[NA] arithmetic help

[Let'sgoflying!]

Your goal is a final solution having 0.060% (v/v) of substance A in the final mixture.

You are starting with a 100 gal solution containing 0.040% substance A.

You have substance A available (100% concentration) to add.

How much substance A (liquid, ml or oz) to add to this 100 gallons?

Feel free to ignore that the addition of Substance A will make the final volume a bit more than 100 gallons - that's irrelevant to this question and doing so will make the calculations easier.

Note: we are told in other readings that adding 600ml of Substance A to 100 gals results in a 0.015% solution if that helps.

(if I left something off, it's not because I'm trying to make an impossible question - just let me know what else is needed)

 

[dmspilot]

Note: we are told in other readings that adding 600ml of Substance A to 100 gals results in a 0.015% solution if that helps.

That isn't right...
1 gal = 3785.41 mL
600 mL / 100 gal = 600 mL / 100 * 3785.41 mL = 0.001585 = 0.1585%
I'm hesitant to answer the question since the problem already has an order of magnitude error.

 

[Albany Tom]

I'll toss out something that should let you solve it. 100 gals with something in it .06% by volume means you have 100 gal x .06/100 of whatever that is, or .06 gallons, which is 128 * .06 oz, which is 7.68 oz. There are about 30ml in an ounce, so you're looking for about 230ml total of whatever it is.

But as dmspilot pointed out, the math doesn't work for the 100% solution added at 600 ml to make .015. It's off by a factor of 10. So somebody is telling you something that isn't right....either that addition of 600, or the concentration of solution, or both. If you're making soap for a car wash, not a big deal. If it's something that you're going to fly in or feed your kids, I'd triple check your sources...something isn't right.

 

[Let'sgoflying!]

Ok, absolutely right. Substance A cannot be 100%.
I don't know what it is but will try to find out.
Can it be solved without knowledge of what % it is?

To avoid confusion I won't modify the original post.

 

[murphey]

Welcome to ChatGPT:
We need to determine how much of 100% substance A to add to the original 100 gallons of solution containing 0.040% substance A to increase the concentration to 0.060%.

Step 1: Define variables

• Initial volume of solution: Vi= 100 gallons
  Initial concentration: Ci=0.040% =0.0004
  Final concentration: Cf=0.060% =0.0006
  Volume of 100% substance A to add: Va (in gallons)

Step 2: Set up the equation

The amount of substance A in the initial solution:
Initial amount of A=100×0.0004=0.04 gallons of substance A.

The amount of substance A added:
Amount of A added=Va×1=Va gallons of A.

The total volume after adding:
Vf=100+Va gallons.

The final amount of substance A in the solution:
Final amount of A=0.04+Va.

Set the final concentration equation:
(.04 + Va)/ (100 + Va)

Step 3: Solve for
0.9994Va=0.02

Va ≈ 0.020.9994 ≈ 0.02001 gallons.

Step 4: Convert gallons to milliliters or ounces
1 gallon = 3785.41 mL, so Va×3785.41≈75.7 mL.

1 gallon = 128 oz, so Va×128≈2.56 oz.

Final answer

You need to add approximately:

• 75.7 mL or
• 2.56 oz of 100% substance A to achieve a final concentration of 0.060%.

 

[Albany Tom]

You'd need to know the percentage to figure out how much to add to make another percentage. Percentage is just how many 100ths of something it is, or .01 x whatever. So 10% is 10/100 or 1/10th or .1 of something. Because 10/100 is .1. Apologies if you get all that. If the 600ml/100 gal /.015% thing is roughly accurate, then sounds like A is 10%. 600 ml is about 20 oz, a 10% solution would be 2 oz of whatever it is, and 2/(100*128) is about .000156, which is .00156%.

Murphey's AI answer looks right IF that solution is 100%, but it's 10x off if you're working with a 10% solution, obviously.

 

[455 Bravo Uniform]

In your original 100 gallons of solution, you have 5.12 liquid oz (0.04%) of your pure substance, with the rest being the solvent (99.96 gallons).

You want a 0.06% mix of your stuff. You have 99.96 gallons of solvent. You want X / 99.96 = 0.0006 (or 99.96 x 0.0006 = X). So X = 7.6769 oz.

You already have 5.12 oz in there, you need 7.6769 oz, so add 2.5569 oz more.

The math is actually easier than all that jazz. You have 0.04% and you want to increase it by 50% to 0.06%. So 50% of the original 5.12 oz is 2.56 oz more.

 

[Let'sgoflying!]

2.6oz more per 100 gal jives exactly with my abacus-style calculations, so I think it must be right.
Much appreciated!

 

[455 Bravo Uniform]

C’mon now, we played for free, at least you can tell us what drink or fuel additive you’re making.

 

[flyingron]

If you're talking about volume and the substances are miscible, adding volume A to volume B doesn't result in volume A+B.

 

[Sac Arrow]

Just for clarification, are you using percentages by weight or volume?

In water treatment chemical dosing calculations, we generally use percentages by weight (or mass) and rectify the difference between mass and volume using the added substances' specific gravity. Normally, commercial chemical strengths are in weight percentage. Plus for dry chemical, volume doesn't work.

Let's make a 1% solution of neat polymer, which has a specific gravity of 0.7.

We take a liter graduated cylinder, weigh out 10 mg of neat polymer, dump it in to the graduated cylinder then fill the rest with water. We're done. We now have a 1% (or 10 mg/L) solution.

Oh, but we don't have a scale. No problem. We take 10 mg of water, divide by 0.7 wt polymer/wt water, and add 14.3 mL of neat polymer.

 

[Daleandee]

Welcome to ChatGPT:
We need to determine how much of 100% substance A to add to the original 100 gallons of solution containing 0.040% substance A to increase the concentration to 0.060%.

Step 1: Define variables

• Initial volume of solution: Vi= 100 gallons
  Initial concentration: Ci=0.040% =0.0004
  Final concentration: Cf=0.060% =0.0006
  Volume of 100% substance A to add: Va (in gallons)

Step 2: Set up the equation

The amount of substance A in the initial solution:
Initial amount of A=100×0.0004=0.04 gallons of substance A.

The amount of substance A added:
Amount of A added=Va×1=Va gallons of A.

The total volume after adding:
Vf=100+Va gallons.

The final amount of substance A in the solution:
Final amount of A=0.04+Va.

Set the final concentration equation:
(.04 + Va)/ (100 + Va)

Step 3: Solve for
0.9994Va=0.02

Va ≈ 0.020.9994 ≈ 0.02001 gallons.

Step 4: Convert gallons to milliliters or ounces
1 gallon = 3785.41 mL, so Va×3785.41≈75.7 mL.

1 gallon = 128 oz, so Va×128≈2.56 oz.

Final answer

You need to add approximately:

• 75.7 mL or
• 2.56 oz of 100% substance A to achieve a final concentration of 0.060%.

I used a different AI assistant last night and received the same answer. I didn't post it as I wasn't certain it was correct ...

 

[murphey]

I used a different AI assistant last night and received the same answer. I didn't post it as I wasn't certain it was correct ...

These things are usually very good on simple math, quantitative calculations and relatively simple code, in most of the contemporary (and some ancient) programming languages. Last year I asked for a Molniya orbit with specific apogee & perigee, and it came back the the physics/astronomy book calculation. Which is fine for school but not for a real launch. I added a few more parameters, and it just barfed. 6 months later, it might have a better response but I'm too lazy to try.