In chemistry, mass percentage indicates the percentage of each component of a mixture. To calculate it, you need to know the molar mass of the elements present in the mixture in grams / mole or the number of grams used to make the solution. You can get this value simply by using a formula, which divides the mass of the component (or solute) by the mass of the mixture (or solution).
Steps
Method 1 of 2: Calculate the Mass Percentage Knowing the Masses
Step 1. Define the mass percentage equation for a mixture
The basic formula is as follows: percentage by mass = (mass of the component / total mass of the mixture) x 100. At the end, you have to multiply by 100, in order to express the value as a percentage.
- Write the equation at the beginning of the problem: percentage by mass = (mass of the component / total mass of the mixture) x 100.
- Both values should be expressed in grams, so that the units of measurement cancel out once the equation is solved.
- The mass of the component you are interested in is the known mass in the problem. If you don't know this, read the next section, which describes how to calculate the percentage by mass without using the mass of the component.
- The total mass of the mixture is calculated by adding the masses of all the components present inside it.
Step 2. Calculate the total mass of the mixture
If you know the masses of all the components of the mixture, just add them together to get the total mass of the solution. This value will be the denominator of the mass percentage formula.
-
Example 1: What is the mass percentage of 5 g of sodium hydroxide dissolved in 100 g of water?
The total mass of the solution is equal to the quantity of sodium hydroxide plus water: 100 g + 5 g for a total mass of 105 g
-
Example 2: What mass values of sodium chloride and water are needed to make 175 g of 15% solution?
In this example, you know the total mass, the desired percentage, and you are asked to find the amount of solute to add to the solution. The total mass is 175 g
Step 3. Find the mass of the component you are interested in
When asked for the "percentage by mass", it refers to the mass of a particular component, expressed as a percentage of the total mass of the mixture. Write the mass of the component you are interested in, which will become the numerator of the mass percentage formula.
- Example 1: the mass of the component you are interested in (sodium hydroxide) is 5 g.
- Example 2: For this example, the mass of the component in question is the unknown that you are trying to calculate.
Step 4. Insert the variables into the mass percentage equation
Once you have determined the values of all the variables, enter them into the formula.
- Example 1: percentage by mass = (mass of the component / total mass of the mixture) x 100 = (5 g / 105 g) x 100.
- Example 2: we need to move the elements of the equation, in order to calculate the unknown (the mass of the component of interest): mass of the component = (percentage by mass * total mass of the solution) / 100 = (15 * 175) / 100.
Step 5. Calculate the percentage by mass
Now that you've completed the equation, just perform the simple math. Divide the mass of the component by the total mass of the mixture and multiply by 100. This will give you the mass percentage of the component you are interested in.
- Example 1: (5/105) x 100 = 0, 04761 x 100 = 4.761%. Consequently, the mass percentage of 5 g of sodium hydroxide dissolved in 100 g of water is 4.761%.
-
Example 2: the inverse formula to obtain the mass of the component is (mass percentage * total mass of the solution) / 100: (15 * 175) / 100 = (2625) / 100 = 26.25 grams of sodium chloride.
The amount of water to add is simply equal to the total mass minus the mass of the component: 175 - 26, 25 = 148, 75 grams of water
Method 2 of 2: Calculate Mass Percentage Without Knowing Masses
Step 1. Define the mass percentage equation of a solution
The basic formula is as follows: percentage by mass = (molar mass of the component / total molecular mass of the mixture) x 100. The molar mass of a component is the mass of one mole of the component, while the total molecular mass is the mass of a mole of the entire mixture. At the end of the equation, you need to multiply by 100 to express the value as a percentage.
- At the beginning of all problems, always write the equation: mass percentage = (molar mass of the component / total molecular mass of the mixture) x 100.
- Both values are expressed in grams per mole (g / mol). This means that you can simplify the units of measurement when you solve the equation.
- When you don't know the masses, you can find the mass percentage of a component within a mixture using the molar mass.
- Example 1: Find the mass percentage of hydrogen in a water molecule.
- Example 2: Find the mass percentage of carbon in a glucose molecule.
Step 2. Write the chemical formula
If the chemical formulas of each mixture are not known, you must write them down. If there is problem data, you can skip this step and proceed to "Find the mass of all elements".
- Example 1: write the chemical formula of water, H.2OR.
- Example 2: write the chemical formula of glucose C.6H.12OR6.
Step 3. Find the mass of all components of the mixture
Search the periodic table for the molecular weight of all the elements present in the chemical formulas. Usually, you can find the mass of an element under its chemical symbol. Write down the masses of all components of the mixture.
- Example 1: Search for the molecular weight of oxygen (15, 9994) and that of hydrogen (1, 0079).
- Example 2: Search for the molecular weight of carbon (12, 0107), oxygen (15, 9994) and hydrogen (1, 0079).
Step 4. Multiply the masses by the molar ratio
Calculate how many moles (molar ratio) of each component are in the mixture. The molar ratio is given by the number accompanying each element of the molecule. Multiply the molecular mass of all elements by the molar ratio.
- Example 1: hydrogen has the number two, while oxygen has the number one. As a result, multiply the molecular mass of hydrogen by 2.00794 X 2 = 2.01588, then leave the molecular mass of oxygen unchanged 15.9994 (multiplied by one).
-
Example 2: carbon has the number 6, hydrogen 12 and oxygen 6. Multiplying each element by its accompanying number, we obtain:
- Carbon (12, 0107 * 6) = 72, 0642
- Hydrogen (1.00794 * 12) = 12.09528
- Oxygen (15.9994 * 6) = 95.9964
Calculate Mass Percent Step 10 Step 5. Calculate the total mass of the mixture
Add the total mass of all components of the solution. Using the masses calculated with the molar ratio, you can get the total mass. This value will become the denominator of the mass percentage equation.
- Example 1: Adding 2.01588 g / mol (the mass of the two moles of hydrogen atoms) with 15.9994 g / mol (the mass of the single mole of the oxygen atom) to obtain 18.01528 g / mol.
- Example 2: Add up all the molecular masses you calculated: carbon + hydrogen + oxygen = 72, 0642 + 12, 09528 + 95, 9964 = 180, 156 g / mol.
Calculate Mass Percent Step 11 Step 6. Locate the mass of the component in question
When asked to find the percentage by mass, you need to calculate the mass of a particular component of the mixture, expressed as a percentage of the total mass of all components. Get the mass of the component in question and write it down. You can calculate it using the molar ratio and that value will become the numerator in the mass percentage equation.
- Example 1: The mass of hydrogen in the mixture is 2.01588 g / mol (the mass of two moles of hydrogen atoms).
- Example 2: The mass of carbon in the mixture is 72.0642 g / mol (the mass of six moles of carbon atoms).
Calculate Mass Percent Step 12 Step 7. Insert the variables into the mass percentage equation
Once you have determined the values of all the variables, use them in the equation defined in the first step: mass percentage = (molar mass of the component / total molecular mass of the mixture) x 100.
- Example 1: mass percentage = (molar mass of the component / total molecular mass of the mixture) x 100 = (2, 01588/18, 01528) x 100.
- Example 2: mass percentage = (molar mass of the component / total molecular mass of the mixture) x 100 = (72, 0642/180, 156) x 100.
Calculate Mass Percent Step 13 Step 8. Calculate the percentage by mass
Now that you have completed the equation, you just have to solve it to get the data you are looking for. Divide the mass of the component by the total mass of the mixture, then multiply by 100. This will give you the mass percentage of the component.
- Example 1: mass percentage = (2, 01588/18, 01528) x 100 = 0, 11189 x 100 = 11, 18%. As a result, the mass percentage of hydrogen atoms in a water molecule is 11.18%.
- Example 2: mass percentage = (molar mass of the component / total molecular mass of the mixture) x 100 = (72, 0642/180, 156) x 100 = 0, 4000 x 100 = 40, 00%. Consequently, the mass percentage of carbon atoms in a glucose molecule is 40%.
