Density Calculations Worksheet I - Free Printable

Let's solve each problem step by step using the density formula:

$$
\text{Density (D)} = \frac{\text{Mass (m)}}{\text{Volume (v)}}
$$

And its rearranged forms:
- $ m = D \times v $
- $ v = \frac{m}{D} $

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1. Find the unknown quantity for a, b, and c:

#### a)
Given:
- $ D = 3 \, \text{g/mL} $
- $ v = 100 \, \text{mL} $
- Find $ m $

Use:
$$
m = D \times v = 3 \, \text{g/mL} \times 100 \, \text{mL} = 300 \, \text{g}
$$

✔ Answer: $ m = 300 \, \text{g} $

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#### b)
Given:
- $ v = 950 \, \text{mL} $
- $ m = 95 \, \text{g} $
- Find $ D $

Use:
$$
D = \frac{m}{v} = \frac{95 \, \text{g}}{950 \, \text{mL}} = 0.1 \, \text{g/mL}
$$

✔ Answer: $ D = 0.1 \, \text{g/mL} $

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#### c)
Given:
- $ D = 0.5 \, \text{g/cm}^3 $
- $ m = 20 \, \text{g} $
- Find $ v $

Use:
$$
v = \frac{m}{D} = \frac{20 \, \text{g}}{0.5 \, \text{g/cm}^3} = 40 \, \text{cm}^3
$$

But note: The question asks for volume in mL.

Since $ 1 \, \text{cm}^3 = 1 \, \text{mL} $, then:

$$
v = 40 \, \text{mL}
$$

✔ Answer: $ v = 40 \, \text{mL} $

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2. Find the unknown quantity:

#### a)
Given:
- $ D = 24 \, \text{g/mL} $
- $ v = 1200 \, \text{mL} $
- Find $ m $

$$
m = D \times v = 24 \, \text{g/mL} \times 1200 \, \text{mL} = 28,800 \, \text{g}
$$

✔ Answer: $ m = 28,800 \, \text{g} $

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#### b)
Given:
- $ v = 100 \, \text{mL} $
- $ m = 1500 \, \text{g} $
- Find $ D $

$$
D = \frac{m}{v} = \frac{1500 \, \text{g}}{100 \, \text{mL}} = 15 \, \text{g/mL}
$$

✔ Answer: $ D = 15 \, \text{g/mL} $

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#### c)
Given:
- $ v = 520 \, \text{mL} $
- $ m = 500 \, \text{g} $
- Find $ D $

$$
D = \frac{m}{v} = \frac{500 \, \text{g}}{520 \, \text{mL}} \approx 0.9615 \, \text{g/mL}
$$

Rounded to three significant figures:
$$
D \approx 0.962 \, \text{g/mL}
$$

✔ Answer: $ D = 0.962 \, \text{g/mL} $

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WORD PROBLEMS:

#### 1. Aluminum block
Given:
- Volume $ v = 15.0 \, \text{mL} $
- Mass $ m = 40.5 \, \text{g} $
- Find density $ D $

Formula:
$$
D = \frac{m}{v}
$$

Substitution with units:
$$
D = \frac{40.5 \, \text{g}}{15.0 \, \text{mL}}
$$

Solution with units:
$$
D = 2.70 \, \text{g/mL}
$$

✔ Answer: Density of aluminum = $ 2.70 \, \text{g/mL} $

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#### 2. Mercury in graduated cylinder
Given:
- Volume $ v = 22.5 \, \text{mL} $
- Mass $ m = 306.0 \, \text{g} $
- Find density $ D $

Formula:
$$
D = \frac{m}{v}
$$

Substitution with units:
$$
D = \frac{306.0 \, \text{g}}{22.5 \, \text{mL}}
$$

Solution with units:
$$
D = 13.6 \, \text{g/mL}
$$

✔ Answer: Density of mercury = $ 13.6 \, \text{g/mL} $

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✔ Final Answers Summary:

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Part 1:

a) $ m = 300 \, \text{g} $
b) $ D = 0.1 \, \text{g/mL} $
c) $ v = 40 \, \text{mL} $

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Part 2:

a) $ m = 28,800 \, \text{g} $
b) $ D = 15 \, \text{g/mL} $
c) $ D = 0.962 \, \text{g/mL} $

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Word Problems:

1. Density of aluminum = $ 2.70 \, \text{g/mL} $
2. Density of mercury = $ 13.6 \, \text{g/mL} $

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All answers include proper units and show correct use of formulas. Let me know if you'd like this formatted as a printable worksheet!