A relative density bottle has a mass of 19 g when empty. When it is completely filled with water, its mass is…

Analysis

To solve this problem, we need to understand the relationship between mass, volume, and relative density. The relative density of a substance is the ratio of the mass of a certain volume of that substance to the mass of an equal volume of water.

Concept

1. Mass of water: The mass of the water alone is the total mass when filled with water minus the mass of the empty bottle.
2. Volume: Since the bottle is the same, the volume of alcohol will be equal to the volume of water.
3. Relative Density (R.D.): $$\text{R.D.} = \frac{\text{Mass of substance}}{\text{Mass of equal volume of water}}$$Therefore,$\text{Mass of substance} = \text{R.D.} \times \text{Mass of equal volume of water}$.

Step-by-Step Solution

Step 1: Calculate the mass of the water.

• Mass of empty bottle = $19\text{ g}$
• Mass of bottle + water = $66\text{ g}$
• Mass of water = $66\text{ g} - 19\text{ g} = 47\text{ g}$

Step 2: Calculate the mass of the alcohol.

• Relative density of alcohol = $0.8$
• Mass of alcohol = $\text{R.D. of alcohol} \times \text{Mass of water}$
• Mass of alcohol = $0.8 \times 47\text{ g} = 37.6\text{ g}$

Step 3: Calculate the total mass of the bottle filled with alcohol.

• Total mass = Mass of empty bottle + Mass of alcohol
• Total mass = $19\text{ g} + 37.6\text{ g} = 56.6\text{ g}$

Conclusion

Comparing our result to the options provided, we see that $56.6\text{ g}$ corresponds to option D.

Exam Tip

Always remember to subtract the mass of the container (the "tare" weight) before performing calculations involving the density of the contents. Many students mistakenly multiply the total mass ($66\text{ g}$) by the relative density, which leads to an incorrect answer. Always isolate the mass of the liquid first!