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Difficulty: Very hardProperties of Matter

An astronaut takes a 100 g100 \text{ g} solid block of a pure substance, which has an initial volume of 20 cm320 \text{ cm}^3, to a planet with twice the gravity of Earth. On the new planet, the block is heated until it completely melts, expanding to a volume of 25 cm325 \text{ cm}^3. Which of the following accurately describes the substance on the new planet compared to its initial state on Earth?

  1. Its mass remains 100 g100 \text{ g}, its weight is doubled, and it undergoes a physical change that decreases its density to 4.0 g/cm34.0 \text{ g/cm}^3.Answer
  2. B
    Its mass and weight both double, and it undergoes a physical change that results in a density of 8.0 g/cm38.0 \text{ g/cm}^3.
  3. C
    Its mass remains 100 g100 \text{ g}, its weight is doubled, and it undergoes a chemical change that decreases its density to 4.0 g/cm34.0 \text{ g/cm}^3.
  4. D
    Its mass and weight both double, and it undergoes a chemical change that results in a density of 8.0 g/cm38.0 \text{ g/cm}^3.

Answer

The correct answer is that its mass remains 100 g, its weight is doubled, and it undergoes a physical change that decreases its density to 4.0 g/cm³.
The mass of an object is constant regardless of the gravitational environment, so it remains 100 g100 \text{ g}. Weight is a force dependent on gravity (W=mgW = mg), so placing the object in an environment with twice the gravity doubles its weight. Melting is a phase change, which is strictly a physical change, not a chemical one. Finally, density is mass divided by volume (D=m/VD = m/V); since the mass is 100 g100 \text{ g} and the new volume is 25 cm325 \text{ cm}^3, the resulting density is 4.0 g/cm34.0 \text{ g/cm}^3.

Step-by-Step Solution

1
Determine the effect of increased gravity on mass and weight.
Mass remains 100 g100 \text{ g}, while weight doubles.
Mass is an intrinsic measure of the amount of matter and is independent of gravity, whereas weight is the gravitational force acting on that mass (W=mgW = mg).
2
Identify the type of change occurring during the melting process.
Melting is classified as a physical change.
A phase change from solid to liquid alters the state and volume of a substance but does not change its fundamental chemical composition.
3
Calculate the final density of the liquid on the new planet.
Density =4.0 g/cm3= 4.0 \text{ g/cm}^3.
Density is calculated as mass divided by volume. Using the constant mass (100 g100 \text{ g}) and the new volume (25 cm325 \text{ cm}^3), the new density is 100 g/25 cm3=4.0 g/cm3100 \text{ g} / 25 \text{ cm}^3 = 4.0 \text{ g/cm}^3.

Key Concept

Distinguishing between mass and weight, classifying phase changes, and calculating density.
Estimated Time:2m 0s
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Topics

Properties of Matter

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