Suppose you have a cylinder filled with diatomic oxygen (O2) and it is running low. The cylinder is shown above, is made of steel, and has a fixed volume of 10 L.

You are asked to determine the number of O2 molecules that are left in the cylinder, so you take a measurement of the temperature to be 20℃. You then note that the pressure gauge reads 100 psi, which you checked at sea level in Bellingham, where the local pressure is one atm (14.7 psi). Calculate the number of O2 molecules left in the container.

Answer:

The number of O₂ molecules that are left in the cylinder is 1.70x10²⁴.

Explanation:

The number of oxygen molecules can be found using the Ideal Gas law:

[tex] PV = nRT [/tex]        

Where:

P: is the pressure = 100 psi

V: is the volume = 10 L

n: is the number of moles =?

T: is the temperature = 20 °C = 293 K

R: is the gas constant = 0.082 L*atm/(K*mol)

Hence, the number of moles is:

[tex]n = \frac{PV}{RT} = \frac{100 psi*\frac{1 atm}{14.7 psi}*10 L}{0.082 L*atm/(K*mol)*293 K} = 2.83 moles[/tex]

Now, the number of molecules can be found with Avogadro's number:

[tex]n_{m} = \frac{6.022 \cdot 10^{23}\: molecules}{1\: mol}*2.83 moles = 1.70 \cdot 10^{24} \: molecules[/tex]

Therefore, the number of O₂ molecules that are left in the cylinder is 1.70x10²⁴.

I hope it helps you!              

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