# How to calculate the mass fraction

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Mass fraction shows in percentage or in fractionsThe content of the substance in any solution or element in the substance. The ability to calculate the mass fraction is useful not only in chemistry lessons, but also when you want to prepare a solution or mixture, for example, for culinary purposes.

Or change the percentage in an existing composition.

Instructions

- 1

The mass fraction is calculated as the ratio of the mass of this component to the total mass of the solution. To get the result as a percentage, you must multiply the resulting quotient by 100.

The formula looks like this:

? = M (solute) / m (solution)

?,% =? * 100

- 2

For example, consider the direct and inverse problems.

For example, you dissolved in 100 grams of water 5Grams of table salt. What percentage of the solution did you get? The decision is very simple. You know the mass of the substance (table salt), the mass of the solution will be equal to the sum of the masses of water and salt. So, you should divide 5 g into 105 g and multiply the result by 100? This will be the answer: 4.7% solution you will get.

Now the inverse problem. You want to prepare 200 grams of a 10% aqueous solution of anything. How much substance to take for dissolution? We act in reverse order, the mass fraction expressed in percentage (10%) is divided by 100. We get 0.1. Now we form a simple equation, where the required amount of matter is denoted by x and, consequently, the mass of the solution as 200 g + x. Our equation will look like this: 0,1 = x / 200g + x. When we solve it, we get that x is about 22.2 g. The result is checked by solving a direct problem.

- 3

It is more difficult to know what quantities of solutionsA certain percentage must be taken to obtain a certain amount of solution with new specified qualities. Here it is required to compose and solve the system of equations. In this system, the first equation is the expression for the known mass of the mixture obtained, through two unknown masses of the initial solutions. For example, if our goal is to get 150 grams of solution, the equation will have the form x + y = 150 g. The second equation? The mass of the dissolved substance equated to the sum of the same substance, in the composition of two miscible solutions. For example, if you want to have a 30% solution, and the solutions that you mix 100%, that is, pure substance, and 15%, then the second equation will look like: x + 0.15y = 45 g. Case For a small, solve the system equation and find out how much it is necessary to add substances to the 15% solution in order to get a 30% solution. Try it.