At STP 4 liters of O2 contains the same total number of molecules as
1L of NH3
2L of Cl2
8L of He
4L of CO2
Reason this out.
If PV = nRT, then solve for n.
n for O2 = PV/RT
If P is the same, V is 4L, R is the same and T is the same, then n = constant*V or 4*constant.
So for any other gas at same conditions, what must be true. For n to be the same and the constant is the same, then the 4 must be the same.
To compare the total number of molecules in different gases, we can use Avogadro's law, which states that equal volumes of gases at the same temperature and pressure contain the same number of molecules. The key is to compare the volumes of the gases and then calculate the respective amounts of moles to determine the total number of molecules.
First, let's determine the number of moles of O2 in 4 liters at STP (Standard Temperature and Pressure).
At STP, 1 mole of any ideal gas occupies a volume of 22.4 liters. Therefore, we can calculate the number of moles of O2 using the following equation:
moles of O2 = (volume of O2 / 22.4 L/mol)
moles of O2 = 4 L / 22.4 L/mol
moles of O2 ≈ 0.179 moles
Now, let's compare the number of moles of O2 with the other gases:
1. NH3:
To determine the number of moles of NH3 in 1 liter, we use the equation:
moles of NH3 = (volume of NH3 / 22.4 L/mol)
moles of NH3 = 1 L / 22.4 L/mol
moles of NH3 ≈ 0.045 moles
Since 0.179 moles of O2 is greater than 0.045 moles of NH3, 4 liters of O2 contains a greater total number of molecules than 1 liter of NH3.
2. Cl2:
To determine the number of moles of Cl2 in 2 liters, we use the same equation:
moles of Cl2 = (volume of Cl2 / 22.4 L/mol)
moles of Cl2 = 2 L / 22.4 L/mol
moles of Cl2 ≈ 0.089 moles
Again, 0.179 moles of O2 is greater than 0.089 moles of Cl2, so 4 liters of O2 contains a greater total number of molecules than 2 liters of Cl2.
3. He:
To determine the number of moles of He in 8 liters, we use the equation:
moles of He = (volume of He / 22.4 L/mol)
moles of He = 8 L / 22.4 L/mol
moles of He ≈ 0.357 moles
Once more, 0.179 moles of O2 is less than 0.357 moles of He, so 4 liters of O2 contains fewer molecules than 8 liters of He.
4. CO2:
To determine the number of moles of CO2 in 4 liters, we again use the equation:
moles of CO2 = (volume of CO2 / 22.4 L/mol)
moles of CO2 = 4 L / 22.4 L/mol
moles of CO2 ≈ 0.179 moles
Here, we find that 0.179 moles of O2 is equal to 0.179 moles of CO2. Therefore, both 4 liters of O2 and 4 liters of CO2 contain the same total number of molecules.
In summary:
- 4 liters of O2 contains a greater total number of molecules compared to 1 liter of NH3 and 2 liters of Cl2.
- 4 liters of O2 contains the same total number of molecules as 4 liters of CO2.
- 4 liters of O2 contains fewer molecules compared to 8 liters of He.