CRHS McIrvin - Avogadros Hypothesis - Free Printable

To solve this problem, we need to use the information given in the text and apply it to the diagrams.

Step 1: Understand the Ratio
The text states that two volumes of hydrogen gas react with one volume of oxygen gas. It also explains that this means two molecules of hydrogen combine with one molecule of oxygen to form water. This gives us a specific ratio for the reaction:
* Hydrogen : Oxygen = 2 : 1

Step 2: Count the Molecules in the Containers
Let's look at the "reactant" side (the left side) of the equation in the image:
* Hydrogen container: There are two boxes shown for hydrogen. Each box has 2 pink circles. Total pink circles (hydrogen atoms/molecules representation) = 4. *Note: In these models, individual circles usually represent atoms, but the text simplifies it to "molecules" combining. Let's look closer. Actually, looking at the product being drawn, it shows 1 yellow circle attached to 2 pink circles. This represents one water molecule ($H_2O$). Therefore, the pink circles are Hydrogen atoms and the yellow circles are Oxygen atoms.*
* Let's re-read carefully: "Represent molecules... React these molecules".
* The diagram shows separate pink circles in the hydrogen box and separate yellow circles in the oxygen box.
* However, standard chemistry modeling for this level often depicts diatomic gases ($H_2$ and $O_2$). But let's look at the counts provided in the boxes.
* Hydrogen Box: Contains 4 pink circles.
* Oxygen Box: Contains 3 yellow circles.

Wait, let's look at the stoichiometry again.
The reaction is $2H_2 + O_2 \rightarrow 2H_2O$.
This means 2 molecules of Hydrogen gas ($H_2$) react with 1 molecule of Oxygen gas ($O_2$).
If the pink circles represent Hydrogen *atoms* and yellow represent Oxygen *atoms*:
* Water is $H_2O$ (2 Hydrogen atoms, 1 Oxygen atom).
* The drawing in the product box shows exactly that: 1 yellow circle bonded to 2 pink circles.

So, the task is to group the available atoms into water molecules ($H_2O$) until no atoms are left over.

Step 3: Analyze the Available Atoms
* Hydrogen (Pink): There are 4 pink circles total.
* Oxygen (Yellow): There are 3 yellow circles total.

Step 4: Form Water Molecules
Each water molecule needs:
* 2 Pink circles
* 1 Yellow circle

Let's see how many complete water molecules we can make with the available supplies:
1. First Molecule: Take 2 Pink and 1 Yellow.
* Remaining Pink: $4 - 2 = 2$
* Remaining Yellow: $3 - 1 = 2$
2. Second Molecule: Take 2 Pink and 1 Yellow.
* Remaining Pink: $2 - 2 = 0$
* Remaining Yellow: $2 - 1 = 1$

Problem Check:
The instructions say "leaving no leftover gas."
With 4 Hydrogen atoms and 3 Oxygen atoms, if we make water ($H_2O$), we will have 1 Oxygen atom left over because we ran out of Hydrogen.
Did I miscount the circles?
Let's look at the image again very closely.
* Hydrogen section: Two squares. Left square has 2 pink dots. Right square has 2 pink dots. Total = 4 pink dots.
* Oxygen section: One square. It has 3 yellow dots. Total = 3 yellow dots.

Is it possible the circles represent *molecules* of gas as the text suggests?
Text: "two molecules of hydrogen combine with one molecule of oxygen".
If pink circle = $H_2$ molecule and yellow circle = $O_2$ molecule:
Then we have 4 $H_2$ and 3 $O_2$.
Reaction: $2 H_2 + 1 O_2 \rightarrow 2 H_2O$.
Ratio is 2 Hydrogen molecules to 1 Oxygen molecule.
We have 4 Hydrogen molecules. To react completely with 4 Hydrogen molecules, we need $4 / 2 = 2$ Oxygen molecules.
We have 3 Oxygen molecules.
If we use 2 Oxygen molecules, we have 1 Oxygen molecule left over.
The prompt says "leaving no leftover gas."

Let's re-examine the image. Maybe I am misinterpreting the "Hydrogen" box.
There is a plus sign between the hydrogen part and the oxygen part.
The hydrogen part consists of TWO distinct boxes.
Box 1: 2 pink circles.
Box 2: 2 pink circles.
Total Hydrogen units = 4.

The oxygen part consists of ONE box.
Box 3: 3 yellow circles.
Total Oxygen units = 3.

If the instruction "leaving no leftover gas" is strict, then the number of atoms/molecules provided *must* be in the perfect ratio.
Perfect ratio for Water ($H_2O$): 2 Hydrogen atoms for every 1 Oxygen atom.
Or 2 Hydrogen molecules ($H_2$) for every 1 Oxygen molecule ($O_2$).

Let's look at the product drawing again. The hand is drawing a cluster of one yellow and two pinks. This confirms the product is a single unit containing 1 Oxygen and 2 Hydrogens.

If we assume the circles are atoms:
We have 4 H and 3 O.
Max water molecules = 2 (using 4 H and 2 O).
Leftover = 1 O atom.
This violates "no leftover gas".

If we assume the circles are diatomic molecules ($H_2$ and $O_2$):
We have 4 $H_2$ and 3 $O_2$.
Reaction: $2 H_2 + O_2 \rightarrow 2 H_2O$.
We can run this reaction twice.
$2 \times (2 H_2 + 1 O_2) = 4 H_2 + 2 O_2$.
This produces 4 water molecules.
Leftover = 1 $O_2$ molecule.
This also violates "no leftover gas".

Is there a different interpretation?
Look at the hydrogen container again. Is it possible the two boxes represent a total of 6 hydrogens? No, clearly 2 and 2.
Is it possible the oxygen container has 2 oxygens? Let me look really closely at the yellow dots.
There is one top, one bottom left, one bottom right. That is definitely 3.

Let's re-read the text above the question.
"You have seen evidence that two volumes of hydrogen gas react with one volume of oxygen gas... to produce water."
"Conclusion that two molecules of hydrogen combine with one molecule of oxygen..."

Perhaps the "Hydrogen" label applies to the first two boxes combined, and the "Oxygen" label applies to the third box.
Maybe the student is supposed to realize that not all particles will react?
But the instruction explicitly says: "leaving no leftover gas."

This implies that the starting amounts *should* allow for a perfect reaction.
Could the yellow circles be something else? No, labeled Oxygen.
Could the pink circles be something else? No, labeled Hydrogen.

Let's look at the handwritten pencil mark. The user is drawing a water molecule.
Maybe I should check if the oxygen box actually contains 2 circles and I'm seeing a shadow or error?
No, the spacing is triangular. Top, bottom-left, bottom-right. It's 3.

Let's reconsider the "Volume" aspect.
Gay-Lussac's law: 2 volumes $H_2$ + 1 volume $O_2$ $\rightarrow$ 2 volumes $H_2O$ (vapor).
Avogadro's hypothesis: Equal volumes contain equal numbers of particles.
So, 2 particles $H_2$ + 1 particle $O_2$ $\rightarrow$ 2 particles $H_2O$.

If the diagram intends for us to use all particles shown:
We have 4 Hydrogen particles and 3 Oxygen particles.
This is a 4:3 ratio.
The required ratio is 2:1 (or 4:2).
There is an excess of Oxygen.

However, in many school worksheets, if there is a discrepancy like this, sometimes the "container" boundaries matter.
Notice the Hydrogen is split into two boxes. The Oxygen is one box.
Maybe the question implies reacting the contents of one hydrogen box with the oxygen?
If we take 1 box of Hydrogen (2 particles) and... wait, we have 3 Oxygen particles. That doesn't fit either.

Let's look at the possibility that the Hydrogen boxes represent $H_2$ molecules (pairs of atoms stuck together)?
In the diagram, the pink circles are separate. They are not touching.
The yellow circles are separate.
Usually, if they were $H_2$, they would be drawn as two touching circles.
Since they are separate, they likely represent atoms.

If they represent atoms, and we must have no leftovers, there is a mistake in the problem statement's counts vs the instruction, OR I am missing a subtle visual cue.

Let's look at the product box again.
The hand is drawing one water molecule so far.
The arrow points from the reactants to the products.

Let's assume the standard scientific answer based on the limiting reagent, but acknowledge the "no leftover" constraint might be a general instruction for the *type* of problem, even if this specific instance has an excess.
OR, perhaps the third yellow dot is not an oxygen atom? No, it's in the oxygen box.

Let's try one more perspective. What if the reaction is different?
No, it says "form water".

Let's assume the question asks you to draw the result of the reaction that *does* happen, and the "no leftover" part is an idealization that fails here, OR the student is expected to identify the limiting reactant and just draw the products formed.
However, "leaving no leftover gas" is a very strong command.

Is it possible that the two hydrogen boxes + the oxygen box are just examples of "containers" and you are supposed to pick the right amounts?
"Represent molecules... in the containers below. React these molecules..."
It implies using what is there.

Let's look at the counts again.
Hydrogen: 4 atoms.
Oxygen: 3 atoms.

If I form 2 water molecules ($H_2O$):
I use 4 H and 2 O.
I have 1 O left.

If the prompt strictly requires no leftovers, is it possible the product is Hydrogen Peroxide ($H_2O_2$)?
Ratio 2 H : 2 O (or 1:1).
We have 4 H and 3 O. Still doesn't fit perfectly.

Let's go with the most chemically accurate interpretation of the visual data, noting the discrepancy if necessary, but providing the drawing that results from the complete consumption of the limiting reactant (Hydrogen), as that is the standard way to handle "react these" problems when ratios aren't perfect. The "no leftover" instruction is likely a template error in the worksheet or assumes the student will identify that one oxygen atom remains unreacted (though the text says "leaving no leftover", which is contradictory).

Wait! Let me look at the Oxygen box again.
Is it possible that the top yellow circle and the bottom two are distinct groups? No.

Let's consider the source: "Modeling Instruction - AMTA 2013".
In Modeling Instruction, they often use "particle diagrams".
Usually, they provide exact stoichiometric amounts.
Example: 4 $H_2$ molecules and 2 $O_2$ molecules.
Here we have 4 pink dots and 3 yellow dots.

Hypothesis: The pink dots are $H_2$ molecules?
If pink dot = $H_2$ molecule, then we have 4 $H_2$.
If yellow dot = $O_2$ molecule, then we have 3 $O_2$.
Reaction: $2 H_2 + O_2 \rightarrow 2 H_2O$.
4 $H_2$ requires 2 $O_2$.
We have 3 $O_2$.
Leftover: 1 $O_2$.

Hypothesis: The pink dots are H atoms.
4 H atoms require 2 O atoms to make 2 $H_2O$.
We have 3 O atoms.
Leftover: 1 O atom.

In both interpretations, there is 1 unit of Oxygen left over.
Given the explicit instruction "leaving no leftover gas," it is highly probable that the worksheet *intended* to show only 2 oxygen atoms, or 6 hydrogen atoms.
However, since I must solve based on the image provided:
The limiting reactant is Hydrogen. All Hydrogen will be used.
We will form 2 water molecules.
There will be 1 oxygen atom/molecule remaining.

How to answer the student?
The student needs to draw the products.
The product of Hydrogen + Oxygen is Water.
One water molecule = 1 Yellow + 2 Pinks.
We have enough Pinks for exactly 2 water molecules (4 pinks / 2 per molecule = 2 molecules).
These 2 molecules will consume 2 Yellows (1 per molecule).
We have 3 Yellows.
So we draw 2 water molecules.
What about the leftover? The prompt says "leaving no leftover". This is a contradiction.
However, in a test/homework setting, if you can't change the inputs, you draw the products formed by the complete reaction of the limiting ingredient.

Alternative interpretation:
Does the "+" sign imply we add the contents? Yes.
Does the arrow imply the result? Yes.

Let's look at the handwritten part. The user has drawn one water molecule.
They need to draw the rest.

Final Decision on Strategy:
I will explain that based on the atoms present, we can make exactly two water molecules. I will point out that this uses up all the hydrogen and most of the oxygen. Although the instructions say "no leftover," the diagram shows an extra oxygen atom that cannot form a complete water molecule because there is no hydrogen left. I will instruct the student to draw the two complete water molecules.

Step-by-step for the final output:
1. Identify the composition of a water molecule from the hint in the image: 1 Oxygen (yellow) + 2 Hydrogen (pink).
2. Count the total available atoms: 4 Hydrogen (pink) and 3 Oxygen (yellow).
3. Calculate how many water molecules can be made:
* Each water molecule needs 2 Hydrogens.
* We have 4 Hydrogens.
* $4 \div 2 = 2$ water molecules.
4. Check if we have enough Oxygen for these 2 molecules:
* Each water molecule needs 1 Oxygen.
* We need 2 Oxygens.
* We have 3 Oxygens.
* Yes, we have enough.
5. Conclusion: Draw 2 water molecules.
* Note: There is 1 Oxygen atom left over. Even though the text says "no leftover," the math of the diagram dictates this result. You cannot make a partial water molecule.

Refining the "No Leftover" conflict:
It is possible the question implies that the "containers" shown are just a supply, and you should only pull out the exact amount needed?
"Represent molecules... in the containers below. React these molecules..."
"React these molecules" implies using the ones shown.
If I were a teacher grading this, I would accept 2 water molecules drawn. If the student draws 2 water molecules and leaves the 3rd oxygen alone, that is scientifically correct. If the student tries to force a 3rd water molecule, it would be chemically wrong ($H_2O_3$? No.).

I will provide the solution to draw two water molecules.

Final Answer Formulation:
* Start with the logic of counting.
* Explain the grouping (2 pink + 1 yellow).
* State the final count of product molecules.

Final Answer:
You need to draw two water molecules in the product box.

Here is the step-by-step breakdown:
1. Identify the recipe for water: Looking at the start of the drawing in the last box, you can see that one water molecule is made of 1 yellow circle (oxygen) and 2 pink circles (hydrogen).
2. Count your ingredients:
* You have 4 pink circles (hydrogen) in total.
* You have 3 yellow circles (oxygen) in total.
3. Build the molecules:
* To make the first water molecule, you use 2 pink and 1 yellow. (Remaining: 2 pink, 2 yellow).
* To make the second water molecule, you use the last 2 pink and 1 more yellow. (Remaining: 0 pink, 1 yellow).
4. Result: You have successfully used all the hydrogen to create 2 complete water molecules.

*(Note: Although the instructions say "no leftover gas," the diagram provides 3 oxygen atoms but only enough hydrogen to use 2 of them. Scientifically, you simply stop when you run out of hydrogen. So, draw the two water molecules.)*

Visual Description for the Student:
Draw two clusters in the final box. Each cluster should look like the one already started: one yellow circle in the middle or top, connected to two pink circles.