Density Calculations Worksheet I: Word Problems | PDF - Free Printable

Let's solve each part of the Density Calculations Worksheet I step by step.

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🔷 Key Formula:

$$
\text{Density} (d) = \frac{\text{Mass} (M)}{\text{Volume} (V)}
$$

- Units:
- Solids: g/cm³
- Liquids: g/mL
- Note: 1 mL = 1 cm³, so they are equivalent for liquids and solids.

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## ✔ Section 1: Find the unknown quantity

a)

Given:
- $ d = 3 \, \text{g/mL} $
- $ V = 100 \, \text{mL} $
- $ M = ? $

Use:
$$
M = d \times V = 3 \, \text{g/mL} \times 100 \, \text{mL} = 300 \, \text{g}
$$

✔ Answer: M = 300 g

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b)

Given:
- $ V = 950 \, \text{mL} $
- $ M = 95 \, \text{g} $
- $ d = ? $

Use:
$$
d = \frac{M}{V} = \frac{95 \, \text{g}}{950 \, \text{mL}} = 0.1 \, \text{g/mL}
$$

✔ Answer: d = 0.1 g/mL

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c)

Given:
- $ d = 0.5 \, \text{g/cm}^3 $
- $ M = 20 \, \text{g} $
- $ V = ? $

Use:
$$
V = \frac{M}{d} = \frac{20 \, \text{g}}{0.5 \, \text{g/cm}^3} = 40 \, \text{cm}^3
$$

✔ Answer: V = 40 cm³

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## ✔ Section 2: Find the unknown quantity (Convert first to g or mL)

a)

Given:
- $ d = 24 \, \text{g/mL} $
- $ V = 1.2 \, \text{L} $ → Convert to mL:
$ 1.2 \, \text{L} = 1.2 \times 1000 = 1200 \, \text{mL} $
- $ M = ? $

$$
M = d \times V = 24 \, \text{g/mL} \times 1200 \, \text{mL} = 28,800 \, \text{g}
$$

✔ Answer: M = 28,800 g

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b)

Given:
- $ V = 100 \, \text{mL} $
- $ M = 1.5 \, \text{kg} $ → Convert to grams:
$ 1.5 \, \text{kg} = 1.5 \times 1000 = 1500 \, \text{g} $
- $ d = ? $

$$
d = \frac{M}{V} = \frac{1500 \, \text{g}}{100 \, \text{mL}} = 15 \, \text{g/mL}
$$

✔ Answer: d = 15 g/mL

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c)

Given:
- $ V = 0.52 \, \text{L} $ → Convert to mL:
$ 0.52 \, \text{L} = 0.52 \times 1000 = 520 \, \text{mL} $
- $ M = 500 \, \text{mg} $ → Convert to grams:
$ 500 \, \text{mg} = 500 \div 1000 = 0.5 \, \text{g} $
- $ d = ? $

$$
d = \frac{M}{V} = \frac{0.5 \, \text{g}}{520 \, \text{mL}} \approx 0.0009615 \, \text{g/mL}
$$

Round to appropriate significant figures (3 sig figs):
$$
d \approx 0.000962 \, \text{g/mL}
$$

Alternatively, in scientific notation:
$$
d = 9.62 \times 10^{-4} \, \text{g/mL}
$$

✔ Answer: d ≈ 0.000962 g/mL or $ 9.62 \times 10^{-4} \, \text{g/mL} $

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## ✔ WORD PROBLEMS

1. A block of aluminum occupies a volume of 15.0 mL and weighs 40.5 g. What is its density?

Given:
- $ M = 40.5 \, \text{g} $
- $ V = 15.0 \, \text{mL} $

$$
d = \frac{M}{V} = \frac{40.5 \, \text{g}}{15.0 \, \text{mL}} = 2.70 \, \text{g/mL}
$$

✔ Answer: Density = 2.70 g/mL

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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. Calculate the density of mercury.

Given:
- $ M = 306.0 \, \text{g} $
- $ V = 22.5 \, \text{mL} $

$$
d = \frac{306.0 \, \text{g}}{22.5 \, \text{mL}} = 13.6 \, \text{g/mL}
$$

✔ Answer: Density of mercury = 13.6 g/mL

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## 📝 Final Answers Summary:

Section 1:

a) M = 300 g
b) d = 0.1 g/mL
c) V = 40 cm³

Section 2:

a) M = 28,800 g
b) d = 15 g/mL
c) d = $ 9.62 \times 10^{-4} \, \text{g/mL} $ (or 0.000962 g/mL)

Word Problems:

1. Density of aluminum = 2.70 g/mL
2. Density of mercury = 13.6 g/mL

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