Unit Ratio Expressions

Chemistry                                                                                                                       Guided Instructional Activity 5-1
Unit 5: Chemical Quantities and Calculations                                                                                        Reading: Chapter 3

Learning Objective: To derive a unit ratio and its inverse from given data, to identify the parts of a ratio, and to use these ratios as conversion factors in dimensional analysis

Working Mode:  Pairs

Keywords:  ratio, unit, number, equality relationship, conversion factor

Instructions:   For each description below, express the equality relationship.  Derive the unit ratio.  Write the unit ratio in both of the possible ways that it can be used.  For both forms of the unit ratio, identify the parts:  Underline the "number, put a box around the "unit" of measure, and circle the "item". 

                                                                                    100   cm   Mg ribbon         simplified
Example:  1 m Mg ribbon = 100 cm Mg ribbon                                                   = unit ratio
                         (equality relationship)                                                                      per 1 meter
                                                                                     1   m    Mg ribbon

1. A jeweler displays a ring with a diamond of 3.08 carats.  The mass of the diamond is 0.64 grams.

Student 1:  Identify an equality relationship between carats and grams using the values given.
Student 2:  Write the two unit ratios for carats in terms of grams and grams in terms of carats.
Student 1:  Solve this conversion using the appropriate unit ratio.  A diamond has a mass of 1.30 g.  What is its mass in carats?
Student 2: Solve this conversion using the correct unit ratio.  If the Hope Diamond is 45.52 carats, what is its mass in grams (g)?

2.  At a temperature of 0⁰C and a pressure of 1 atm., 22.4 L of neon gas contains 6.02 x 10²³ atoms of neon. 

Student 1:  Identify an equality relationship between the volume of gas and number of atoms.

Student 2:  Write the two unit ratios for number of atoms in terms of volume and volume in terms of numbers of atoms. 

Student 1:  Solve this conversion using the appropriate unit ratio.  Determine the number of neon atoms in 13.6 L of neon at a temperature of 0⁰C and a pressure of 1 atmosphere. 

Student 2:  Solve this conversion using the correct unit ratio.  A  sample of neon gas at a temperature of 0⁰C and a pressure of 1 atmosphere contains 4.82 x10²³ atoms of neon.  What is the volume of the sample in liters (L)?