Is the Blood Alcohol Level High Enough for a DWI?

In summary: I still make mistakes.In summary, Homework Equations state that a person will receive a DWI if his/her blood alcohol level (BAL) is 100mg per dL of blood or higher. Assuming the cop isn't cool and just follows you home, the drunk driver would get a ticket. Significant figures were forgotten, and the answer is 150 mg/dL instead of 152 mg/dL.
  • #1
Planarian
9
0

Homework Statement


A person will receive a DWI if his/her blood alcohol level (BAL) is 100mg per dL of blood or higher. Suppose a person is found to have a BAL of 0.033 mol of ethanol per liter of blood. Will the person receive a DWI? Assuming the cop isn't cool and just follows you home.

Homework Equations


molarity and basic metric conversions.

The Attempt at a Solution


100mg/dL = 1000mg/dL = 1g/dL?

0.033 mol of C2H5OH (ethanol) x 46.07g/1 mol = 1.52g/L of C2H5OH

Therefore the drunk driver would get a ticket.

I think this is correct. I did the problem backwards. What's the best way to get mg/dL from the 0.033 mols of C2H5OH?

Thanks for the help :D
 
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  • #2
Planarian said:
100mg/dL = 1000mg/dL

Sure, and 2 = 7 :tongue2:

0.033 mol of C2H5OH (ethanol) x 46.07g/1 mol = 1.52g/L of C2H5OH

Conversion moles -> grams is OK, but I can't see L on the left side of the equation. Well, you probably meant mol/L, but omitting units is a sure way of making mistake one day.
 
  • #3
I meant 100g/dL not 100mg/dL


You're right. 0.033 mol/L. it is in the original question, yes I for got to add that in.-now that you have successfully shown me all my typos, can you please answer my original question? What is the correct way of answering this problem to come up with a solution of mg/dL. I can ask my professor if its too much trouble.

I'm trying to learn how to be more anal with my calculations. I know it is a big part of chemistry. I have a social science degree so math is my weak point.

Thanks for your help.
 
  • #4
Planarian said:
I meant 100g/dL not 100mg/dL


You're right. 0.033 mol/L. it is in the original question, yes I for got to add that in.

I'm trying to learn how to be more anal with my calculations. I know it is a big part of chemistry. I have a social science degree so math is my weak point.

100g/dL still doesn't make sense.

how about this, define your conversions more robustly:
1L = 10dL
therefore 100mg/dL = 1000mg/L = 1g/L(this is your alcohol limit in terms of Litres)

I'll assume your mol calculation is correct (it seems good), then there are 1.52g of Ethanol in 0.033 mol of Ethanol.

So the person has 1.52g of Ethanol per litre of blood. This is higher than the 1g/L limit, so he should be arrested for DUI.
 
  • #5
Planarian said:
now that you have successfully shown me all my typos, can you please answer my original question? What is the correct way of answering this problem to come up with a solution of mg/dL.

You were on the right track, just the view was obscured by small errors. Sorry for not stating that clearly.
 
  • #6
Borek said:
You were on the right track, just the view was obscured by small errors. Sorry for not stating that clearly.

It's cool, I think I figured it out from your help. Please let me know if this is right.

So to get from 1.52 g/L of C2H5OH to mg/dL

1.52g/L (1000mg/1g per liter) = 1520 mg/L

(1520 mg) / (10 dL/ 1L) = 152 mg/dL of C2H5OH

The answer in the back of the book is 150 mg/dL so my molar mass calc.s are different from the books, but close enough.


I was doing this:
1520 mg/L = (1520mg) (10dL/1L) and getting 15200 mg/dL (I forgot that it is mg PER dL, ha. makes sense now)

__I do need to pay closer attention to units/states/detail. Thanks for pointing this out Borek. Criticism helps even though I don't enjoy it. I've made SEVERAL errors on my exams this same way costing me letter grades in some cases :grumpy:. Any good suggestions to avoid this, besides the obvious double checking? I'm slightly A.D.D.
 
  • #7
Planarian said:
The answer in the back of the book is 150 mg/dL so my molar mass calc.s are different from the books, but close enough.

Significant figures. You were told ethanol is 0.033M, so your answer should have 2 SF - that means 150 (or more correctly 1.5x102 mg/dL), not 152.
 
  • #8
Sig. fig.s! ahhh yes. I forgot 150 is only 2 significant figures. tricky.

Thanks again.
 
  • #9
Planarian said:
__I do need to pay closer attention to units/states/detail. Thanks for pointing this out Borek. Criticism helps even though I don't enjoy it. I've made SEVERAL errors on my exams this same way costing me letter grades in some cases :grumpy:. Any good suggestions to avoid this, besides the obvious double checking? I'm slightly A.D.D.

I'm not sure of the best way to stop silly mistakes, I still often make them. I try to set out every problem by starting with a template that I'm comfortable with and use very often. I make a sketch and write down all the information I know. I then jot down some formulae that I think may be handy. I stop here and do a quick double check to make sure I've written down the information correctly. Then I do my conversions from strange units, to units that make more sense to me and that I know will be easier to use (kg, N, l, m, seconds, Pa, etc) that kind of depends on what formulae you'll be using and what you're comfortable with. The thing that helps the most is just the following the routine and keeping the same pattern. Methodically working through the problem will stop your mind from trying to jump to the answer too quickly allowing silly mistakes to creep into the part that you're actually busy with.
 
  • #10
redargon said:
I'm not sure of the best way to stop silly mistakes, I still often make them. I try to set out every problem by starting with a template that I'm comfortable with and use very often. I make a sketch and write down all the information I know. I then jot down some formulae that I think may be handy. I stop here and do a quick double check to make sure I've written down the information correctly. Then I do my conversions from strange units, to units that make more sense to me and that I know will be easier to use (kg, N, l, m, seconds, Pa, etc) that kind of depends on what formulae you'll be using and what you're comfortable with. The thing that helps the most is just the following the routine and keeping the same pattern. Methodically working through the problem will stop your mind from trying to jump to the answer too quickly allowing silly mistakes to creep into the part that you're actually busy with.

VERY helpful, thank you!
 
  • #11
BAL 100 mg/dL
Person 0.033 mol/L C2H5OH

0.033 mol/L * 46.07g C2H5OH/1 mol (cancel out mols) * 1000 mg/1 g (cancel out g) * 1 L /10 dL (cancel out L) = 152.031...sig. figs...[1.5 x10^2 mg/dL]

:D easy.
 

1. What is blood alcohol level (BAL)?

Blood alcohol level, also known as blood alcohol concentration (BAC), is a measure of the amount of alcohol present in the bloodstream. It is used to determine the level of intoxication of an individual.

2. How is blood alcohol level measured?

Blood alcohol level is measured by taking a sample of blood from the individual and analyzing it for the concentration of alcohol using a breathalyzer or a blood test. The result is typically expressed as a percentage of alcohol in the blood.

3. What factors affect blood alcohol level?

The amount of alcohol consumed, the rate of consumption, body weight, and gender are some of the factors that can affect blood alcohol level. Other factors include food intake, medications, and overall health.

4. What is the legal limit for blood alcohol level?

The legal limit for blood alcohol level varies depending on the country and state. In the United States, the legal limit is 0.08% for individuals over 21 years old and 0.04% for commercial drivers. However, it is important to note that any amount of alcohol can impair an individual's ability to drive safely.

5. How long does it take for blood alcohol level to return to zero?

The liver processes alcohol at a rate of about one drink per hour. Therefore, it typically takes one hour for the blood alcohol level to decrease by 0.015%. However, the rate of alcohol metabolism can vary depending on factors such as body weight, gender, and overall health.

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