# PPM conversion

## Homework Statement

A 185 m3 room must be filled with 4 ppm NO2 gas (Nitrogen dioxide). The gas comes in cylinder of 200 bar and 50 liters (20x50 = 10,000 liters) and 50 ppm. How many cylinders are needed?

## Homework Equations

1 ppm = 1/1,000,000 (parts per million)
(can't think of more relevant equations)

## The Attempt at a Solution

To be honest I do not know how to begin. The ppm part is completely new to me.

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Borek
Mentor
If ppm is 1/1,000,000, what mass of the NO2 is needed for 1 ppm if there are 1,000,000 kg of the air?

If ppm is 1/1,000,000, what mass of the NO2 is needed for 1 ppm if there are 1,000,000 kg of the air?

Molar mass of NO2 is 46 g/mol.

Does that mean we need 1/1,000,000th of the above?

Borek
Mentor
Molar mass doesn't matter for now. Try to answer my question.

Note: question is incomplete, as it doesn't state if it is v/v or w/w ppm, these are two different cases (which will give slightly different answers).

What do you mean by v/v or w/w ppm?

Sorry, your question is not clear enough.

Borek
Mentor
v/v - volume by volume (as in 1 L in 1,000,000 L)

w/w - weight by weight (as in 1 kg in 1,000,000 kg).

I am afraid my question is extremely basic and quite clear, if you have problems answering it you will have problems solving the original questions.

Let's try from the other end - if there are 10 kg of substance in 1,000,000 kg of the air, what is its ppm concentration?

That is 10/1,000,000 = 0.00001 or 10 ppm

Btw the original question is in v/v.

Borek
Mentor
OK, v/v means it will be easier to solve.

10 L in 1,000,000 L is 10 ppm.

What gas volume is present in 1,000,000 L of air if the concentration is 1 ppm?

Chestermiller
Mentor
For gases, ppm usually refers to mole fraction x 106. What I can't figure out is how the mole fraction can increase from 4 ppm to 50 ppm, unless some reaction is occurring. Is there an equilibrium reaction involved?

OK, v/v means it will be easier to solve.

10 L in 1,000,000 L is 10 ppm.

What gas volume is present in 1,000,000 L of air if the concentration is 1 ppm?

That is 1 liter.

For gases, ppm usually refers to mole fraction x 106. What I can't figure out is how the mole fraction can increase from 4 ppm to 50 ppm, unless some reaction is occurring. Is there an equilibrium reaction involved?

No, there is no chemical/equilibrium reaction involved.

Borek
Mentor
That is 1 liter.

So, can you calculate what volume of NO2 required, knowing the volume of the room?

I must admit I initially missed then 50 ppm part and I am not sure how to understand it. Perhaps it just means NO2 will be diluted.

They require a solution of 50 ppm NO2 with some unreactive gas in the cylinder.

Borek
Mentor
So it is just dilution most likely.

How many liters of NO2 in 185 m3 at 4 ppm?

The amount is not given. All the given values are mentioned in the question.

I know this is quite tricky one.

Borek
Mentor
There is nothing tricky about the problem.

You were already able to calculate volume of gas present in 1,000,000 L of air when the concentration is 1 ppm. Volume of NO2 in 185 m3 at 4 ppm is identical kind of a problem, just with different numbers. No magic here, simple application of exactly the same principle.

Are you trying to imply that since 185 m3 equals to 185,000 liters, the 4 ppm of NO2 amounts to 21.6 liters?

Borek
Mentor
I am not "trying to imply" anything, I am trying to make you think.

No idea how you got 21.6 liters, and unfortunately it is not the correct number.

I am not "trying to imply" anything, I am trying to make you think.

No idea how you got 21.6 liters, and unfortunately it is not the correct number.

I understand that you are trying to help me out here and I appreciate it.

What I don't get is how to change the 185 m3 into ppm and then calculate how much 4 ppm amounts to.

Borek
Mentor
Sorry, you have lost me. You don't change 185 m3 to ppm, one is volume, the other is concentration, you can't change one into another.

Let's try again:

In 1,000,000 liters 1 ppm means 1 L - that's what we already know.

In 1,000,000 liters 4 ppm means ..... L.

In 1,000 m3 4 ppm means ..... L.

In 100 m3 4 ppm means ..... L.

In 185 m3 4 ppm means ..... L.

In 1,000,000 liters 4 ppm means 4 L.

In 1,000 m3 4 ppm means 0.004 L.

In 100 m3 4 ppm means 0.0004 L.

In 185 m3 4 ppm means 0.00074 L?

And now?

Borek
Mentor
You are on the right track, but you missed fact that we switched from liters to cubic meters.

Oh yes. So 4 ppm in 185 m3 equals to 0.74 liters.

What is the next step?

Borek
Mentor
Repeat the calculations for a cylinder - how many liters of NO2 in a cylinder?