A vase is said to be solid platinum. It displaces \(18.65 \mathrm{~mL}\) of water and has a mass of \(157 \mathrm{~g}\). Could the vase be solid platinum?

Understanding the density of materials is a fundamental concept in chemistry and physics. Density is defined as the mass of a material per unit volume. This intrinsic property can help identify a substance or determine its purity.

For instance, in the given exercise, the question revolves around evaluating if a vase could be made of solid platinum by considering its density. To make this determination, one needs to know the mass and volume of the vase and the typical density of platinum. Once you know these values, you can perform a simple calculation: divide the mass by the volume to find the density of the vase. Then compare it to the known density of platinum, which is about 21450 kg/m^3. If the densities match or are very close, it's plausible that the vase is made of solid platinum. The precision of this assessment depends on how meticulously the mass and volume measurements are taken and how well defined the reference density of platinum is.

The mass to volume ratio is another way of expressing the concept of density. It is the amount of mass per unit volume and is represented by the equation \[\begin{equation} Density = \frac{Mass}{Volume} \end{equation}\].In the context of our exercise, we first measure the mass and volume directly. The mass is given in grams and the volume in milliliters. However, for uniformity in scientific calculations and to comply with the International System of Units (SI), it's often necessary to convert these measurements into kilograms and cubic meters, respectively.

This conversion is imperative because comparisons must be made using the same units. Once the mass and volume are expressed in consistent SI units, calculating the density of the vase becomes straightforward. The steps provided in the solution effectively guide students through this process, leading them to conclude whether the vase's density is comparable to that of platinum.

Unit conversion in chemistry is crucial for accurate calculations and meaningful comparisons. Different regions or experiments may use various units to measure mass and volume, which could potentially complicate things when comparing data. Learning how to convert between units — for example, grams to kilograms or milliliters to cubic meters — is therefore an essential skill.To convert mass given in grams to kilograms, as required in our exercise, remember that 1 kilogram equals 1000 grams. Similarly, convert volume from milliliters to cubic meters knowing that 1 milliliter is equivalent to 1e-6 cubic meters (or 1 cubic centimeter, as commonly known in chemistry).

Keep these conversion factors in mind:

• 1 kg = 1000 g
• 1 m^3 = 1e6 mL
• 1 mL = 1e-3 L
• 1 m^3 = 1000 L

Incorporating these conversions is a critical step in chemistry calculations. A failure to convert units correctly can lead to errors in the result, which in our exercise might mean incorrectly determining whether the vase is made of platinum. Therefore, consistency in units is vital to scientific accuracy and integrity.