Unit Conversions and Dimensional Analysis

Introduction

Unit conversions and dimensional analysis are essential skills in General, Organic, and Biological (GOB) Chemistry. These techniques allow chemists to convert between different units of measurement, solve real-world problems, and ensure accurate calculations in laboratory and everyday contexts.

Key Concepts in Unit Conversions

• Unit Conversion: The process of changing a quantity expressed in one set of units to another set of units using conversion factors.

• Dimensional Analysis (Factor-Label Method): A systematic approach to problem-solving that uses conversion factors to move from one unit to another.

• Conversion Factor: A ratio (fraction) that expresses how many of one unit are equal to another unit. For example, 1 kg = 2.205 lb.

• Significant Figures: The number of meaningful digits in a measured or calculated quantity. Answers should be rounded to the correct number of significant figures based on the data provided.

Applications and Example Problems

2.98: Calculating Total Mass and Converting Units

• Problem: Find the total mass of seafood delivered (in kg and lb).

• Steps:

  1. Add the masses:

  2. Convert kilograms to pounds using :

• Example: If you have 10 kg of apples, how many pounds is that?

2.99: Currency and Mass Unit Conversion

• Problem: Convert the price of grapes from euros/kg to dollars/lb.

• Steps:

  1. Convert euros to dollars:

  2. Convert kg to lb:

• Key Point: Always align units so that unwanted units cancel out, leaving the desired unit.

2.100: Multi-Step Currency and Mass Conversion

• Problem: Find the cost in cents of an avocado weighing 0.45 lb, given the price in pesos/kg and exchange rate.

• Steps:

  1. Convert pounds to kilograms:

  2. Find cost in pesos:

  3. Convert pesos to dollars:

  4. Convert dollars to cents:

• Example: If a fruit costs 30 pesos/kg and weighs 0.5 lb, what is the cost in dollars at 20 pesos/dollar?

2.101: Counting Items from Mass

• Problem: How many onions are needed for 4.0 lb, if each onion is 115 g?

• Steps:

  1. Convert pounds to grams:

  2. Divide by mass per onion: onions (round as appropriate)

• Key Point: Use the average mass of one item to determine the total number needed for a given mass.

2.102: Calculating Total Mass from Revenue

• Problem: Find the total kilograms of potatoes sold if 1.75/lb.

• Steps:

  1. Find total pounds sold:

  2. Convert pounds to kilograms:

• Example: If a store earns 2.00/lb, how many kilograms were sold?

2.103: Distance, Rate, and Time Calculations

• Problem: How many minutes to walk 7500 ft at 55.0 m/min?

• Steps:

  1. Convert feet to meters:

  2. Divide by rate:

• Key Point: Use the formula .

2.104: Speed, Distance, and Time in Different Units

• Problem: How long to drive 1700 km at 63 mi/h?

• Steps:

  1. Convert kilometers to miles:

  2. Divide by speed:

• Example: If a trip is 500 km and the speed is 50 mi/h, how long does it take?

2.105: Volume Displacement and Mass Calculation

• Problem: Find the mass of lead that displaces 70 mL of water (from 215 mL to 285 mL).

• Steps:

  1. Volume displaced:

  2. Use density of lead (from Table 2.8, typically ):

  3. Mass = Volume × Density:

• Key Point: The mass of a solid can be found by multiplying its volume (from water displacement) by its density.

• Additional info: Density of lead is typically .

Common Conversion Factors

Summary

• Always write out units and use conversion factors to cancel unwanted units.

• Check significant figures in your final answer.

• Dimensional analysis is a powerful tool for solving a wide range of chemistry problems.