Calculate the number of atoms in 50 dm^3 nitrogen gas
PV=nRT
find n, the number of moles, and then multiply by Avogadro's Number.
... and then double that, since the gas is N2
To calculate the number of atoms in a given volume of gas, we need to use the Avogadro's number, which represents the number of atoms or molecules in one mole of a substance.
The Avogadro's number is approximately 6.022 x 10^23 atoms/molecules per mole.
First, we need to convert the given volume from dm^3 to liters since the Avogadro's number is defined for the SI unit of liter.
1 dm^3 = 1 liter
So, 50 dm^3 = 50 liters.
Next, we need to determine the number of moles of nitrogen gas in this volume.
To do this, we can use the ideal gas equation: PV = nRT.
Since the volume (V) and the temperature (T) are given and the pressure (P) is not specified, we can assume the pressure is constant (e.g., atmospheric pressure) in this calculation.
R is the ideal gas constant, which is 0.0821 L⋅atm/mol⋅K.
Thus, the equation becomes PV = nRT.
Substituting in the known values:
(1 atm) * (50 L) = n * (0.0821 L⋅atm/mol⋅K) * (273.15 K)
Solving for n, we get:
n ≈ (1 atm * 50 L) / (0.0821 L⋅atm/mol⋅K * 273.15 K)
n ≈ 1.871 moles
Finally, we can use Avogadro's number to determine the number of atoms:
Number of atoms = n * Avogadro's number
Number of atoms ≈ 1.871 moles * 6.022 x 10^23 atoms/mole
Number of atoms ≈ 1.125 x 10^24 atoms
Therefore, there are approximately 1.125 x 10^24 atoms in 50 dm^3 of nitrogen gas.
To calculate the number of atoms in a given amount of gas, such as nitrogen gas in this case, we need to use the concept of Avogadro's number and the formula of molar volume.
1. Start by converting the given volume from cubic decimeters (dm^3) to liters (L). Since 1 dm^3 is equal to 1 L, there is no need for conversion in this case.
2. Next, recognize that nitrogen gas (N2) is made up of nitrogen molecules, and we need to calculate the number of molecules first.
3. Use the ideal gas equation "PV = nRT" (where P = pressure, V = volume, n = number of moles, R = ideal gas constant, and T = temperature) to calculate the number of moles of nitrogen gas. However, since the equation gives the moles of gas, we still need to determine the number of molecules.
4. Rearrange the equation to solve for n:
n = (PV) / (RT)
5. Determine the values needed for the equation:
- P: The pressure should be given or assumed.
- V: The volume in liters, which is 50 L in this case.
- R: The ideal gas constant is 0.0821 L.atm/(mol.K).
- T: The temperature, assume room temperature (298 K).
6. Plug in the values into the equation:
n = [(P) * (V)] / [(R) * (T)]
7. Calculate the number of moles of nitrogen gas.
8. Now, recall that one mole of a gas contains Avogadro's number of molecules, which is approximately 6.022 x 10^23.
9. Multiply the number of moles of nitrogen gas by Avogadro's number to get the number of molecules.
10. Finally, since one molecule of nitrogen gas (N2) consists of two nitrogen atoms, multiply the number of molecules calculated by 2 to get the total number of atoms.
Following these steps, you can calculate the number of atoms in 50 dm^3 of nitrogen gas.