number of atoms in 50dm^3 of nitrogen gas
There are 6.02E23 molecules of N2 in 22.4 L so there will be
6.02E23 x (50 dm^3/22.4 dm^3) in a 50 dm^3 sample. Since N occurs as N2 in nature there will be twice as many atoms.
To find the number of atoms in a given amount of gas, you need to know the Avogadro's number and the molar volume of the gas.
1. Avogadro's number (NA) is approximately 6.022 × 10^23 atoms/mole. This constant represents the number of atoms or molecules in one mole of any substance.
2. Molar volume is the volume occupied by one mole of gas at a specific temperature and pressure. For gases at standard temperature and pressure (STP), the molar volume is 22.4 liters per mole.
To calculate the number of atoms in 50 dm^3 of nitrogen gas, follow these steps:
1. Convert the volume from dm^3 to liters.
50 dm^3 = 50 liters
2. Calculate the number of moles of nitrogen gas using the Ideal Gas Law equation:
PV = nRT
where P is the pressure (STP = 1 atm), V is the volume (in liters), n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is the temperature (STP = 273 K).
n = (PV) / (RT)
n = (1 atm * 50 L) / (0.0821 L·atm/(mol·K) * 273 K)
n ≈ 2.02 moles
3. Finally, calculate the number of atoms by multiplying the number of moles by Avogadro's number:
Number of atoms = n * Avogadro's number
Number of atoms = 2.02 moles * 6.022 × 10^23 atoms/mole
Therefore, the number of atoms in 50 dm^3 of nitrogen gas is approximately 1.216 × 10^24 atoms.
To calculate the number of atoms in a given volume of gas, you need to use the ideal gas law formula and Avogadro's number.
1. Start by converting the given volume from dm³ to m³
50 dm³ = 50 × 10⁻³ m³
2. Next, we need to calculate the number of moles of nitrogen gas using the ideal gas law formula:
PV = nRT
Where:
P = pressure (assume it is constant)
V = volume in m³
n = number of moles
R = ideal gas constant (approximately 8.314 J/(mol·K))
T = temperature (assume it is constant)
Since we are solving for moles:
n = (PV) / (RT)
3. Substitute the values into the formula:
n = (P × V) / (R × T)
Since we don't have specific values for pressure and temperature, assume they are at standard conditions:
P = 1 atm = 101325 Pa
T = 273 K
R = 8.314 J/(mol·K)
n = (101325 Pa × 50 × 10⁻³ m³) / (8.314 J/(mol·K) × 273 K)
4. Calculate the number of moles.
5. Finally, to find the number of atoms, multiply the number of moles by Avogadro's number (6.022 × 10²³ atoms/mol).
Keep in mind that this calculation assumes that the nitrogen gas is an ideal gas at standard conditions. The actual number of atoms in the given volume may vary depending on the conditions.