# How to find weight if the mass fraction is known

If the percentage of substances in this mix or alloy, that is their mass fraction is known, then it is possible to calculate the mass of each substance in it. For this purpose it is necessary to know the mass of all mix or mass at least of one of components.

## It is required to you

• - scales;
• - ability to make and transform proportions.

## Instruction

1. By means of scales measure the mass of substance, the mass fraction of one of elements of which is known. As all substance of this weight undertakes 100%, make a proportion, having found the relation of a mass fraction as a percentage to 100%, and equate this relation to the relation of mass of an element and all substance. Having transformed a formula, receive value of mass of an element of mix or alloy. Weight will be equal to the work of a mass fraction of an element on the mass of all substance divided into 100 m0= (M•ω % of)/100%. For example, if it is known that in an ingot of bronze weighing 4 kg the mass fraction of copper makes 80%, then the mass of pure copper will be equal to m0= (4 kg·80 of % of)/100%. When calculating receive value of 3.2 kg.

2. In case mix or alloy consists of many substances, and the mass fraction of each of them is known, find their weight. For this purpose apply the calculation specified in the previous point to each substance. Before calculation surely make sure that all mass fractions of substances in the sum give 100%, otherwise calculation will be incorrect. After calculation is made, and the mass of substances will be found, make sure that the total mass of all substances is equal to the mass of initial substance. For example, in 160 g of solution 10% of sulfuric acid, 5% of nitric and 85% of water contain. The mass of sulfuric acid will be m0= (160 of %)/100%=16g, the mass of m0= nitric acid (160 of %)/100%=8g, and the mass of m0= water (160 kg·85 of % of)/100%=136 g. When checking it will be received: 16+8+136=160g.

3. If the mass of one of elements, and its mass fraction is known, then, without weighing substance, determine its weight. The mass of all substance corresponds to 100% of a mass fraction. Then, having made a proportion, equate the relation of mass fractions to the relation of the corresponding masses. Calculate the mass of all substance, having increased the mass of its component by 100% and having divided into its mass fraction as a percentage of M= (% m0•100)/ω %. For example, if it is known that for receiving 10% solution of table salt 12 g of this substance were added to water, then the mass of all solution will be M= (12•100% of)/10%=120 g.

Author: «MirrorInfo» Dream Team