Welcome to Mass Percent Made Easy, brought

to you by Ketzbook In this video, we are going to learn how to

calculate the mass percent of a solution and how to calculate the mass of the solute or

solvent if you know the mass percent concentration. But first, what is mass percent? Mass percent is a way to measure concentration. “Per” means for each, and “cent” is

Latin for 100, so percent refers to the amount of solute dissolved in 100 units of solution. “Mass” simply refers to how we measure

both the solute and the solution. For example, the fat content in milk is measured

in mass percent. What is 2% milk? It means that 100 grams of that milk contains

2 grams of fat. There are two grams of fat for each 100 grams

of 2% milk. The equation that we will use to calculate

mass percent is: mass percent equals the mass of the solute divided by the total mass of the solution all multiplied by 100 to turn the fraction into a percent. Let’s try some examples to see how this

works. Calculate the mass percent concentration of a 38.5 gram aqueous solution that contains 1.96 grams of sodium bromide. Before we solve this problem, let’s make

some sense of it. First, the term aqueous means that water is

the solvent. Next, the problem tells us that we are solving

for the mass percent. 38.5 grams is the mass of the solution, and

1.96 grams is the mass of the solute. Remember that the solute is the thing that

is dissolved in the solvent. Now we’re ready to plug in some numbers

to calculate the mass percent. 1.96 grams goes on the top of the fraction

and 38.5 grams goes on the bottom of the fraction. This fraction is then multiplied by 100%. In your calculator, type 1.96 divided by 38.5

times 100, which gives us the answer of 5.09 percent. As for the units, notice that grams on the

top and bottom of the fraction cancel each other out. This is true for any kind of percent or any

kind of parts per calculation. The units on the top and bottom of the fraction

must be the same so that they cancel out. Percent functions as the units of our answer,

but in reality percent is merely a way to represent a dimensionless ratio. Okay, let’s try another problem. What is the mass percent of 125 grams of fructose

dissolved in 375 mL of water? Once again, we are solving for the mass percent

concentration, 125 grams is the mass of the solute, and 375 mL is the volume of the solvent. Volume? What do we do with volume? Water is the solvent, so this is relatively

simple because the density of water is approximately 1 g/mL at room temperature. So for water, 1 mL has a mass of 1 gram. That means that 375 mL is the same as 375

grams. As long as we don’t need any more than 3

significant figures and as long as the water is not too warm, this approximation works

fine. If we did need more precision, we would have

to calculate the mass of the solvent based on its density at the given temperature. Now we can plug in some numbers. The mass percent is equal to the mass of the

solute divided by the mass of the solution all times 100 percent. We put 125 grams in for the mass of the solute. You may be tempted to put 375 grams in the

bottom, but that is only the mass of the solvent. The mass of the solution is the mass of the

solvent PLUS the mass of the solute, that is 375 plus 125. That works out to 125 divided by 500 times

100, or 25%. Suppose, however, we wanted to solve for something

different, such as the mass of the solute. Let’s try this next problem. How much sodium fluoride is in a 221 g tube

of toothpaste that has 0.24% sodium fluoride? In this case, we are solving for the mass

of the solute. 221 grams is the mass of the solution, and 0.24% is the mass percent concentration of sodium fluoride. We can set the problem up the same as always. The mass percent is 0.24%, which is equal

to the mass of the solute divided by the mass of the solution or 221 grams, all multiplied

by 100%. The only difference this time is that what we are solving for is on the right side of the equation, so we will need to do a bit of rearranging. First, let’s remove the units because percent

is on both sides of the equation, and we know that the mass of the solute has the units of grams. Next, we can multiply both sides of the equation

by 221, which cancels it out on the right. Finally, we can divide both sides of the equation

by 100 to cancel it out on the right side as well. This leaves us with the mass of the solute

being equal to 221 times 0.24 divided by 100, which calculates to be 0.53 grams. That is approximately one tenth the lethal

dose of sodium fluoride for adults, but it is enough to be dangerous for small children,

so caution should be exercised when allowing children to use any fluoride containing product. Okay, let’s try one last problem. How could you make a 7.8% aqueous solution

of glucose using 5.0 g of glucose? Like always, let’s first identify the knowns

and the unknowns in the problem. 7.8% is the mass percent concentration of

the solution we want to make, and 5 grams is the mass of the solute we need to use. The question doesn’t specifically say what we are solving for, but we can infer it from what is missing. Mass percent equals the mass of the solute divided by the mass of the solution all times 100 percent. The mass percent is 7.8, and the mass of the

solute is 5. That leaves the mass of the solution as the

only unknown, so we should solve for that. However, when you make a solution, it is more

practical to weigh the solvent all by itself, so we should ultimately solve for the mass

of the solvent. In order to solve this problem, we need to

do a little bit of rearranging. The variable we are solving for cannot be

in the denominator, so the first thing we need to do is multiply both sides of the equation

by the mass of the solution. Mass of the solution then cancels out on the

right side of the equation. Next, we need to get the mass of the solution

all by itself, so we divide both sides by 7.8. The 7.8 on the top and bottom of the fraction

cancel each other out. This leaves us with the mass of the solution equals 5 times 100 divided by 7.8, which calculates to be 64.1. Because the units for the mass of glucose are grams, the units for the mass of solution are also grams. We are almost done, but as we mentioned earlier,

it is easier in the lab to weigh the solvent separately, so we need to calculate the mass

of the solvent all by itself. The mass of the solution equals the mass of

the solvent plus the mass of the solute, and we know that the mass of the solute is 5 grams. In other words, the mass of the solvent is

64.1 minus 5 or 59.1 grams. By the way, the reason I have included an

extra significant figure for this quantity is because it is not based on a measurement

but something we will make in the lab, so we want it to be as precise as possible. Now that we have the numbers we need, we can

go ahead and weigh everything we need. Weigh the glucose in a weighing boat or a

clean weighing container. Although we could use a graduated cylinder to measure the water, it is better to weigh the water. Once we have the correct amounts, simply combine

them in a beaker or flask, and stir it a little until it is all dissolved. The resulting solution is a 7.8 percent aqueous

glucose solution. Thanks for watching. If you found this video useful, please like

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you have below, and check me out at ketzbook.com.

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