Introductory Chemistry: An Active Learning Approach
Introductory Chemistry: An Active Learning Approach
6th Edition
ISBN: 9781305079250
Author: Mark S. Cracolice, Ed Peters
Publisher: Cengage Learning
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Chapter 20, Problem 68E
Interpretation Introduction

Interpretation:

Whether the radioactivity of US or US2 is more is to be predicted. If 0.5moles of each compound is prepared, the compound which is more radioactive is to be stated. The explanation for both the answers is to be stated.

Concept introduction:

Half-life is defined as the time required for the number of nuclides to reach half of the original value. Half-life is defined as the time required for the number of nuclides to reach half of the original value. The remaining mass of a sample is calculated by the formula shown below.

R=S×(1/2)n

Where,

n is the number of half-lives.

R is the remaining amount of a sample after n half-lives.

S is the initial amount of a sample.

Expert Solution & Answer
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Answer to Problem 68E

The compound US will exhibit more amount of radioactivity.

The radioactivity of 0.5 mole of US is same as the radioactivity of 0.5 mole of US2.

Explanation of Solution

The amount of uranium in 50g of US is calculated by the formula shown below.

AmmountofUinUS=50g×MolarmassUMolarmassUS...(1)

The value of molar mass of uranium and US is 238g/mol and 270g/mol respectively.

Substitute the value of molar mass of uranium and US in equation (1).

AmmountofUinUS=50g×MolarmassUMolarmassUS=50g×238g/mol270g/mol=50×0.881g=44.05g

The amount of uranium in 50g of US2 is calculated by the formula shown below.

AmmountofUinUS2=50g×MolarmassUMolarmassUS2...(2)

The value of molar mass of uranium and US2 is 238g/mol and 302g/mol respectively.

Substitute the value of molar mass of uranium and US2 in equation (2).

AmmountofUinUS2=50g×MolarmassUMolarmassUS=50g×238g/mol302g/mol=50×0.788g=39.4g

The amount of uranium in 50g of US is more than the amount present in 50g of US2. Therefore, 50g of US will exhibit more radioactivity.

The amount of any substance present in one mole is equal to the molar mass of that substance.

Therefore, the amount of uranium in one mole of US is 238g. The amount of uranium in one mole of US2 is also 238g.

Therefore the 0.5mole of US and US2 will have the same amount of uranium. Therefore, the radioactivity of 0.5 mole of US is same as the radioactivity of 0.5 mole of US2.

Conclusion

The compound US will exhibit more amount of radioactivity.

The radioactivity of 0.5 mole of US is same as the radioactivity of 0.5 mole of US2.

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Chapter 20 Solutions

Introductory Chemistry: An Active Learning Approach

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