Question

For a precious stone, 'carat' is used for specifying its mass. If 1 carat $=3.168$ grains (a unit of mass) and 1 gram $=15.4$ grains, find the total mass in kilogram of the ring that contains a $0.500$ carat diamond and $7.00$ gram gold.

Name: Problem 24, Chapter 2: Numerical problems in Physical Chemistry for IIT-JEE
Uploaded: 2021-08-26T04:28:29-08:00
Duration: 2 min 10 s
Channel: Suman Saurav Thakur
Description: For a precious stone, 'carat' is used for specifying its mass. If 1 carat =3.168 grains (a unit of mass) and 1 gram =15.4 grains, find the total mass in kilogram of the ring that contains a 0.500 carat diamond and 7.00 gram gold.

   For a precious stone, 'carat' is used for specifying its mass. If 1 carat $=3.168$ grains (a unit of mass) and 1 gram $=15.4$ grains, find the total mass in kilogram of the ring that contains a $0.500$ carat diamond and $7.00$ gram gold.

Numerical problems in Physical Chemistry for IIT-JEE

P. Bahadur, Shalabh… 2010 Edition

Chapter 2, Problem 24

Instant Answer

Solved by Expert Suman Saurav Thakur

08/26/2021

Step 1

We know that 1 carat is equal to 3.168 grains and 1 gram is equal to 15.4 grains. So, we can write the weight of the diamond in grams as: \[0.500 \, \text{carats} \times \frac{3.168 \, \text{grains}}{1 \, \text{carat}} \times \frac{1 \, \text{gram}}{15.4 \, Show more…

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For a precious stone, 'carat' is used for specifying its mass. If 1 carat $=3.168$ grains (a unit of mass) and 1 gram $=15.4$ grains, find the total mass in kilogram of the ring that contains a $0.500$ carat diamond and $7.00$ gram gold.

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Key Concepts

Unit Conversion

This concept involves changing a quantity expressed in one set of units to another using conversion factors. In mass conversion problems, you multiply by factors that relate different units (such as carats, grains, grams, and kilograms) to obtain the correct measure in the desired unit.

Dimensional Analysis

Dimensional Analysis is the process of ensuring that units cancel appropriately during a calculation, resulting in the final answer expressed in the correct unit of measurement. It is a systematic method to check that the correct conversion factors have been used in each step.

Proportional Reasoning

Proportional Reasoning involves using ratios and relationships between units to convert from one measurement to another. It is essential for accurately determining quantities when each unit can be expressed as a proportion of another.

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