Oxygen molecules contain two oxygen atoms, and carbon dioxide molecules contain one atom of carbon and two atoms of oxygen. How does the total number of molecules in 1 liter of oxygen compare with the total number of atoms in 1 liter of carbon dioxide if they are both at the same tempature and pressure?
Thank you.
total number of atoms: 3*avagradrosnumber
total number of O2 molecules: avagradnumber
this is for one volume, 1/22.4 mole of each CO2 and O2
To compare the total number of molecules in 1 liter of oxygen with the total number of atoms in 1 liter of carbon dioxide at the same temperature and pressure, we need to use Avogadro's law and the molecular formulas of oxygen and carbon dioxide.
Avogadro's law states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This means that for every liter of gas, the number of molecules is the same.
Let's find the number of molecules in 1 liter of oxygen:
1. We know that the molecular formula of oxygen is O2, meaning each oxygen molecule consists of 2 oxygen atoms.
2. The molar mass of oxygen is 32 g/mol.
3. Using Avogadro's constant (6.022 x 10^23 molecules/mol), we can find the number of molecules in 1 liter of oxygen.
Calculating the number of molecules in 1 liter of oxygen:
- Molar mass of oxygen (O2) = 32 g/mol
- Number of molecules in 1 mole (Avogadro's constant) = 6.022 x 10^23 molecules/mol
Number of moles of oxygen in 1 liter:
- 1 mole of oxygen has a volume of 22.4 liters at standard temperature and pressure (STP) conditions.
- Therefore, 1 liter of oxygen is (1/22.4) of a mole.
Number of molecules in 1 liter of oxygen:
- Multiply the number of moles of oxygen (1/22.4) by Avogadro's constant (6.022 x 10^23 molecules/mol) to get the total number of molecules.
Now, let's find the total number of atoms in 1 liter of carbon dioxide:
1. The molecular formula of carbon dioxide is CO2, meaning each carbon dioxide molecule contains 1 carbon atom and 2 oxygen atoms.
Calculating the total number of atoms in 1 liter of carbon dioxide:
- For every molecule of carbon dioxide, we have 1 carbon atom and 2 oxygen atoms.
- Since equal volumes contain the same number of molecules, the number of atoms in 1 liter of carbon dioxide is the same as the number of molecules.
Comparing the total number of molecules in 1 liter of oxygen with the total number of atoms in 1 liter of carbon dioxide:
- Using Avogadro's law, we know that equal volumes of gases at the same temperature and pressure contain an equal number of molecules.
- Therefore, the total number of molecules in 1 liter of oxygen is equal to the total number of atoms in 1 liter of carbon dioxide.
In conclusion, the total number of molecules in 1 liter of oxygen is equal to the total number of atoms in 1 liter of carbon dioxide if they are both at the same temperature and pressure.