Dicyclopentadiene has a density of 0.98 g/mL. Cyclopentadiene has a density of 0.80 g/mL. Which has a greater volume, 0.5 grams of dicyclopentadiene or 0.5 grams of cyclopentadiene? Either explain your reasoning or show your calculations. (2 pts)
The Correct Answer and Explanation is:
Volume=DensityMass
Given:
- Mass of both substances = 0.5 grams
- Density of dicyclopentadiene = 0.98 g/mL
- Density of cyclopentadiene = 0.80 g/mL
Calculations:
Volume of dicyclopentadiene:0.5 g0.98 g/mL≈0.51 mL\frac{0.5 \text{ g}}{0.98 \text{ g/mL}} \approx 0.51 \text{ mL}0.98 g/mL0.5 g≈0.51 mL
Volume of cyclopentadiene:0.5 g0.80 g/mL=0.625 mL\frac{0.5 \text{ g}}{0.80 \text{ g/mL}} = 0.625 \text{ mL}0.80 g/mL0.5 g=0.625 mL
Answer:
0.5 grams of cyclopentadiene has a greater volume than 0.5 grams of dicyclopentadiene.
Explanation
To compare the volume occupied by equal masses of dicyclopentadiene and cyclopentadiene, we use the basic principle of density, which is defined as mass per unit volume. When mass is held constant, the substance with the lower density will occupy more volume.
In this case, both samples have the same mass: 0.5 grams. However, dicyclopentadiene has a density of 0.98 g/mL, while cyclopentadiene is less dense at 0.80 g/mL. Since volume is calculated as mass divided by density, a lower density leads to a larger volume for the same mass.
Mathematically, when we divide 0.5 g by each density, we find that the dicyclopentadiene occupies approximately 0.51 mL, while cyclopentadiene occupies 0.625 mL. This confirms that cyclopentadiene takes up more space despite having the same mass.
This result aligns with the physical meaning of density. If a substance is less dense, its molecules are more spread out, allowing a smaller mass to occupy a larger space. Conversely, denser substances have more mass packed into each unit of volume, meaning the same mass will result in a smaller volume.
In practical terms, this concept is critical in fields like chemistry and engineering, where understanding how much space a given mass of a material will occupy can affect container sizing, reaction yields, or transport logistics. Thus, in this comparison, cyclopentadiene has the greater volume due to its lower density.
