas. Since the question doesn't provide information about the pressure or temperature, we'll assume standard conditions of pressure and temperature.
Standard pressure (P) = 1 atmosphere = 101325 Pascals
Standard temperature (T) = 273.15 Kelvin
We can now calculate the number of moles (n) using the ideal gas equation:
PV = nRT
n = PV / RT
n = (101325 * 0.05) / (8.314 * 273.15)
n = 4.89378 moles (rounded to 5 decimal places)
Finally, we can calculate the number of atoms using Avogadro's number (6.022 x 10^23 atoms/mol):
Number of atoms = n * Avogadro's number
Number of atoms = 5 * 6.022 x 10^23
Number of atoms = 3.011 x 10^24 atoms
Therefore, there are approximately 3.011 x 10^24 atoms in 50 dm³ of nitrogen gas.