Calculating Cylinders Needed to Fill Room with NO2 Gas

[Lars Bos]

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.

 

[Borek]

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?

 

[Lars Bos]

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]

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).

 

[Lars Bos]

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

Sorry, your question is not clear enough.

 

[Borek]

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?

 

[Lars Bos]

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

Btw the original question is in v/v.

 

[Borek]

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]

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?

 

[Lars Bos]

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.

 

[Lars Bos]

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]

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.

 

[Lars Bos]

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

 

[Borek]

So it is just dilution most likely.

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

 

[Lars Bos]

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

I know this is quite tricky one.

 

[Borek]

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.

 

[Lars Bos]

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]

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.

 

[Lars Bos]

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]

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.

 

[Lars Bos]

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]

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

 

[Lars Bos]

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

What is the next step?

 

[Borek]

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