Density Calculations Worksheet featuring problems on finding density, volume, and mass with unit conversions.

Let's solve the Density Calculations Worksheet step by step. I'll go through each section and provide clear explanations.

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Section 1: Find the unknown quantity

We are given the formula for density:

> Density (D) = Mass (M) / Volume (V)
> Or rearranged:
> - Mass (M) = Density × Volume
> - Volume (V) = Mass / Density

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#### Problem 1:
- D = ?
- M = 20 g
- V = 10 mL

$$
D = \frac{M}{V} = \frac{20\, \text{g}}{10\, \text{mL}} = 2\, \text{g/mL}
$$

✔ Answer: D = 2 g/mL

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#### Problem 2:
- D = 4 g/mL
- V = 660 mL
- M = ?

$$
M = D \times V = 4\, \text{g/mL} \times 660\, \text{mL} = 2640\, \text{g}
$$

✔ Answer: M = 2640 g

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#### Problem 3:
- D = 0.95 g/mL
- V = ?
- M = 70 g

$$
V = \frac{M}{D} = \frac{70\, \text{g}}{0.95\, \text{g/mL}} \approx 73.68\, \text{mL}
$$

✔ Answer: V ≈ 73.7 mL (rounded to one decimal place)

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Section 2: Find the unknown quantity (CONVERT FIRST to g or mL)

We must convert units before calculating.

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#### Problem 1:
- D = 24 g/mL
- V = 1.5 L → convert to mL
- M = ?

Convert liters to milliliters:
1 L = 1000 mL → 1.5 L = 1500 mL

Now calculate mass:

$$
M = D \times V = 24\, \text{g/mL} \times 1500\, \text{mL} = 36,000\, \text{g}
$$

✔ Answer: M = 36,000 g

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#### Problem 2:
- D = ?
- M = 1.5 kg → convert to grams
- V = 1700 mL

Convert kilograms to grams:
1 kg = 1000 g → 1.5 kg = 1500 g

Now calculate density:

$$
D = \frac{M}{V} = \frac{1500\, \text{g}}{1700\, \text{mL}} \approx 0.882\, \text{g/mL}
$$

✔ Answer: D ≈ 0.88 g/mL (rounded to two significant figures)

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#### Problem 3:
- D = 0.85 g/mL
- M = 500 mg → convert to grams
- V = ?

Convert milligrams to grams:
1000 mg = 1 g → 500 mg = 0.5 g

Now find volume:

$$
V = \frac{M}{D} = \frac{0.5\, \text{g}}{0.85\, \text{g/mL}} \approx 0.588\, \text{mL}
$$

✔ Answer: V ≈ 0.59 mL (rounded to two significant figures)

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Word Problems

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#### Problem 1:
> A block of aluminum occupies a volume of 15.0 cm³ and weighs 40.5 g. What is its density?

Use the formula:

$$
D = \frac{M}{V} = \frac{40.5\, \text{g}}{15.0\, \text{cm}^3} = 2.7\, \text{g/cm}^3
$$

✔ Answer: Density = 2.7 g/cm³

*(Note: 1 cm³ = 1 mL, so this is equivalent to 2.7 g/mL)*

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#### Problem 2:
> Mercury metal is poured into a graduated cylinder that holds exactly 22.5 mL. The mercury used to fill the cylinder weighs 306.0 g. What is the density of mercury?

$$
D = \frac{M}{V} = \frac{306.0\, \text{g}}{22.5\, \text{mL}} = 13.6\, \text{g/mL}
$$

✔ Answer: Density = 13.6 g/mL

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✔ Final Answers Summary:

#### Section 1:
1. D = 2 g/mL
2. M = 2640 g
3. V = 73.7 mL

#### Section 2:
1. M = 36,000 g
2. D = 0.88 g/mL
3. V = 0.59 mL

#### Word Problems:
1. Aluminum density = 2.7 g/cm³
2. Mercury density = 13.6 g/mL

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