Need help with this threshold limit value (TLV) chemistry problem

[steelermania]

Homework Statement

Here's the question:

A 35mL vial of a liquid substance was dropped and broke. The liquid vaporized very quickly. If the room is 7.0 x 3.2 x 2.3 meters, would the people inside be in danger given the density of the liquid is 3.12 g/mL and the TLV is 0.66 mg/cubic meter?

Relevant Equations

Not sure what the forum wants me to put here, since this is my first time posting, but no equations are directly given (but the density and volume formulas seem to be needed).

I'm getting 2119.36 for the concentration of mg/cubic meter of this substance...it just feels wrong though.

Steps I followed:

First, I figured out how many grams of the substance there were using the density formula, then saw how many were present per cubic meter after calculating the volume of the room. The ratio is WAY more than what was given. All conversions were done as needed.

 

[Bystander]

Homework Statement: Here's the question:

A 35mL vial of a liquid substance was dropped and broke. The liquid vaporized very quickly. If the room is 7.0 x 3.2 x 2.3 meters, would the people inside be in danger given the density of the liquid is 3.12 g/mL and the TLV is 0.66 mg/cubic meter?
Homework Equations: Not sure what the forum wants me to put here, since this is my first time posting, but no equations are directly given (but the density and volume formulas seem to be needed).

it just feels wrong though.

What "just feels wrong?" Problem statement is limited to two significant figures; try limiting your answer, and "feel" again.

 

[steelermania]

What "feels wrong" is that the answer is four digits. 0.66 vs 2119 and change.
I'm not the best with sig figs and am not sure how they'd help in calculating here. It just feels like the concentration here is a LOT more than what they say here.

What step am I missing?

 

[Bystander]

Is

LOT more

greater than or less than? All the problem asks is "yes or no."

 

[steelermania]

2119 is greater than 0.66 by a country mile. Did I do the math right in the steps though to get what the problem asked? I'm just confused because 0.66 is so much smaller than a 2119.

Something tells me there was a miscalculation in there but I've checked it three times and it always comes out to be the same.

 

[steelermania]

So am I right here or should I revisit something in the problem?

 

[Bystander]

It's called a "sitting duck;" fowlers on the Chesapeake used to pole "punt guns" up to flocks of waterfowl, this is a duck that has had its wings clipped and its little webbed feet nailed to a board, and the two gauge muzzle of the punt gun actually poled over its head and neck before you, the student, are allowed to pull the trigger.

 

[steelermania]

So I'm one step short here but have done all of the other work?
I'm just confused and frustrated...do I just have to convert the measurement or is it more about just answering that the people in the room need to evacuate?

 

[Bystander]

I'm just confused and frustrated...

As you should be; the problem statement is beyond trivial; the overdose is sufficient/excessive for "knockdown" dosage.

 

[steelermania]

Maybe I'm just overthinking this thing?

My problem is that I'm not the best with significant figures or scientific notation so I always second guess myself.

I'm going to go with "there's too much of this vaporized substance in the room" as my answer...if that's wrong, do I need to convert another number?

 

[steelermania]

Also, thank you for the advice...I'm still second guessing myself though...mayby e I'm second guessing the problem itself because the amount is so high compared to the safe level.

My apologies for asking so many questions of reassurance, I'm just really not confident at all.

 

[Bystander]

You're getting several thousand times the TLV, which is what you're supposed to find; no conversion is needed, people holding their breath might be able to escape. It's a bit disconcerting...agreed this is an unsettling excess concentration to find.

 

[steelermania]

I think the unsettling part is what gets me...I think I was expecting something between 1 and 10 for an "over the TLV" value. Seems the issue is in the problem itself--whoever wrote it must not value safety!

Thank you for everything!

 

[Borek]

Did I do the math right in the steps though to get what the problem asked?

Short answer, one that doesn't value question, its author, his/her intentions, life, the Universe and everything: yes.

2.1×10³ mg/m³ would be a better way of stating the result (accounting for significant digits).