I II III Measurement & Dimensional Analysis

Learning Objective  The Learners Will (TLW) express and manipulate chemical quantities using scientific conventions and mathematical procedures such as measurement conversion and dimensional analysis  TEKS 2.G.

Agenda  Part 3 – Measurement Conversions Reviewed A. SI Prefix Conversions – Shorthand Method B. Dimensional Analysis – The “Factor-Label Method” of solving problems

I II III Unit Conversions MEASUREMENT

A. SI Prefix Conversions mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro-  nano-n10 -9 pico-p kilo-k10 3 move decimal left Move decimal right BASE UNITl,m,g10 0 Scientific Notation is Back!!!!!!!!

A. SI Prefix Conversions 1.Find the absolute difference between the exponents of the two prefixes 2.Move the decimal that many places To the left or right? If going from larger factor to smaller, move decimal to right If going from smaller factor to larger, move decimal to left

= A. SI Prefix Conversions NUMBER UNIT NUMBER UNIT 532 m = _______ km 0.532

A. SI Prefix Conversions YOUR TURN 1) 20 cm = ______________ m 2) L = ______________ mL 3) 45  m = ______________ nm 4) 805 dm = ______________ km ,000 32

Practice Set 1) 5 cm = ______________ mm 2) L = ______________ kL 3) 40  m = ______________ nm 4) 750 m = ______________ km 5) 50,000 g = ______________ kg

B. Dimensional Analysis  You might not recognize the fancy name, but you do use it every day  For example –  Making change for a dollar bill in dimes  Converting how many minutes until this boring class ends into seconds  Determining how many teaspoons of medicine to take to equal two tablespoons

B. Dimensional Analysis  Also called the “Factor-Label” Method  Units, or “labels” are canceled, or “factored” out

B. Dimensional Analysis  Steps: 1. Identify starting & ending numbers and associated units (labels). 2. Line up conversion factors so units (labels) cancel. This may mean inverting or doing the butterfly. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

B. Dimensional Analysis  Step 1:  What are known factors and units?  What conversion factors do you have, know, or need?  What are you solving for? You have a belt that is 40 inches long. How long is it in centimeters? Starting = 40 inchesEnding = x cm Conversion factor 2.54 cm per inch or 2.54 cm 1 in.

B. Dimensional Analysis  Step 2: Lining up conversion factors: 1 in = 2.54 cm 2.54 cm 1 in = 2.54 cm 1 in 1 in = 1 1 = In a word problem, think of the word “per” as the fraction line. If conversion factor is written as 2.54 cm = 1 in., think of “equals sign” as fraction line

B. Dimensional Analysis  Step 3: Multiply all top numbers & divide by each bottom number inchescm 40 inches 2.54 cm 1 in = cm

B. Dimensional Analysis  Step 4: Check units and answer  We have cm and our math looks good

B. Dimensional Analysis  1.How many milliliters are in 1.00 quart of milk? 1.00 qt 1 L qt = 946 mL qtmL 1000 mL 1 L 

B. Dimensional Analysis  2. You have 1.5 pounds of gold. Find its volume in cm 3 if the density of gold is 19.3 g/cm 3. lbcm lb 1 kg 2.2 lb = 35 cm g 1 kg 1 cm g

B. Dimensional Analysis  3. How many liters of water would fill a container that measures 75.0 in 3 ? 75.0 in 3 (2.54 cm) 3 (1 in) 3 = 1.23 L in 3 L 1 L 1000 cm 3

B. Dimensional Analysis 4. Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? 8.0 cm1 in 2.54 cm = 3.2 in cmin

B. Dimensional Analysis 5. Industrial’s football team needs 550 cm for a 1st down. How many yards is this? 550 cm 1 in 2.54 cm = 6.0 yd cmyd 1 ft 12 in 1 yd 3 ft

B. Dimensional Analysis 6. A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire? 1.3 m 100 cm 1 m = 86 pieces cmpieces 1 piece 1.5 cm

B. Dimensional Analysis  A very useful technique for solving complex conversion problems, especially in engineering, chemistry, physics, medicine

B. Dimensional Analysis Review the Steps to Using Dimensional Analysis More practice as a group and as individuals – Problem Sets  Chemistry Textbook – page 95, problems 15 – 19  Dimensional Analysis Problem Set Dimensional Analysis Problem Set