In determining the density of olive oil (see Table 2.2), one student took exactly 25.00 mL and found the mass to be 22.95 g. A second student took exactly 50.00 mL and found the mass to be 45.90 g. Will each student arrive at the same value for the density? Do each calculation and explain the result
In determining the density of olive oil (see Table 2.2), one student took exactly 25.00 mL and found the mass to be 22.95 g. A second student took exactly 50.00 mL and found the mass to be 45.90 g. Will each student arrive at the same value for the density? Do each calculation and explain the result
The Correct Answer and Explanation is:
Answer:
To determine if both students will arrive at the same value for the density of olive oil, we calculate density using the formula: Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}
Calculations:
Student 1: Density=22.95 g25.00 mL=0.918 g/mL\text{Density} = \frac{22.95 \, \text{g}}{25.00 \, \text{mL}} = 0.918 \, \text{g/mL}
Student 2: Density=45.90 g50.00 mL=0.918 g/mL\text{Density} = \frac{45.90 \, \text{g}}{50.00 \, \text{mL}} = 0.918 \, \text{g/mL}
Explanation:
Both students arrive at the same density of 0.918 g/mL for olive oil, even though they used different volumes. This outcome is expected because density is an intensive property, meaning it does not depend on the amount of substance used. As long as the substance is pure and measured accurately, the density remains constant regardless of the sample size.
In this case, both students appear to have measured mass and volume accurately and consistently. The ratio of mass to volume for both samples is identical, confirming the reliability of their measurements and the uniformity of the olive oil sample.
This demonstrates a key concept in chemistry and physics: density is characteristic of a substance, just like melting point or boiling point. It’s used to identify materials and check for purity. If either student had obtained a different density, it might have suggested measurement errors (e.g., incorrect mass, air bubbles in the volume measurement, or contaminated sample).
In conclusion, both students correctly calculated the same density for olive oil, reinforcing the principle that density remains constant for a given substance under consistent conditions.
