Calculate Mass of NO2 in a Liter of Air

[physicsman2]

Homework Statement

NO2 is a known air-pollutant resulting from the combustion of petroleum in vehicles. Suppose at 6:00 am, there are 0.920 ppm NO2 in a liter of air. Calculate the mass (in grams) of the NO2 present in a liter, assuming there are 2.46x10^22 molecules of air in 1.00 L. (1 ppm = 10-6)

Homework Equations

particle to mole to mass conversion
PV=nRT(maybe)

The Attempt at a Solution

I have no idea how to do this. The only thing I could think of is changing the number of molecules to some mass by changing it to moles than use the molar mass of NO2 to get mass
I would appreciate any help on this. Thanks.

 

[mgb_phys]

You are given the number of molecules in a liter of air
You know that 920/1000000 of these are NO2

Do you know the mass of NO2 in AMU?
Do you know the mass of a single AMU in grams

 

[physicsman2]

i know the molar mass of NO2 is 46g/mol. I don't think you need amu, unless the molar mass is the amu. Would I need to use the ideal gas law?

 

[mgb_phys]

i know the molar mass of NO2 is 46g/mol. I don't think you need amu, unless the molar mass is the amu.

The molar mass is the mass in grams of 1mole of molecules. An amu is 1g/1mole.
So you work out how many moles there are and multiply by 46h

Would I need to use the ideal gas law?

No

 

[physicsman2]

ok, so after dividing 2.46x10^22 by 6.022x10^23 and multiplying by 46, i get 1.87g. What do I have to do after this, I'm kinda confused. I know the answer should be 1.73x10^-6 but I don't know how to get it.
Thanks a lot.

 

[mgb_phys]

There are 2.46x10^22 molecules in 1 litre of air
0.920ppm is NO2 so 0.92e-6 of these are NO2

So we have 2.46x10^22 * 0.92x10^-6 = 2.26x10^16 molecules of NO2 / litre
You know 6.02x10^23 molecues of NO2 weigh 46g

So how much does 2.26x10^16 molecules weigh?

 

[mgb_phys]

ps with numbers like this it's always worth doing an estimate first.
We know that 1mol of a gas is 24litres at room temp/pressure
So 24litres would be 46g, then 1 litre NO2 is about 2g.

But we know that NO2 is only 1ppm - so the answer should be around 2 micro grams

 

[physicsman2]

thanks a lot. i see how that answer was found now.