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 or subscribe.
Feel free to share any comments or questions you have below, and check me out at ketzbook.com.