Help is needed for converting units of a simple formula

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To convert a volume mixing ratio from [m3/m3] to [molecules/cm3], it is essential to understand the relationship between gas volume, moles, and molecules, utilizing the ideal gas law (PV = nRT) and Avogadro's hypothesis. The air density of 1 kg/m3 at 293K provides the necessary parameters to calculate the pressure, which is crucial for determining the number of moles present. Once the moles are calculated, they can be converted to molecules using Avogadro's number. The discussion emphasizes the need for clarity on how to transition from a dimensionless ratio to a physically meaningful concentration. Understanding these conversions is vital for accurately assessing gas concentrations in air.
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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!
 
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[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.
 
Do you know Avogadro's hypothesis?

And do you know how to convert gas volume to number of moles? Number of moles to number of molecules?
 
Borek said:
Do you know Avogadro's hypothesis?

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.
 
anuttarasammyak said:
[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.
 
Hint: density at a given temperature is enough to find the pressure.
 
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