# Help is needed for converting units of a simple formula

han_123
please post this type of questions in the homework forums, filling out the template
How would you convert a volume mixing ratio [m3/m3] to the units of [molecules/cm3]? The temperature is given to be 293K and the air density is 1 kg/m3. Please help!

Gold Member
[m3/m3] has no physical dimension but [molecules/cm3] has physical dimension of L^-3. I am afraid some more details of the exercise are required to help you.

Mentor

And do you know how to convert gas volume to number of moles? Number of moles to number of molecules?

• Bystander
han_123

And do you know how to convert gas volume to number of moles? Number of moles to number of molecules?
Hi! Well not exactly. I know there is the ideal gas formula PV = nRT and that a mole contains the Avogadro number of molecules.

However, I am confused about how to convert a volume mixing ratio [m3/m3] or [mol/mol] to the units of [molecules/cm3] when only the temperature is given to be 293K and the air density is 1 kg/m3.

The goal is to find whenever a gas is mixed into an airspace at a certain ratio then how many molecules of that gas are to be found in one cm3.

han_123
[m3/m3] has no physical dimension but [molecules/cm3] has physical dimension of L^-3. I am afraid some more details of the exercise are required to help you.
The volume mixing ratio can also be given in [mol/mol]. How do you convert a mol of gas into the number of molecules when only the air density and temperature are given?

The goal is to find whenever a gas is mixed into an airspace at a certain ratio then how many molecules of that gas are to be found in one cm3.

Mentor
Hint: density at a given temperature is enough to find the pressure.