## Using proportions with liquid solutions

If you need double the dose of medication, you need to give double the volume of the liquid that it is dissolved in and so on. This is the simple principle behind the Volume Required formula.

Learn how you could solve these problems *before* applying the formula.

Let's return to the GOFUEL mixture from a previous video. Let's recall that this is a sachet of GOFUEL, it is in powder form, and this sachet contains 40 grams of powder. This is a bottle of water and this bottle contains one litre of water. We’re going to empty the sachet into the water so it dissolves evenly. And in this session, we are going to understand what the value of the concentration means.

Here is our bottle with the sachet mixed evenly through... It’s a nice blackcurrant flavour now. So we know that now that there is 40 grams of GOFUEL per litre of water. The concentration is just telling you about the proportion of solution that there is in the liquid or—in the case of liquid medication—what drug strength is in the liquid, if it is syrup-like, cough medicine, or saline for an IV.

And, logically enough, the more liquid you administer, the more of the solute or the drug you receive in a proportional way. We can express the concentration in this way, as 40 grams per liter. One litre is equivalent to 1000 millilitres so we can express it this way… And that allows us to cancel some zeros from the numerator and the denominator, so that it is reduced to four grams per 100 milliliters.

Because four grams is also equivalent to 4000 micrograms, we can use the 4000 micrograms so we can express the concentration in this way. Remember, you always have to state your units, or else the number becomes meaningless. Once again, this allows us to cancel some zeros. And the concentration of our mixtures can be stated most simply this way. However, all of the above concentrations are equal and correct, it all depends on which units you want to use.

So the question is just how much go fuel powder does a person get if they drink a certain amount of liquid. It makes sense that if you drink the whole 1 L you’ll take in 40 g of go fuel. What if you drink half of a litre, than you’ll get half of the 40 g which is 20 mg; or maybe, 250 ml which is a quarter of a litre; then you will get a quarter of the total go fuel, which is 10 g. And if you had 200 mL which is a fifth of a bottle, you will get one-fifth of the 40 grams which is eight grams. Point 75 litres represents three-quarters of the litre bottle, and 75% or three-quarters of the GOFUEL bottle is 30 grams.

We could of solve these question in another way (keep in mind the other concentrations we calculated). We know for our sports drink solution that every mL contains 40 mg of go fuel; so if we have 500 millilitres of water, 500 lots of 40 mg is 20000 mg—as we found before—and notice that the mL cancel there leaving only the unit of mg.

If we drink 250 ml of the water, we will be receiving 250 lots of the 40 mg per mL, which is 10,000 mg; and the working out for that is similar. Now, if we drank 1250 ml of the liquid and that is more than we have in the bottle, but that’s no problem because we can still focus how much go fuel we get if we had more of our blackcurrant mixture. 1250 x 40 is 50,000 mg -and the working out is the same again; and you could express that as 50,000 mg or 50 g if you prefer. But you must state the unit because it makes all the difference.

So, in all the concentration gives a measure of the medication for each unit of liquid. Using this you can figure out how much medication or in this case go fuel powder is in these certain amount of liquid. If you have one-third of the liquid for example, you’ll have one-third of the medication and this relationship is proportional. What if a fraction you drink or receive out of the total, this is the same as the fraction of drug strength that you take out of the total available.