Calculate the number of (a) atoms in 50 dm^3 nitrogen gas (b)nucleons in 10 cm^3 fluorine gas
you know Avogadro's Number, AN=6.023*10^23
Also, 1 mole occupies 22.4L (22400 cm^3) at STP.
(a) (50dm^3)/(22400cm^3) * AN = ?
(b) (10cm^3)/(22400cm^3) * AN * 19 = ?
(because F has 19 nucleons/atom)
2 atoms N for every molecule N2.
1 mol occupies 22.4 dm^3; therefore,
mols F2 = 50 dm^3 x (1 mol/22.4 dm^3) = ?
# atoms = twice that.
b.Which F2? I assume F-19
Calculate mols F2 as above.
Then remember there are 19 nucleons in 1 molcule Fe.
There are two F atoms/molecule so twice that.
Dang. I forgot about the molecules, not atoms.
That Fe should be F2. Sorry about that
(a) Well, if we want to calculate the number of atoms in 50 dm^3 of nitrogen gas, we need to channel our inner nitrogen enthusiast.
First, we need to know the volume occupied by one mole of nitrogen gas at standard temperature and pressure (STP). It turns out that one mole of any gas at STP occupies a volume of 22.4 liters or 22.4 dm^3.
So, if we have 50 dm^3 of nitrogen gas, we can say that it is approximately equal to 50/22.4 moles of nitrogen gas.
And since we know that one mole of any substance contains 6.022 x 10^23 particles (Avogadro's number), we can multiply the number of moles by Avogadro's number to find the number of atoms.
So, you ready for the punchline?
The number of atoms in 50 dm^3 of nitrogen gas is approximately 6.022 x 10^23 times (50/22.4).
(b) Now, let's calculate the number of nucleons in 10 cm^3 of fluorine gas.
But before we do that, let's give a quick chemistry lesson: A nucleon is either a proton or a neutron. You could think of nucleons as the comedy duo of the atomic nucleus. They really know how to bring the atomic party to life!
So, fluorine is a bit of a party animal itself and has 9 protons and 10 electrons. Since the atomic number of fluorine is 9, we know that it has 9 protons (and also 9 electrons... they never like to get separated).
Now, to calculate the number of nucleons in 10 cm^3 of fluorine gas, we need to calculate the number of moles of fluorine gas.
To do that, we can use the ideal gas law, but since we're getting deep into atomic comedy here, let's get straight to the punchline:
The number of nucleons in 10 cm^3 of fluorine gas is approximately equal to 9 times (10/22.4), where 9 comes from the number of protons in fluorine.
To calculate the number of atoms (a) in a given volume of gas, we need to convert the volume to liters and then use Avogadro's constant. Avogadro's constant is defined as 6.022 × 10^23 particles per mole.
(a) To calculate the number of atoms in 50 dm^3 of nitrogen gas:
Step 1: Convert the volume from cubic decimeters (dm^3) to liters (L).
1 dm^3 = 1 L
So, 50 dm^3 = 50 L
Step 2: Use Avogadro's constant to calculate the number of moles of nitrogen gas.
Number of moles = Volume (in liters) / 22.4 L (molar volume at standard temperature and pressure)
Number of moles = 50 L / 22.4 L
Number of moles = 2.23 moles (approx.)
Step 3: Multiply the number of moles by Avogadro's constant to get the number of atoms.
Number of atoms = Number of moles × Avogadro's constant
Number of atoms = 2.23 moles × 6.022 × 10^23 atoms/mole
Number of atoms = 1.342 × 10^24 atoms
Therefore, there are approximately 1.342 × 10^24 atoms in 50 dm^3 of nitrogen gas.
(b) To calculate the number of nucleons in 10 cm^3 of fluorine gas:
The nucleons refer to the total number of protons and neutrons in the nucleus of an atom.
Step 1: Convert the volume from cubic centimeters (cm^3) to liters (L).
1 cm^3 = 1 × 10^-3 L
So, 10 cm^3 = 10 × 10^-3 L = 0.01 L
Step 2: Use Avogadro's constant to calculate the number of moles of fluorine gas.
Number of moles = Volume (in liters) / 22.4 L
Number of moles = 0.01 L / 22.4 L
Number of moles = 4.46 × 10^-4 moles (approx.)
Step 3: Multiply the number of moles by Avogadro's constant to get the number of fluorine atoms.
Number of nucleons = Number of moles × Avogadro's constant × atomic mass of fluorine
Atomic mass of fluorine = 19
Number of nucleons = 4.46 × 10^-4 moles × 6.022 × 10^23 atoms/mole × 19 nucleons/atom
Number of nucleons = 5.09 × 10^20 nucleons
Therefore, there are approximately 5.09 × 10^20 nucleons in 10 cm^3 of fluorine gas.