Solved Per Density Worksheet Name Ms. Johnson Chemistry Date ... - Free Printable

Let's solve each part of this Density Worksheet step by step, using the information provided in the figures and the principles of density.

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Key Concept: Density

Density is defined as:

$$
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
$$

We are told:
- Each dot represents a particle.
- Particles of the same size have the same mass.
- So, more dots → greater total mass (if all particles are identical).
- The volume of a block is proportional to its size (i.e., larger box = larger volume).

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## ✔ Problem 1: Figure 1 – Compare A and B

Figure 1:

- Block A: smaller box, filled with dots.
- Block B: larger box, same number of dots as A.

Let’s assume both blocks have the same number of particles, but B is larger in size.

#### a. Fill in the table:

| Property | Relationship | Reasoning |
|--------|--------------|---------|
| Mass | A = B | Both blocks have the same number of particles, and each particle has the same mass. Therefore, total mass is equal. |
| Volume | A < B | Block B is physically larger than block A, so it occupies more space. |
| Density | A > B | Density = mass/volume. Since mass is the same but volume of B is larger, density of A is greater. |

> 💡 Example: Imagine two boxes — one small and one large — both containing 10 identical marbles. The small box is denser because the same mass is packed into less volume.

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## ✔ Problem 2: Figure 2 – Compare A, B, and C

Figure 2:

- All three blocks (A, B, C) have different sizes and numbers of particles.
- Dots represent particles; same-sized particles → same mass per dot.

Let’s analyze each block:

#### Count the dots:
- A: 8 dots (2×2×2)
- B: 9 dots (3×3×1)
- C: 12 dots (3×2×2)

Now compare their volumes based on shape:

- A: Small cube (assume 2 units × 2 × 2 → volume = 8)
- B: Flat rectangle (3×3×1 → volume = 9)
- C: Larger rectangular prism (3×2×2 → volume = 12)

So:
- Volume: A = 8, B = 9, C = 12 → increasing order: A < B < C

Mass:
- Mass ∝ number of particles
- A: 8 particles → mass = 8m
- B: 9 particles → mass = 9m
- C: 12 particles → mass = 12m

So:
- Mass: A < B < C

Now calculate density:
- Density = mass / volume

Let’s compute approximate densities:

- A: $ \frac{8m}{8} = m $
- B: $ \frac{9m}{9} = m $
- C: $ \frac{12m}{12} = m $

✔ All three have the same density!

Even though they differ in mass and volume, the ratio (mass/volume) is constant.

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#### a. Fill in the table:

| Property | Relationship | Reasoning |
|--------|--------------|---------|
| Mass | A < B < C | C has the most particles, then B, then A. Each particle has same mass. |
| Volume | A < B < C | C is largest in size, then B, then A. |
| Density | A = B = C | Mass and volume increase proportionally, so mass/volume remains constant. |

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## ✔ Problem 3: Figure 3 – Compare E and F

Figure 3:

- Two blocks: E and F
- Each dot is a particle, but now larger particles have larger mass.
- So: particle size affects mass.

Let’s examine:

- Block E: Smaller particles (smaller dots), many of them.
- Block F: Fewer particles, but larger ones (bigger dots).

Assume:
- In E: 6 small particles
- In F: 4 large particles

But since larger particles have larger mass, we need to consider that.

Let’s assign hypothetical masses:
- Let small particle mass = $ m $
- Large particle mass = $ M $, where $ M > m $

But how much larger? We don’t know exact values, but we can reason qualitatively.

However, observe:
- The boxes are the same size, so volume is the same for E and F.

Now count particles:
- E: 6 small particles → total mass = $ 6m $
- F: 4 large particles → total mass = $ 4M $

But since large particles are bigger, and assuming the particles fill the space, we must consider whether the number of particles or particle size dominates.

But here's the key: Each dot represents a particle, and larger particles have larger mass.

So:
- If a particle is larger, it takes up more space and has more mass.

Let’s suppose:
- The large particles in F are larger than the small ones in E, so each has more mass.
- But there are fewer of them.

But look at the total volume of the block: same for both E and F.

So:
- Volume(E) = Volume(F) → same

Now, which has more mass?

We need to compare total mass.

Suppose:
- In E: 6 small particles → each mass = $ m $
- In F: 4 large particles → each mass = $ M $

But if the large particles are significantly larger, say $ M > 1.5m $, then $ 4M > 6m $, so F has more mass.

But do we know?

Wait — visually, the dots in F are about twice the diameter of those in E.

If particles are spherical, volume ∝ radius³ → so if radius doubles, volume increases by factor of 8.

So if the large particle has twice the radius, its volume is 8 times larger → assuming same density, mass is 8 times larger.

But wait — the problem says: "particles of a larger size have larger mass", so yes, larger particles → larger mass.

But how many?

Let’s estimate from the figure:

- E: ~6 small dots
- F: ~4 large dots

But the large dots appear to be about 1.5–2x the diameter of small ones.

Let’s assume:
- Radius ratio ≈ 1.5 → volume ratio = $ (1.5)^3 = 3.375 $
- So a large particle has ~3.375× the mass of a small one.

Then:
- Total mass of E: $ 6m $
- Total mass of F: $ 4 × 3.375m = 13.5m $

So F has much more mass.

Also, volume is same (same box size).

Therefore:
- Mass: E < F
- Volume: E = F
- Density: E < F

Because density = mass/volume → F has more mass in same volume → higher density.

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#### a. Fill in the table:

| Property | Relationship | Reasoning |
|--------|--------------|---------|
| Mass | E < F | F has fewer particles, but each is larger and thus has more mass. The larger particles contribute significantly more mass overall. |
| Volume | E = F | Both blocks occupy the same physical space (same size box). |
| Density | E < F | Density = mass/volume. Volume is equal, but F has greater mass, so F is denser. |

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## ✔ Final Answers Summary

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Problem 1: Figure 1 – A vs B

| Property | Relationship | Reasoning |
|--------|--------------|---------|
| Mass | A = B | Same number of particles, same mass per particle → same total mass. |
| Volume | A < B | Block B is physically larger. |
| Density | A > B | Same mass, but B has larger volume → lower density. |

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Problem 2: Figure 2 – A, B, C

| Property | Relationship | Reasoning |
|--------|--------------|---------|
| Mass | A < B < C | C has most particles, then B, then A. |
| Volume | A < B < C | C is largest in volume, then B, then A. |
| Density | A = B = C | Mass and volume increase proportionally → same density. |

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Problem 3: Figure 3 – E vs F

| Property | Relationship | Reasoning |
|--------|--------------|---------|
| Mass | E < F | F has larger particles, which have greater mass per particle. Even though fewer in number, their total mass exceeds that of E. |
| Volume | E = F | Both blocks are the same size. |
| Density | E < F | Same volume, but F has more mass → higher density. |

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✔ Boxed Final Answers (as requested):

Problem 1:

- Mass: A = B
- Volume: A < B
- Density: A > B

Problem 2:

- Mass: A < B < C
- Volume: A < B < C
- Density: A = B = C

Problem 3:

- Mass: E < F
- Volume: E = F
- Density: E < F

Let me know if you'd like this formatted as a printable worksheet!