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What do the growth of a plant and the rusting
of a truck have in common? Both processes

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involve mass transfer. In this video, you'll
learn how to apply the concept of a control

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volume and the law of conservation of mass
to real-world scenarios.

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This video is part of the Conservation video
series.

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In order to analyze or modify a system, it
is important to understand how the laws of

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conservation place constraints on that system.

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Hi. My name is Mark Bathe and I am a professor
in the Department of Biological Engineering

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at MIT.

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By watching this video, you will be able to
apply the law of conservation of mass to real-world

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scenarios.

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Before watching this video, however; you should
have had experience with basic reaction stoichiometry.

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In the 18th century, Antoine Lavoisier, a
French scientist, showed that there is no

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overall change in mass when a reaction takes
place in a sealed container.

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This observation is called the law of mass
conservation.

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What would Lavoisier say about a plant's growth...
...or a car rusting?

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Can conservation of mass be applied to these
scenarios?

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Of course it can.

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By using a conceptual tool called a "control
volume," we can more easily apply the law

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of mass conservation to these scenarios.

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What is a control volume? A control volume
is a fictitious boundary that separates a

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system of interest from its surroundings.
A control volume is NOT a tangible, solid

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boundary. Nor does the control volume have
to be a specific shape or size. A control

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volume can transmit energy or mass. A control
volume should be seen merely as a tool, and

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defining a control volume is a matter of convenience.
Depending on the question being investigated

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some control volumes may be more convenient
than others.

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Before we go back to the growing plant or
the rusting car example, let's go through

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a more visual example to demonstrate the idea
of a control volume.

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Here we have a sink filling with water.
What if we wanted to know how much water is

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accumulating in the basin? What control volume
might we choose to help us answer this question?

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Well, what if we were to define the faucet
as our control volume? We could look at the

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flow into and out of the control volume. Would
this give us enough information to figure

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out how much water is accumulating in our
basin? No.

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What if we defined the whole bathroom as our
control volume? We could look at the flow

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going through all of the plumbing in the bathroom.
Would this give us enough information to figure

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out how much water is accumulating in our
basin?

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Yes, but we'd also have a lot of information
to deal with. This probably wouldn't be the

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most efficient way to solve the problem.

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What if instead we defined the basin itself
as the control volume? Ah-ha. We could look

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at the flow going into and out of the control
volume and figure out how much water is actually

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accumulating in our basin. We have enough
information to figure out what we want to

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know, but not so much information that it
is cumbersome to deal with.

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Now, we will see how we can use the concept
of a control volume and general chemistry

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knowledge to better understand the application
of the conservation of mass to the growing

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plant and rusting car scenarios.

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Back to the growing plant. Let's say that
over some period of time, the plant grows

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and gains a mass of 25grams. Although the
plant isn't living in a sealed container,

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we can still apply the law of mass conservation
to the growing plant by specifying a control

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volume and accounting for the mass entering
and exiting that control volume.

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Most plants make their food using photosynthesis.
The overall reaction for photosynthesis is

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carbon dioxide plus water plus light energy
yields glucose plus oxygen. We'll assume that

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the plant's mass comes from glucose and it's
downstream products.

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Now please take a minute to think about what
control volume we might specify to apply the

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law of mass conservation to the plant's growth.
[short pause]

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If we think of the plant as our control volume,
we can apply the law of conservation of mass

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to perform a mass balance on the system.
Any mass that is accumulated in our system

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must equal any mass that entered the system
minus any mass that left the system. This

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is the law of mass conservation.

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What mass is entering the control volume?
Carbon dioxide and water.

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What mass is exiting the system? Oxygen.

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Drawing a diagram like this helps us keep
track of the information that we know and

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the information that we don't know.

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Note that we ignored the light energy because
we are performing a mass balance. We can substitute

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25 grams in for the accumulation term in the
mass balance equation. Now please pause the

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video here and see if you can figure out how
much carbon dioxide and water entered the

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system and how much oxygen exited the system.
Please continue playing the video to see the

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worked solutions.

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Using basic stoichiometry, we can see that
37 grams of carbon dioxide entered the system...

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15 grams of water also entered the system...

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And 27 grams of oxygen exited the system.

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We can compare these results to our mass balance
and see that our inputs minus our output equals

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the mass gained by the plant.
So, the law of mass conservation not only

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holds, but it gives us important insight into
the process of a growing plant. Fantastic!

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Now, let's turn to our next example, that
of a rusting car.

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The car has rusted, but the rust has fallen
off of the car, resulting in a decrease in

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the mass of the car.

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Measurements show that the car has lost mass,
but has mass really not been conserved?

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Let's think about this scenario a little more
carefully. What is happening when a car rusts?

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Can we write an equation to explain what is
happening chemically?

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Rusting happens by iron oxidation. This reaction
can be written as 3O2 + 4Fe -> 2Fe2O3. Measurements

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show that the car lost 10g of mass.
Now please take a minute to think about what

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control volume we might specify to apply the
law of mass conservation to the rusting car.

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[short pause]

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If we define the car as our system or control
volume, a concept that we introduced earlier,

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we can perform a mass balance on the car.
Remember, any mass that is accumulated in

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our system should equal any mass that entered
the system minus any mass that left the system.

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Our system, the car, lost 10g of mass. This
is a negative accumulation.

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During the rusting process, did any mass enter
our system? Yes, the mass due to the oxygen

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that reacted with the iron on the car's body.

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In our scenario, where a car has rusted and
the rust fell off of the car, has any mass

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left our system? Yes. The mass of the rust,
or iron oxide.

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Now please pause the video here and see if
you can figure out how much oxygen entered

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the system and how much iron oxide exited
the system. Please continue playing the video

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to see the worked solutions.

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Using basic stoichiometry, we can see that
4.3 grams of oxygen entered the system...

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and 14.3 grams of iron oxide exited the system.

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We can compare this to our mass balance to
see that our mass in minus our mass out equals

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the negative accumulation of mass of our car.

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Again, the law of conservation of mass has
served as a useful tool to learn something

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important about our system.

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This video illustrated how the law of conservation
of mass can be applied to real-world scenarios.

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Although real-world scenarios might seem overwhelming
at first, we can use a problem-solving tool

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called a control volume to help narrow our
focus. The law of conservation of mass allows

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us to perform a mass balance on the control
volume. In other words, any mass that has

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accumulated in our system must equal any mass
that entered the system minus any mass that

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exited the system.

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This simple idea will provide a basis for
understanding systems throughout your time

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at SUTD and beyond.

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FAANTASTIC! (will have to "cut and paste"
this audio from earlier)