Question

according to the law of conservation of matter, we know that the total number of atoms does not change in a chemical reaction and thus mass is conserved. the reactant in this model is hydrogen peroxide. hydrogen peroxide decomposes to produce water and oxygen gas. how many water molecules must be added to complete this model?

Explanation:

Step1: Analyze Reactant Atoms

Reactant: 2 \(H_2O_2\) molecules. Each \(H_2O_2\) has 2 H and 2 O, so total H: \(2\times2 = 4\), total O: \(2\times2 = 4\).

Step2: Analyze Product Atoms (Oxygen)

Product oxygen: 1 \(O_2\) molecule (2 O atoms). Remaining O for water: \(4 - 2 = 2\) O. Each \(H_2O\) has 1 O, so O in water: 2 ⇒ 2 \(H_2O\)? Wait, no—wait, H: total H is 4. Each \(H_2O\) has 2 H, so \( \frac{4}{2} = 2\) \(H_2O\) molecules? Wait, no, the model: reactant has two \(H_2O_2\) (each is two orange "atoms"? Wait, maybe the diagram: left has two \(H_2O_2\) (each is two orange circles? Wait, the reactant is two \(H_2O_2\) (so 2 molecules, each with 2 H and 2 O). Product has one \(O_2\) (two orange circles). So H atoms: 2×2 = 4, O atoms: 2×2 = 4. Product O: 2 (from \(O_2\)), so O in water: 4 - 2 = 2. Each water (\(H_2O\)) has 1 O, so 2 O ⇒ 2 water molecules? Wait, but each water has 2 H, so 2 waters have 4 H, which matches reactant H (4). Wait, but the options: the first option has three small orange? No, wait the question is about water molecules. Wait, maybe the diagram: reactant is two \(H_2O_2\) (each is two orange "molecules"? Wait, no, the left side: two groups of two orange circles (so two \(H_2O_2\) molecules). Right side: "?" (water) + one \(O_2\) (two orange circles). So atoms: H and O. Let's count:

Reactant: 2 \(H_2O_2\) → H: 2×2=4, O: 2×2=4.

Product: \(O_2\) (2 O) + \(x\) \(H_2O\) (each \(H_2O\) has 2 H and 1 O).

So for H: \(2x = 4\) ⇒ \(x = 2\)? Wait, no, maybe the diagram's "water" molecules: each water is a molecule with 2 H and 1 O. Wait, but the options: the first option (leftmost) has three small orange? No, wait the options are four boxes: first has three small, second two medium, third one large, fourth four small. Wait, maybe the model uses circles: H is small, O is medium? Wait, no, the problem says "water molecules". Wait, the decomposition of \(H_2O_2\) is \(2H_2O_2
ightarrow 2H_2O + O_2\). So the balanced equation is \(2H_2O_2
ightarrow 2H_2O + O_2\). So from 2 \(H_2O_2\), we get 2 \(H_2O\) and 1 \(O_2\). So the number of water molecules is 2? Wait, but the options: maybe the diagram's reactant is two \(H_2O_2\) (so two molecules), product has one \(O_2\), so need two water molecules. Wait, but the options: the second box has two medium orange circles? Wait, maybe the answer is 2, but the options: wait the question is "How many water molecules must be added to complete this model?" Let's re-express the balanced equation: \(2H_2O_2
ightarrow 2H_2O + O_2\). So from 2 \(H_2O_2\), produce 2 \(H_2O\) and 1 \(O_2\). So the number of water molecules is 2. Wait, but the options: looking at the boxes, the second box (middle-left) has two medium orange circles? Maybe that's 2 water molecules? Wait, no, maybe I misread. Wait, the key is conservation of mass: atoms must balance. So H: 4, O: 4. Product O: 2 (from \(O_2\)), so O in water: 2. Each water has 1 O, so 2 water molecules. Wait, but the first option has three small, second two medium, third one large, fourth four small. Wait, maybe the "water molecules" are represented by two medium circles? So the answer is 2, which would correspond to the second box (two medium orange circles). Wait, but the question is about the number of water molecules. Wait, the balanced equation is 2 \(H_2O_2\) → 2 \(H_2O\) + 1 \(O_2\), so 2 water molecules. So the number is 2.

Answer:

2 (Assuming the second option with two medium orange circles is the correct representation, but based on atom balance, 2 water molecules are needed.)