Table of contents

1. Matter and Measurements4h 31m
2. Atoms and the Periodic Table5h 23m
3. Ionic Compounds2h 18m
4. Molecular Compounds2h 18m
5. Classification & Balancing of Chemical Reactions3h 17m
6. Chemical Reactions & Quantities2h 27m
7. Energy, Rate and Equilibrium3h 46m
8. Gases, Liquids and Solids3h 25m
9. Solutions4h 10m
10. Acids and Bases3h 29m
11. Nuclear Chemistry56m
BONUS: Lab Techniques and Procedures1h 38m
BONUS: Mathematical Operations and Functions47m
12. Introduction to Organic Chemistry1h 34m
13. Alkenes, Alkynes, and Aromatic Compounds2h 12m
14. Compounds with Oxygen or Sulfur1h 6m
15. Aldehydes and Ketones1h 1m
16. Carboxylic Acids and Their Derivatives1h 11m
17. Amines39m
18. Amino Acids and Proteins1h 51m
19. Enzymes1h 37m
20. Carbohydrates1h 41m
21. The Generation of Biochemical Energy2h 8m
22. Carbohydrate Metabolism2h 22m
23. Lipids2h 26m
24. Lipid Metabolism1h 45m
25. Protein and Amino Acid Metabolism1h 37m
26. Nucleic Acids and Protein Synthesis2h 54m

1. Matter and Measurements

Dimensional Analysis

GOB Chemistry

1. Matter and Measurements

Dimensional Analysis

Previous problemNext problem

0:58 minutes

Problem 95

Textbook Question

Gemstones are weighed in carats, where 1 carat = 200 mg exactly. What is the mass in grams of the Hope diamond, the world's largest blue diamond, at 44.4 carats?

Verified step by step guidance

Step 1: Understand the relationship between carats and milligrams. The problem states that 1 carat is equal to 200 milligrams (mg).

Step 2: Write the given information. The mass of the Hope diamond is 44.4 carats.

Step 3: Set up a conversion factor to convert carats to milligrams. Use the relationship: \( 1 \text{ carat} = 200 \text{ mg} \). Multiply the given carats by this conversion factor.

Step 4: Convert the result from milligrams to grams. Use the relationship: \( 1 \text{ g} = 1000 \text{ mg} \). Divide the mass in milligrams by 1000 to get the mass in grams.

Step 5: Combine the steps into a single calculation: \( \text{Mass in grams} = 44.4 \text{ carats} \times \frac{200 \text{ mg}}{1 \text{ carat}} \times \frac{1 \text{ g}}{1000 \text{ mg}} \). Simplify the expression to find the final mass in grams.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

58s

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Carat Measurement

A carat is a unit of weight used for gemstones and pearls, where one carat is equivalent to 200 milligrams. This measurement is crucial in the jewelry industry as it helps determine the value and size of gemstones. Understanding carats is essential for converting gemstone weights into grams or other units.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. In this context, converting carats to grams involves using the conversion factor that 1 carat equals 0.2 grams. Mastery of unit conversion is vital for accurately calculating weights and understanding measurements in different contexts.

Mass and Weight

Mass refers to the amount of matter in an object, typically measured in grams or kilograms, while weight is the force exerted by gravity on that mass. In this question, we focus on mass, as we are converting the weight of the Hope diamond from carats to grams. Recognizing the distinction between mass and weight is important in scientific calculations.

Watch next

Master Dimensional Analysis with a bite sized video explanation from Jules

Start learning

Related Videos

Related Practice

Textbook Question

Obtain a package of your favorite snack food and examine the nutritional information on the label. Confirm the caloric value listed by using the conversions listed in the table in the Chemistry in Action feature 'Energy from Food' (p. 191). Alternatively, you can use the estimates for caloric value for a given food as provided in the table.

b. How long would you have to engage in each of the physical activities to burn the calories contained in your snack?

1544

views

Textbook Question

The length of this rug is 38.4 in. and the width is 24.2 in.

<IMAGE>

d. Calculate the area of the rug, in square centimeters, to the correct number of significant figures. (Area = Length x Width)

1249

views

Textbook Question

A shipping box has a length of 7.00 in., a width of 6.00 in., and a height of 4.00 in.

<IMAGE>

b. What is the width of the box, in centimeters?

1875

views

Textbook Question

A shipping box has a length of 7.00 in., a width of 6.00 in., and a height of 4.00 in.

<IMAGE>

a. What is the length of the box, in centimeters?

1976

views

Textbook Question

In France, grapes are 1.95 euros per kilogram. What is the cost of grapes, in dollars per pound, if the exchange rate is 1.14 dollars/euro?

1432

views

Textbook Question

In Mexico, avocados are 48 pesos per kilogram. What is the cost, in cents, of an avocado that weighs 0.45 lb if the exchange rate is 18 pesos to the dollar?

1365

views

Textbook Question

To treat a bacterial infection, a doctor orders 4 tablets of amoxicillin per day for 10 days. If each tablet contains 250 mg of amoxicillin, how many ounces of the medication are given in 10 days?

1511

views

Textbook Question

An athlete with a body mass of 65 kg has 3.0% body fat. How many pounds of body fat does that person have?

1446

views

Show more practices

Download the Mobile app

Privacy

Do not sell my personal information

Accessibility

Patent notice

Sitemap