Chemistry and Measurements: Problem Solving Using Unit Conversion

Problem Solving Using Unit Conversion

Overview

• The focus is on using conversion factors to change from one unit to another.

Problem-Solving Process

The problem-solving process for unit conversion involves:

• Analyzing the problem.
• Identifying the given unit and the needed unit.
• Writing a plan to convert the given unit to the needed unit.
• Identifying one or more conversion factors that cancel units and provide the needed unit.
• Setting up the calculation.

Example 1: Converting Pounds to Kilograms

• Problem: Convert 178 lb to kilograms.
• Step 1: Analyze the Problem
  • Given: 178 lb
  • Need: kilograms
  • Connect: conversion factor (kg/lb)
• Step 2: Write a Plan
  • lb → kg
• Step 3: Equalities and Conversion Factors
  • Equality: 1 kg = 2.20 lb
  • Conversion factors: $\frac{1 \text{ kg}}{2.20 \text{ lb}}$, $\frac{2.20 \text{ lb}}{1 \text{ kg}}$
• Step 4: Set up the Problem
  • $178 \text{ lb} \times \frac{1 \text{ kg}}{2.20 \text{ lb}} = 81 \text{ kg}$

Learning Check 1: Converting Meters to Centimeters

• Problem: A rattlesnake is 2.44 m long. How many centimeters long is the snake?
• Step 1: Analyze the Problem
  • Given: 2.44 m
  • Need: centimeters
  • Connect: conversion factor (cm/m)
• Step 2: Write a Plan
  • m → cm
• Step 3: Equalities and Conversion Factors
  • Equality: 1 m = 100 cm
  • Conversion factors: $\frac{100 \text{ cm}}{1 \text{ m}}$, $\frac{1 \text{ m}}{100 \text{ cm}}$
• Step 4: Set up the Problem
  • $2.44 \text{ m} \times \frac{100 \text{ cm}}{1 \text{ m}} = 244 \text{ cm}$

Using Two or More Conversion Factors

• Often, multiple conversion factors are needed to complete a unit change.
• Set up the problem so that each factor cancels the preceding unit until the needed unit is obtained.

Example 2: Dosage Calculation

• Problem: Convert 0.150 mg of Synthroid to the number of tablets, given that each tablet contains 50. mcg.
• Step 1: Analyze the Problem
  • Given: 0.150 mg of Synthroid
  • Need: number of tablets
  • Connect: 1 tablet = 50. mcg of Synthroid
• Step 2: Write a Plan
  • mg → mcg → tablets
• Step 3: Equalities and Conversion Factors
  • Equalities: 1 mg = 1000 mcg, 1 tablet = 50. mcg
  • Conversion factors: $\frac{1000 \text{ mcg}}{1 \text{ mg}}$, $\frac{1 \text{ mg}}{1000 \text{ mcg}}$, $\frac{1 \text{ tablet}}{50. \text{ mcg}}$, $\frac{50. \text{ mcg}}{1 \text{ tablet}}$
• Step 4: Set up the Problem
  • $0.150 \text{ mg} \times \frac{1000 \text{ mcg}}{1 \text{ mg}} \times \frac{1 \text{ tablet}}{50. \text{ mcg}} = 3 \text{ tablets}$

Learning Check 2: Converting Days to Minutes

• Problem: How many minutes are in 1.6 days?
• Step 1: Analyze the Problem
  • Given: 1.6 days
  • Need: minutes
  • Connect: conversion factors (h/day, min/h)
• Step 2: Write a Plan
  • days → hours → minutes
• Step 3: Equalities and Conversion Factors
  • Equalities: 1 day = 24 h, 1 h = 60 min
  • Conversion factors: $\frac{24 \text{ h}}{1 \text{ day}}$, $\frac{1 \text{ day}}{24 \text{ h}}$, $\frac{60 \text{ min}}{1 \text{ h}}$, $\frac{1 \text{ h}}{60 \text{ min}}$
• Step 4: Set up the Problem
  • $1.6 \text{ days} \times \frac{24 \text{ h}}{1 \text{ day}} \times \frac{60 \text{ min}}{1 \text{ h}} = 2300 \text{ min}$

Learning Check 3: Calculating Time from Distance and Pace

• Problem: If your pace on a treadmill is 65 m/min, how many minutes will it take for you to walk a distance of 7.5 km?
• Step 1: Analyze the Problem
  • Given: 7.5 km
  • Need: minutes
  • Connect: conversion factors (m/km, 65 m/min)
• Step 2: Write a Plan
  • km → m → minutes
• Step 3: Equalities and Conversion Factors
  • Equalities: 1 km = 1000 m, 65 m = 1 min
  • Conversion factors: $\frac{1000 \text{ m}}{1 \text{ km}}$, $\frac{1 \text{ km}}{1000 \text{ m}}$, $\frac{1 \text{ min}}{65 \text{ m}}$, $\frac{65 \text{ m}}{1 \text{ min}}$
• Step 4: Set up the Problem
  • $7.5 \text{ km} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ min}}{65 \text{ m}} = 120 \text{ min}$