To determine which statement accurately describes the significance of the calculated density value, we must first understand what density is and how it relates to different substances.
Density is defined as mass per unit volume and is given by the formula:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
From the experiment, the scientist has the following data:
- Mass of the substance = 50 grams
- Volume of the substance = 25 cm³
Using the formula for density, we can calculate the density of the substance:
[tex]\[ \text{Density of the substance} = \frac{50 \text{ grams}}{25 \text{ cm}³} = 2 \text{ g/cm}³ \][/tex]
Now, we need to interpret the significance of a density of 2 g/cm³.
1. Density of Water (for reference): The density of water at room temperature is approximately 1 g/cm³.
Next, we will review each of the given statements:
A. The density value indicates that the substance is twice as heavy as water.
- This statement implies that for some given volume, the mass of the substance is twice that of water. Since the density of water is 1 g/cm³, for the same volume, the mass of this substance would indeed be twice that of water because its density is twice that of water. However, "twice as heavy" typically should be interpreted in a specific context where volume is fixed, which might not always be clear.
B. The density value implies that the substance occupies twice the volume of water.
- This statement would be appropriate if we were comparing equal masses of the substance and water. In fact, since the density of the substance is 2 g/cm³ and water is 1 g/cm³, for the same mass, the volume of this substance would actually be half that of water, not twice. Hence, this statement is incorrect.
C. The density value suggests that the substance is twice as dense as water.
- This statement is correct. The density of the substance (2 g/cm³) is indeed twice the density of water (1 g/cm³).
D. The density value indicates that the substance is more compact or tightly packed than water.
- This statement is also technically correct. A higher density indicates that the substance has more mass per unit volume, meaning it is more compact or tightly packed compared to water.
After evaluating all the options, the most accurate significance of the calculated density value is:
C. The density value suggests that the substance is twice as dense as water.
This statement directly and accurately describes the relationship between the given substance and water in terms of density.
