Table of Contents

## Definition of Mass Percentage

Mass percentage is a way of expressing a concentration or describing the component in a particular mixture.

The solution composition can be described in mass percentage, which shows the mass of solute present in a given mass of solution.

The quantity of solute is expressed in mass or by moles. For a solution, the mass percent is described as the grams of solute per grams of solution, multiplied by 100 to get the percentage.

## Summary

The mass/mass percent (% m/m) is defined as the mass of a solute divided by the mass of a solution times 100:

%m/m=mass of solute / mass of solution×100%

mass of solution = mass of solute + mass solvent

If you can measure the masses of the solute and the solution, determining the mass/mass percent is easy. Each mass must be expressed in the same units to determine the proper concentration.

## Mass Percentage is a Way of Expressing the Concentration of Solution

There are several ways of expressing the concentration of a solution by using a percentage. The mass percentage is one of the ways to express the concentration of a dissolved substance in a solution.

The mass percentage refers to the ratio (expressed in percents) of a mass of a compound in the solution to the total mass of the solution.

For instance, calculate the mass percent concentration for the solution obtained by dissolving 10 g of sodium chloride (NaCl) and 6g of sodium bicarbonate (NaHCO_{3}) in 120g of water.

Add up the mass of all compounds in the solution, including the solvent, to calculate the total mass of the solution.

### Examples

- Suppose that you prepared a solution by dissolving 25.0g of sugar into 100g of water. The percent by mass would be calculated by;
**Percent by mass**=25g sugar / 125g solution x 100% = 20% sugar - Sometimes you may want to make up a particular mass of a solution of a given percent by mass and need to calculate what mass of the solvent to use.
**For example**, you need to make 3000g of a 5% solution of sodium chloride. You can rearrange and solve for the mass of solute.

mass of solute = percent by mass / 100% x mass of solution = 5% / 100%x 3000g =150g NaCl

You would need to weigh out 150g of NaCl and add it to 2850g of water. Notice that it was necessary to subtract the mass of the NaCl (150g) from the mass of solution (3000g) to calculate the mass of the water that would need to be added.

## Mass Percentage Formula

Mass percent is the mass of the element or solute divided by the mass of the compound or solute. The result is multiplied by 100 to give a percent. The formula for the amount of an element in a compound is:

mass percent = (mass of element in 1 mole of compound / mass of 1 mole of compound) x 100

The formula for a solution is:

mass percent = (grams of solute / grams of solute plus solvent) x 100

or

mass percent = (grams of solute / grams of solution) x 100

The final answer is given as %.

## Steps for Finding the Mass Percentage

Followings are the steps to find mass percent

**Step-1:** Define the equation for the mass percent of a compound. The essential formula for mass percent of a compound is:

mass percent = (mass of chemical ÷ total mass of compound) x 100.

You want to multiply by 100 at the top to specify the value as a percentage.

**Step-2:** Calculate the entire mass of the compound. Once you know the masses of all the elements or compounds being added together; then you merely got to add them to calculate the entire mass of the ultimate compound or solution. And this may be the denominator within the mass percent calculation.

**Step-3:** Identify the mass of the chemical in question. When asked to seek out the “mass percent,” you’re being asked to seek out the mass of a specific chemical (the chemical-in-question) as a percentage of the entire mass of all elements. Then write down the mass of the chemical-in-question. This mass is the numerator within the mass percent calculation.

**Step-4:** The variables into the mass percent equation. So once you’ve got determined the values for every variable, plug them into the equation.

**Step-5:** Calculate the mass percent. The equation is filled in, so now solve to calculate the mass percent. Divide the mass of the chemical by the entire mass of the compound and multiply by 100. This may offer you the mass percent of the chemical.

## Mass Percentage Examples

Here are some examples of mass percentage:

### Example-1

Ordinary bleach is 5.25% NaOCl by mass, which means each 100g of bleach contains 5.25g NaOCl.

### Example-2

Find the mass percentage of 6 g sodium hydroxide dissolved in 50 g of water. (**Note**: since the density of water is nearly 1, this type of question often gives the volume of water in milliliters.)

First find the total mass of the solution:

total mass = 6g sodium hydroxide + 50g water

Therefore, total mass = 56g

Now, you can find the mass percentage of the sodium hydroxide using the formula:

the mass percent = (grams of solute / grams of solution) x 100

mass percent = (6g NaOH / 56g solution) x 100

mass percent = (0.1074) x 100

answer = 10.74% NaOH.

### Example-3

Find the masses of sodium chloride and water required to obtain 175 g of a 15% solution.

This problem is a bit different because it gives you the mass percentage and asks you to then find how much solute and solvent are needed to yield a total mass of 175 grams.

Start with the usual equation and fill in the given information:

mass percent = (grams solute / grams solution) x 100

15% = (x grams sodium chloride / 175 g total) x 100

Solving for x will give you the amount of NaCl:

x = 15 x 175 / 100

x = 26.25 grams NaCl

So, now you know how much salt is needed. The solution consists of the sum of the amount of salt and water. Simply subtract the mass of salt from the solution to obtain the mass of water that is required:

the mass of water = total mass – mass of salt

mass of water = 175 g – 26.25 g

Therefore, mass of water = 147.75 g.

### Example-4

What is the mass percent of hydrogen in water?

First, you need the formula for water, which is H_{2}O. Next you look up the mass for 1 mole of hydrogen and oxygen (the atomic masses) using a periodic table.

hydrogen mass = 1.008 grams per mole

oxygen mass = 16.00 grams per mole

Next, you use the mass percentage formula. The key to performing the calculation correctly is to note there are 2 atoms of hydrogen in each water molecules.

So, in 1 mole of water there are 2 x 1.008 grams of hydrogen. The total mass of the compound is the sum of the mass of the two hydrogen atoms and one oxygen atom.

the mass percent = (mass of element in 1 mole of compound / mass of 1 mole of compound) x 100

mass percent hydrogen = [(2 x 1.008) / (2 x 1.008 + 16.00)] x 100

mass percent hydrogen = (2.016 / 18.016) x 100

Therefore, mass percentage hydrogen = 11.19%

### Example-5

An aqueous solution of sodium chloride (CaCl_{2}) is prepared. Determine the mass of 5%(m/m) solution of calcium chloride that can be prepared using 100g of calcium chloride.

**Solution:** The interpretation of mass/mass per cent number shows that 5g of CaCl_{2} is used to prepare 100g of solution.

Therefore,

g solution = (100g CaCl_{2} x 100g solution) / 5g CaCl_{2}

g solution = 2 x 103g solution

Hence, 2 x 103g of 5% (m /m) solution can be prepared using 100g CaCl_{2}.

### Example-6

Determine how many grams of sugar is present in 1.500g pf 1.50% solution of sugar in water.

**Solution:** Since mass percentage gives the mass of sugar in 100g of solution.

The two conversion factors can be solved as follows,

1.50g sugar / 100g solution are inverted to 100g solution / 1.50g sugar

the given solution by the first conversion

G sugar = (1.500g solution x 1.5g solution) / 100g solution

G sugar = 22.5g sugar

Hence, 22.5g sugar is present in 1.500g of 1.50% solution.

### Example-7

Find the mass percentage of 6g sodium hydroxide dissolved in 50g of water. (Note: since the density of water is nearly 1, this type of question often gives the volume of water in millilitres.)

**Solution:** First find the total mass of the solution:

total mass = 6g sodium hydroxide + 50g water total mass = 56g

Now, you can find the mass percentage of the sodium hydroxide using the formula:

mass percent = (grams of solute / grams of solution) x 100 mass percent = (6g NaOH / 56g solution) x 100

mass percent = (0.1074) x 100 = 10.74% NaOH.

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