Chapter 3, Problem 1CLE

Equivalency, conversion factor, solving quantitative problems, analyze, identify, construct, check.

Interpretation Introduction

Interpretation:

A brief description of the relationship among the each of following groups of terms is to be given for the equivalency, conversion factor, solving quantitative problems, analyze, identify, construct, check.

Concept introduction:

The term equivalency can be defined as the two quantities that are equivalent in value. For example, 0.025 furlong and 1 rod will represent the same physical length and can be expressed as 0.025 furlong = 1 rod. When an equivalency is expressed as fractional value it is called as conversion factor. The application of equivalence and conversion factors are considered as a central part to solving quantitative problems in chemistry.

Answer to Problem 1CLE

Equivalency is denoted as the two quantities that are equivalent in value. Ex: 0.025 furlong and 1 rod. The two quantities furlong and rod will represent the same physical length and can be expressed as 0.025 furlong = 1 rod. When an equivalency is expressed as fractional value it is called as conversion factor. The conversion factor of equivalency 0.025 = 1 rod is 0.025/1 rod. Similarly, there are four different steps for solving quantitative problems such as; 1) analyze the problem statement, (2) identify the equivalencies, which is need to solve the problem, (3) construct the solution set up, and (4) check the solution for the given problem.

Explanation of Solution

The term equivalency can be defined as the two quantities that are equivalent in value. For example, 0.025 furlong and 1 rod will represent the same physical length and can be expressed as 0.025 furlong = 1 rod.

When an equivalency is expressed as fractional value it is called as conversion factor. The conversion factor of equivalency 0.025 = 1 rod is 0.025/1 rod. Two conversion factors can be written for a given equivalency value. In many problems, the equivalence will not be explicitly expressed.

Alternatively, 7 days = 1 week. For this statement, two conversion factors can be obtained.

$\frac{\text{1}\text{week}}{\text{7}\text{days}}\text{and}\frac{\text{7}\text{days}}{\text{1}\text{week}}$

If the quantity in the given assignment is in week, the above expression can be written as,

$\frac{\text{7}\text{days}}{\text{1}\text{week}}\text{×3}\text{weeks = 21}\text{days}$

Generally, in order to solve the problems, the following points need to be verified.

1) Analyze: It includes the determination of the given quantity, such as quantity = value x unit. The property of the given quantity and the property of the wanted quantity is to be described. Finally, the unit of the wanted quantity will be stated.

2) Identify: It includes the identification of equivalence to solve the given problem. Then, change the equivalence to conversion factor.

3) Construct: It is solution setup. In this process, the units will be confirmed for their correct cancelation and calculation of values for the answer.

4) Check: This process will be taken in two levels such as making sense (did we obtain a reasonable value) and what was learned (what is the new knowledge obtained from the calculation).

Conclusion

Thus, a brief description of the relationship among the each of following groups of terms is checked.