Question

use the following information to answer question 7.

mass and volume of two samples
\

$$\begin{tabular}{|c|c|} \\hline sample a & sample b \\\\ \\hline mass: 22.0 g & mass: 7.5 g \\\\ volume: 120 cm\\(^3\\) & volume: 2.2 cm\\(^3\\) \\\\ \\hline \\end{tabular}$$

1. the sample with the greater density is \\(i\\), whose particle spacing, when compared to the other sample, would look like \\(ii\\).

the statement above is best completed by the answers in row:

\

$$\begin{tabular}{|c|c|c|} \\hline row & \\(i\\) & \\(ii\\) \\\\ \\hline a. & sample a & image of sparse particles \\\\ \\hline b. & sample a & image of closely packed particles \\\\ \\hline c. & sample b & image of sparse particles \\\\ \\hline d. & sample b & image of closely packed particles \\\\ \\hline \\end{tabular}$$

Explanation:

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<reasoning>

Calculate the density of Sample A

Using the Density Calculation knowledge point
\[
\text{Density}_A = \frac{\text{Mass}}{\text{Volume}} = \frac{22.0\text{ g}}{120\text{ cm}^3} \approx 0.183\text{ g/cm}^3
\]

Calculate the density of Sample B

Using the Density Calculation knowledge point
\[
\text{Density}_B = \frac{\text{Mass}}{\text{Volume}} = \frac{7.5\text{ g}}{2.2\text{ cm}^3} \approx 3.41\text{ g/cm}^3
\]

Compare densities to identify blank i

Using the Density Calculation knowledge point
\[
3.41\text{ g/cm}^3 > 0.183\text{ g/cm}^3 \implies \text{Density}_B > \text{Density}_A
\]
Thus, the sample with the greater density is Sample B.

Relate density to particle spacing for blank ii

Using the Particle Theory of Matter and Spaces Between Particles knowledge points
\[
\text{Greater Density} \implies \text{More particles per unit volume} \implies \text{Closely packed particles}
\]
The diagram representing closely packed particles with minimal spacing is the dense grid of circles shown in row D.

Match findings to the correct option

Combining the results:

• Blank i: Sample B
• Blank ii: Closely packed particle diagram (row D)

</reasoning>

<answer>
<mcq-option>(A) Sample A, widely spaced particles</mcq-option>
<mcq-option>(B) Sample A, closely packed particles</mcq-option>
<mcq-option>(C) Sample B, widely spaced particles</mcq-option>
<mcq-correct>(D) Sample B, closely packed particles</mcq-correct>
</answer>

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Answer:

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<reasoning>

Calculate the density of Sample A

Using the Density Calculation knowledge point
\[
\text{Density}_A = \frac{\text{Mass}}{\text{Volume}} = \frac{22.0\text{ g}}{120\text{ cm}^3} \approx 0.183\text{ g/cm}^3
\]

Calculate the density of Sample B

Using the Density Calculation knowledge point
\[
\text{Density}_B = \frac{\text{Mass}}{\text{Volume}} = \frac{7.5\text{ g}}{2.2\text{ cm}^3} \approx 3.41\text{ g/cm}^3
\]

Compare densities to identify blank i

Using the Density Calculation knowledge point
\[
3.41\text{ g/cm}^3 > 0.183\text{ g/cm}^3 \implies \text{Density}_B > \text{Density}_A
\]
Thus, the sample with the greater density is Sample B.

Relate density to particle spacing for blank ii

Using the Particle Theory of Matter and Spaces Between Particles knowledge points
\[
\text{Greater Density} \implies \text{More particles per unit volume} \implies \text{Closely packed particles}
\]
The diagram representing closely packed particles with minimal spacing is the dense grid of circles shown in row D.

Match findings to the correct option

Combining the results:

• Blank i: Sample B
• Blank ii: Closely packed particle diagram (row D)

</reasoning>

<answer>
<mcq-option>(A) Sample A, widely spaced particles</mcq-option>
<mcq-option>(B) Sample A, closely packed particles</mcq-option>
<mcq-option>(C) Sample B, widely spaced particles</mcq-option>
<mcq-correct>(D) Sample B, closely packed particles</mcq-correct>
</answer>

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