The Math of Dilution
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 Post subject: The Math of Dilution

Post Posted: Sun Jun 20, 2010 8:20 pm 

 


I need to dilute some alcohol in a 1:1 (aka 50/50 or 50%) mix with water today, but to complicate things the alcohol I have to start with is a 70% alcohol mix meaning it is already 30% water and I can't simply add one part alcohol to one part water if I want the right mix.

Since the existing alcohol mix is a nice round multiple of ten (10, 20, 30, ... 90, 100) it is pretty easy to find out how much water I need to add if I want a 1:1 mix. The first thing I do is split my existing alcohol mix into 10 parts and arrange those 10 parts into alcohol and water sides. Like I did with these pennies.

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70% of ten parts is seven parts. So seven pennies go on one side, and three pennies go on the other. Now I can clearly see that there are four more parts of alcohol in my existing mix than there are parts of water. If I want an even 50/50 or 1:1 mix of alcohol to water, I need to add 4 parts of water.

How much water is one part though ?

If I look on the side of my alcohol container, I see that it holds 32 fluid ounces. If I ask Google, what is 32 ounces divided by 10 into ounces Google will tell me 3.2 ounces. So each part of my 10 parts is 3.2 ounces.

What if I want to know how many cups of water I need to add though ? I ask Google what is 3.2 ounces times 4 into cups and it tells me 1.6 cups.

So, if I add 1.6 cups (or 12.8 ounces) of water to my existing bottle of alcohol, I will have as much of a 1:1 mix as I can possibly get from it. :D


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 Post subject: The Math of Dilution

PostPosted: Sun Jun 20, 2010 8:20 pm 




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 Post subject: Re: The Math of Dilution

Post Posted: Sun Jun 20, 2010 10:47 pm 

 


That's pretty cool how how you figured out how to get a 50/50 mix of the water and alcohol, but I'm curious as to what you were needing that mixture for?


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 Post subject: Re: The Math of Dilution

Post Posted: Sun Jun 20, 2010 11:36 pm 

 


To spray my tomato plant with, in an attempt to get rid of Spider Mites.


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 Post subject: Re: The Math of Dilution

Post Posted: Mon Jun 21, 2010 8:21 am 

 


Oh yeah.... so how did that work? Still have the spider mites?


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 Post subject: Re: The Math of Dilution

Post Posted: Mon Jun 21, 2010 11:08 am 

 


It's too early to tell. I sprayed early this morning just before the sun came up with the alcohol/water. I soaked the entire plant with the mix, as well as the 5 gallon bucket I have it in (inside and out) and a foot or so around that. Then after the time it took me to go inside and put a half-gallon of plain water in my pump sprayer I hosed the plant down again with water and gave it a good watering. I gave it a good soaking both times, using the mister on the sprayer at first to get some of that alcohol on every bit of the plant, then with the rougher spray to really blast the crevices between branches and under leaves.

I didn't want to mix the entire bottle of alcohol this morning because the only thing I had to put it in was my pump sprayer and I didn't want to use the whole thing at once. Instead, I measured out 200 ML in my measuring cup, then added water to that. Using my 4 parts to add bit from earlier, I knew I needed 40 ML of water for 100 ML of the bottled alcohol and 80 ML for the 200 ML I was using. Since this isn't rocket science I just filled the measuring cup between the 75 ML and 100 ML mark with water.

I found an empty 2 liter bottle I can use to to mix the rest of the alcohol to a 1:1 mix with water so I don't have to do anymore mixing in the future. Now that I realize my measuring cup has milliliters on it I can ask Google what 32 ounces minus 200 milliliters into milliliters is and get the result 746.35 ML.

746ML * 0.4 (four parts) = 298.3 ML -- So if I add 300 ML of water to the rest of my bottle of alcohol I should have a 1:1 mix.

Now to check my result now against what I'd figured for the whole bottle.

I used 80 ML of water earlier, plus the 300 ML I'm going to use now, Google says 380 milliliters into cups is right around 1.606 cups which when figuring in my little rounding errir with 746ML a minute ago, is right on target. :D


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