Measurements and Problem Solving in Chemistry UNIT 2 Measurements and Problem Solving in Chemistry

The Standard Units Scientists have agreed on a set of international standard units for comparing all our measurements called the SI units Système International = International System Quantity Unit Symbol length meter m mass gram g time second s temperature Kelvin/Celsius K/°C volume liter L Tro, Chemistry: A Molecular Approach

Length Measure of the two-dimensional distance an object covers often need to measure lengths that are very long (distances between stars) or very short (distances between atoms) SI unit = meter About 3.37 inches longer than a yard Commonly use centimeters (cm) Tro, Chemistry: A Molecular Approach

Mass Measure of the amount of matter present in an object weight measures the gravitational pull on an object, which depends on its mass Weight and mass are NOT the same thing SI unit = gram (g) Commonly measure mass in grams (g) or milligrams (mg) Tro, Chemistry: A Molecular Approach

Time measure of the duration of an event SI units = second (s) Tro, Chemistry: A Molecular Approach

Volume The amount of space an object takes up. Could be expressed in units of liters (liquid) Could be expressed in units of length cubed, m3 (solid)

Temperature measure of the average amount of kinetic energy higher temperature = larger average kinetic energy heat flows from the matter that has high thermal energy into matter that has low thermal energy until they reach the same temperature heat is exchanged through molecular collisions between the two materials Tro, Chemistry: A Molecular Approach

Temperature Scales Fahrenheit Scale, °F Celsius Scale, °C used in the U.S. Celsius Scale, °C used in all other countries Kelvin Scale, K absolute scale no negative numbers directly proportional to average amount of kinetic energy 0 K = absolute zero Tro, Chemistry: A Molecular Approach

Fahrenheit vs. Celsius a Celsius degree is 1.8 times larger than a Fahrenheit degree the standard used for 0° on the Fahrenheit scale is a lower temperature than the standard used for 0° on the Celsius scale Tro, Chemistry: A Molecular Approach

Kelvin vs. Celsius the size of a “degree” on the Kelvin scale is the same as on the Celsius scale though technically, we don’t call the divisions on the Kelvin scale degrees; we called them kelvins! so 1 kelvin is 1.8 times larger than 1°F the 0 standard on the Kelvin scale is a much lower temperature than on the Celsius scale Tro, Chemistry: A Molecular Approach

Example 1.2 Convert 40.00 °C into K and °F Find the equation that relates the given quantity to the quantity you want to find Given: Find: Equation: 40.00 °C K Since the equation is solved for the quantity you want to find, substitute and compute Find the equation that relates the given quantity to the quantity you want to find Given: Find: Equation: 40.00 °C °F Solve the equation for the quantity you want to find Substitute and compute

Related Units in the SI System All units in the SI system are related to the standard unit by a power of 10 The power of 10 is indicated by a prefix multiplier The prefix multipliers are always the same, regardless of the standard unit Report measurements with a unit that is close to the size of the quantity being measured Tro, Chemistry: A Molecular Approach

Common Prefix Multipliers in the SI System Symbol Decimal Equivalent Power of 10 mega- M 1,000,000 Base x 106 kilo- k 1,000 Base x 103 deci- d 0.1 Base x 10-1 centi- c 0.01 Base x 10-2 milli- m 0.001 Base x 10-3 micro- m or mc 0.000 001 Base x 10-6 nano- n 0.000 000 001 Base x 10-9 pico p 0.000 000 000 001 Base x 10-12 Tro, Chemistry: A Molecular Approach

Volume Derived unit Measure of the amount of space occupied any length unit cubed Measure of the amount of space occupied SI unit = cubic meter (m3) Commonly measure solid volume in cubic centimeters (cm3) Commonly measure liquid or gas volume in milliliters (mL) Tro, Chemistry: A Molecular Approach

What is the volume of the fish? Water displacement What is the volume of the fish?

Density

Mass & Volume two main physical properties of matter mass and volume are extensive properties the value depends on the quantity of matter extensive properties cannot be used to identify what type of matter something is if you are given a large glass containing 100 g of a clear, colorless liquid and a small glass containing 25 g of a clear, colorless liquid - are both liquids the same stuff? even though mass and volume are individual properties, for a given type of matter they are related to each other! Tro, Chemistry: A Molecular Approach

Density Ratio of mass:volume is an intensive property value independent of the quantity of matter Density : solids > liquids >>> gases except ice is less dense than liquid water! Tro, Chemistry: A Molecular Approach

Tro, Chemistry: A Molecular Approach Mass vs. Volume of Brass Tro, Chemistry: A Molecular Approach

y = 8.38x Volume vs. Mass of Brass Mass, g Volume, cm3 20 40 60 80 100 120 140 160 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 Volume, cm3 Mass, g Tro, Chemistry: A Molecular Approach

Density Tro, Chemistry: A Molecular Approach

Animation of Density Tro, Chemistry: A Molecular Approach

Example 1. 3 Decide if a ring with a mass of 3. 15 g that displaces 0 Example 1.3 Decide if a ring with a mass of 3.15 g that displaces 0.233 cm3 of water is platinum Find the equation that relates the given quantity to the quantity you want to find Given: Find: Equation: mass = 3.15 g volume = 0.233 cm3 density, g/cm3 Since the equation is solved for the quantity you want to find, and the units are correct, substitute and compute Compare to accepted value of the intensive property

Measurement and Significant Figures

What Is a Measurement? quantitative observation comparison to an agreed- upon standard every measurement has a number and a unit Tro, Chemistry: A Molecular Approach

A Measurement the unit tells you what standard you are comparing your object to the number tells you what multiple of the standard the object measures the uncertainty in the measurement scientific measurements are reported so that every digit written is certain, except the last one which is estimated Tro, Chemistry: A Molecular Approach

Reading a Measuring Device using Significant Figures Record all the numbers you can see Make ONE Guess!

Tro, Chemistry: A Molecular Approach

What is the Length? We can see the markings between 1.6-1.7cm We can’t see the markings between the .6-.7 We must guess between .6 & .7 We record 1.65 cm as our measurement

What is the length of the wooden stick? 1) 4.5 cm 2) 4.55 cm 3) 4.547 cm

Precision and Accuracy

How many significant figures are in each of the following numbers? 0.0035 1.080 2371 2.97 × 105 100,000 Tro's "Introductory Chemistry", Chapter 2

How many sig figs? 6 3 5 2 4 All digits count Leading 0’s don’t Trailing 0’s do 0’s count in decimal form 0’s don’t count w/o decimal 0’s between digits count as well as trailing in decimal form 45.8736 .000239 .00023900 48000. 48000 3.982106 1.00040

Determine the Correct Number of Significant Figures for Each Calculation and 1.01 × 0.12 × 53.51 ÷ 96 = 0.067556 = 0.068 56.55 × 0.920 ÷ 34.2585 = 1.51863 = 1.52 Result should have 2 sf. 7 is in place of last sig. fig., number after is 5 or greater, so round up. 3 sf 2 sf 4 sf 2 sf 4 sf Result should have 3 sf. 1 is in place of last sig. fig., number after is 5 or greater, so round up. 3 sf 6 sf Tro's "Introductory Chemistry", Chapter 2

Determine the Correct Number of Significant Figures for Each Calculation and Round and Report the Result, Continued 0.987 + 125.1 – 1.22 = 124.867 = 124.9 0.764 – 3.449 – 5.98 = -8.664 = -8.66 3 dp Result should have 1 dp. 8 is in place of last sig. fig., number after is 5 or greater, so round up. 1 dp 2 dp Result should have 2 dp. 6 is in place of last sig. fig., number after is 4 or less, so round down. 3 dp 3 dp 2 dp Tro's "Introductory Chemistry", Chapter 2

Example 1.6—Perform the Following Calculations to the Correct Number of Significant Figures, Continued b) Tro's "Introductory Chemistry", Chapter 2

Uncertainty in Measured Numbers uncertainty comes from limitations of the instruments used for comparison, the experimental design, the experimenter, and nature’s random behavior to understand how reliable a measurement is we need to understand the limitations of the measurement accuracy is an indication of how close a measurement comes to the actual value of the quantity precision is an indication of how reproducible a measurement is Tro, Chemistry: A Molecular Approach

Accuracy vs. Precision