Question

Diamonds are measured in carats, and 1 carat $=0.200 \mathrm{~g}$. The density of diamond is $3.51 \mathrm{~g} / \mathrm{cm}^{3}$. What is the volume of a $5.0$ -carat diamnnd?

   Diamonds are measured in carats, and 1 carat $=0.200 \mathrm{~g}$. The density of diamond is $3.51 \mathrm{~g} / \mathrm{cm}^{3}$. What is the volume of a $5.0$ -carat diamnnd?

Chemistry

Steven S. Zumdahl,… 7th Edition

Chapter 1, Problem 57

Instant Answer

Solved by Expert Shalini Tyagi

03/04/2023

Step 1

We know that 1 carat is equal to 0.200 grams. So, for a 5.0 carat diamond, the mass in grams would be: \[5.0 \, \text{carats} \times 0.200 \, \frac{\text{g}}{\text{carat}} = 1.0 \, \text{g}\] Show more…

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Diamonds are measured in carats, and 1 carat $=0.200 \mathrm{~g}$. The density of diamond is $3.51 \mathrm{~g} / \mathrm{cm}^{3}$. What is the volume of a $5.0$ -carat diamnnd?

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Key Concepts

Unit Conversion

Unit conversion involves changing the measurement of a quantity from one set of units to another, using a conversion factor. In this problem, carats are converted into grams using the conversion relationship, which is essential for ensuring that all quantities are in a consistent unit system for further calculations.

Density

Density is a measure of mass per unit volume and is typically expressed in units such as grams per cubic centimeter (g/cm³). It indicates how much mass is packed into a given volume and is crucial for determining one variable when the other two (mass and volume) are known.

Volume Calculation

Volume calculation in the context of density involves using the formula volume = mass/density. This equation allows determination of the volume occupied by a given mass of a substance, provided that the density is known, and is fundamental in various fields such as physics and material science.

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