# Славиша Нешић

## Agriculture / beekeeping / How much suger for one liter of sirup?

This task is very well known to beekeepers, technology engineers in beverage production as well as chemists:

By mixing of 1kg sugar with 1 liter of water (1L of water weights about 1kg) we shall get 2kg of sugar syrup, naturally. What is it's volume?

On the other hand, we could ask: how much sugar does it take to make one liter of 1:1 syrup concentration? In beekeepers' practice sugar syrup is usually made in one of several typical formulations. For that reason beekeepers remember how much sugar they need to make their favorite concentration of syrup and without hesitation they make their solution right away. However if they need some other specific concentration, they resort to a little experiment and measurement by which they deduce how much sugar and water they need for one liter of syrup.

In this text hereby I shall present my own formula that I have "constructed" and by which I calculate the suger and water formulation needed for one leter of deliberate concentration! So you do not need to search for solution tables, nor inquiring colegues nor making experiments.

First let me explain the concentration calculus for those not acquainted in it. Let W[%] be the percantage of syrup needed to be made. E.g. W=60 means that you want 60% sugar syrup. Also, if you want 3:2 syrup concentration, that means you want three parts of sugar to two parts of water; i.e. three parts of sugar is contained in 5 parts of solution; if you want that expressed in percantages:

$\frac{3}{{2 + 3}} = \frac{3}{5} = 60\%$

So the sugar syrup concentration can be expressed as 60% as well as 3:2 ratio solution - in both cases we talk exactly the same solution differently expressed. If the concentration is expressed as ratio of components, the first figure refers to solute (sugar) and the other one is the solvent (water).

## Formula

Now for one leter of sugar syrup of W[%] concentration you will use sugar in grams:

$\frac{{2710}}{{271/W - 1}}$

And you will add water in mililiters according to formula:

$\frac{{2710 \cdot (100 - W)}}{{271 - W}}$

E.g. if you put w=50 in formulas above you will get the beekeepers' well known ratio 1:1 sugar syrup, 613g sugar with 613mL of water.

Now you got the Slavisa formula for sugar syrup!