Question

what is the mass of ice in grams of a 0.485 cm³ sample if its density is 0.917 g/cm³ at 273 k?

1. what is the volume of lanthanum in cubic centimeters of a 0.187 g sample if its density is 6.15 g/cm³?
2. what is the mass of manganese in grams of a 0.412 cm³ sample if its density is 7.33 g/cm³?
3. what is the volume of water in milliliters of a 2.93 g sample if its density is 0.998 g/ml at 293 k?
4. what is the density of ytterbium in grams per cubic centimeter if a 1.12 g sample has a volume of 0.161 cm³?

Explanation:

Step1: Recall density formula

The core density formula is $
ho = \frac{m}{V}$, where $
ho$ = density, $m$ = mass, $V$ = volume. Rearrange as needed for each question.

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Question 1

Step1: Rearrange for mass

$m =
ho \times V$

Step2: Substitute values

$m = 0.917\ \text{g/cm}^3 \times 0.485\ \text{cm}^3$

Step3: Calculate result

$m = 0.917 \times 0.485 = 0.445$

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Question 2

Step1: Rearrange for volume

$V = \frac{m}{
ho}$

Step2: Substitute values

$V = \frac{0.187\ \text{g}}{6.15\ \text{g/cm}^3}$

Step3: Calculate result

$V = \frac{0.187}{6.15} = 0.0304$

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Question 3

Step1: Rearrange for mass

$m =
ho \times V$

Step2: Substitute values

$m = 7.33\ \text{g/cm}^3 \times 0.412\ \text{cm}^3$

Step3: Calculate result

$m = 7.33 \times 0.412 = 3.02$

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Question 4

Step1: Rearrange for volume

$V = \frac{m}{
ho}$

Step2: Substitute values

$V = \frac{2.93\ \text{g}}{0.998\ \text{g/mL}}$

Step3: Calculate result

$V = \frac{2.93}{0.998} = 2.94$

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Question 5

Step1: Use density formula

$
ho = \frac{m}{V}$

Step2: Substitute values

$
ho = \frac{1.12\ \text{g}}{0.161\ \text{cm}^3}$

Step3: Calculate result

$
ho = \frac{1.12}{0.161} = 6.96$

Answer:

1. $0.445\ \text{g}$
2. $0.0304\ \text{cm}^3$
3. $3.02\ \text{g}$
4. $2.94\ \text{mL}$
5. $6.96\ \text{g/cm}^3$