Unit 2 Measurement and Calculations

Objective 1…S.I. Units and the Metric System ‘S.I.’ stands for the International System of Units. Units that you will use in chemistry include: length = meter (m) volume = mass = kilogram (kg) density = grams/milliliter (g/mL) cubic meter (m 3 ) grams/cubic centimeter (g/cm 3 ) OR *** 1 mL = 1 cm 3 time = temperature = pressure = second Kelvin (K) Pascal (Pa)

Objective 1 cont... v Sometimes it is more convenient to use different variations of the S.I. Units! v For example: ‘1 day’‘86,400 seconds’ - It is much easier to say ‘1 day’ than ‘86,400 seconds’. 1 gram one thousandth of a kilogram - It is much easier to say a paper clip has a mass of 1 gram than one thousandth of a kilogram. 26 kilometers 26,000 meters - It is much easier to say a marathon is 26 kilometers than 26,000 meters. v Each pair contains the same measurement, just different units. v These units are found in the metric system!

v The metric system is base 10 system that only requires the movement of the decimal point to change units. Objective 1 cont... v The prefixes of the metric system are: Mega (M) = **Kilo (k) = Hecto (h) = Deka (da) = **Unit = (liter) (meter) (gram) Deci (d) = Centi (c) = **Milli (m) = mighty king Henry drinks ultra dark chocolate milk units (10 6 ) units (10 3 ) 100 units (10 2 ) 10 units (10 1 ) 1 unit (10 0 ) 0.1 units (10 -1 ) 0.01 units (10 -2 ) units (10 -3 ) **Notice…everything revolves around the unit!!! **width of a dime **about the distance across Texas

Objective 1 cont... v To convert b/n units, start at the given and ‘jump’ to the unknown. v If you jump to the left, move the decimal that many places to the left. v If you jump to the right, move the decimal that many places to the right. Mega kilo hecto deka unit deci centi milli v Practice: 32.4 g = _________ kg mL = _________ daL m = _________ dm jumped up 3 times = decimal to the left 3 times jumped up 3 times = decimal to the left 3 times jumped up 4 times = decimal to the left 4 times jumped up 4 times = decimal to the left 4 times jumped down once = decimal to the right once jumped down once = decimal to the right once. 6,287 6,287

Objective 2….Scientific Notation: - A method of representing very large or very small numbers in the form: M x 10 n M x 10 n  M is a number between 1 and 10  n is an integer

Step #1: Insert an understood decimal point. Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10 n Objective 2 cont….

2.5 x The exponent is the number of places we moved the decimal. Objective 2 cont….

Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10 n Objective 2 cont….

5.79 x The exponent is negative because the number we started with was less than 1. Objective 2 cont….

PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION ADDITION AND SUBTRACTION Objective 2 cont….

Review: Scientific notation expresses a number in the form: M x 10 n 1  M  10 n is an integer Objective 2 cont….

4 x x 10 6 IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged. 7 x 10 6 Objective 2 cont….

4 x x 10 6 The same holds true for subtraction in scientific notation. 1 x 10 6 Objective 2 cont….

4 x x 10 5 If the exponents are NOT the same, we must move a decimal to make them the same. Objective 2 cont….

4.00 x x x x 10 6 Move the decimal on the smaller number! 4.00 x 10 6 Objective 2 cont….

A Problem for you… 2.37 x x Objective 2 cont….

2.37 x x Solution… x Objective 2 cont….

x Solution… x x Objective 2 cont….

A Problem for you… (2 x 10 3 ) x (3 x 10 2 ) Solution: Multiply the first factors (2 x 3)= 6 Add the exponents (3 + 2)= 5 Combine the factors: 6 x 10 5 Objective 2 cont….

Objective 3…Significant Digits v Used in ALL chemistry calculations! v Indicates how accurate your measurements are. v All #s that add value /meaning to data…not just place holders. v All non-zero digits are always significant. v To count significant digits... *** If a # is greater than 1 w/ no decimal... - locate where the decimal should be. - move left to the 1st non-zero digit. - this digit and everything to the left is significant. Exs decimal decimal 1st sig. dig. 1st sig. dig decimal decimal 1st sig. dig. 1st sig. dig. 5 sig. digs. 5 sig. digs. 3 sig. digs. 3 sig. digs.

Objective 3 cont... *** If a # is greater than 1 w/ a decimal present… - ALL digits are significant!!! - if someone takes time out of their life to intentionally write a decimal…that makes everything significant! Exs sig. digs. 9 sig. digs. 8 sig. digs. 8 sig. digs. 5 sig. digs. 5 sig. digs.

Objective 3 cont... *** If a # is less than 1 … - locate the decimal. - move right to the 1st non-zero digit. - this digit and everything to the right is significant. Exs decimal decimal 1st sig. dig. 1st sig. dig decimal decimal 1st sig. dig. 1st sig. dig. 6 sig. digs. 6 sig. digs. 1 sig. dig. 1 sig. dig.

Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement.Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement =  18.7 (3 sig figs) Objective 3 cont...

v Sig. digs. in multiplications and division calculations... v # of sig. digs. in your answer must be the same as the smallest # of sig. digs. involved in the calculation. v Ex x 1.9 x = 3 s.d. 3 s.d. 2 s.d. 2 s.d. 4 s.d. 4 s.d on calculator…your ans. is ÷ 2.51 = on calculator…your ans. is 4 s.d. 4 s.d. 3 s.d. 3 s.d v When rounding, always keep the desired # of left-most sig. digs. and use normal rounding rules to determine your last sig. dig.

Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty. Objective 4: Making Measurements

Why Is there Uncertainty?  Measurements are performed with instruments  No instrument can read to an infinite number of decimal places Which of these balances has the greatest uncertainty in measurement?

Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. Precision refers to the degree of agreement among several measurements made in the same manner.Precision refers to the degree of agreement among several measurements made in the same manner. Neither accurate nor precise Precise but not accurate Precise AND accurate

Whose data is most accurate/precise? Three chemistry students measured the mass and volume of a piece of zinc to determine it’s density. The table below shows the data: JohnSamSara Trial g/mL7.65 g/mL7.04 g/mL Trial g/mL7.65 g/mL7.55 g/mL Trial g/mL7.64 g/mL7.26 g/mL Average7.15 g/mL7.65 g/mL7.28 g/mL Compare the students data. Whose data is the most accurate and precise?

Types of Error Random Error (Indeterminate Error) - measurement has an equal probability of being high or low.Random Error (Indeterminate Error) - measurement has an equal probability of being high or low. Systematic Error (Determinate Error) - Occurs in the same direction each time (high or low), often resulting from poor technique or incorrect calibration.Systematic Error (Determinate Error) - Occurs in the same direction each time (high or low), often resulting from poor technique or incorrect calibration.

Percent Error A way to evaluate the accuracy of data. Percent Error = Ratio of the error to the accepted value │ Accepted value – Measured value │ Accepted value X 100%

Percent Error If your measurement of a liquid is mL but the actual amount is mL, what is the percent error of the measurement? mL – mL 1.6 mL ________________________________________ _______________ mL mL = X 100% = 1.3%

Percent Deviation A way to evaluate the precision of the data. Percent Deviation = Ratio of your measurements change from the average compared to the average value │ Mean value – Measured value │ Mean value X 100%

Percent Deviation If one of your measurements of the length of a string was 22.7 cm and the mean measurement was 22.9 cm, what is the percent deviation of the measurement? 22.9 cm – 22.7 cm 0.2 cm ________________________________________ __ _____________ 22.9 cm 22.9 cm = X 100% = 0.9%

Objective 4: Making Measurements Part 1 – number Part 2 - scale (unit) Examples: 20 grams 6.63 x Joule seconds Measurement - quantitative observation consisting of 2 parts

Objective 4 cont… v Lab equipment that measures to the smallest place value is the most accurate. v i.e... A graduated cylinder (marks one mL) is more accurate than a beaker (marks 50 mL). v What measurement is the arrow is pointing at on this ruler? cm cm cm cm cm cm v ALWAYS estimate one place past the most accurate mark!!! v This ruler measures to the tenth of a cm, so we must estmate to the hundredth.

Objective 4 cont... v What is the measurement of liquid in this graduated cylinder? mL v Where should the meniscus be read from? v What place value should this measurement go to? v What is the measurement? bottom of dip bottom of dip v What is the smallest place value on this equipment? ones place ones place tenths place tenths place 32.5 mL 32.5 mL

Objective 4 cont... v Now the BIG ONE!!!! v What is the mass on this quadruple-beam balance? v What is the smallest place value on this equipment? v What place value should this measurement go to? v What is the measurement? hundredths place hundredths place thousandths place thousandths place grams grams

Objective 4 cont... v What is the mass on this quadruple-beam balance? v What is the smallest place value on this equipment? hundredths place hundredths place v What place value should this measurement go to? thousandths place thousandths place v What is the measurement? grams grams

Objective 5-6…Conversions and Dimensional Analysis v D.A. is a mathematical process that allows you to do complicated conversions in one equation. v Rules... - draw grid (long horizontal line) - place given value and units in top left hand side of grid - to cancel a unit, place the same unit diagonal to the 1st - conversion ratios (top/bottom values) must = each other - draw a vertical line after each conversion ratio v D.A. allows you to cancel units to get to your desired outcome. v Ex… How many seconds are in 37.2 years? - You are looking for the same amount of time…just different units! - to calculate: × everything on top and ÷ everything on bottom.

Objective 5-6 cont... How many seconds are in 37.2 years? v Practice years 1 year days 1 day 24 hours 1 hour 60 minutes 1 minute 60 seconds = ** multiply everything on top and divide everything on bottom! ** how many sig. digs. should be in your answer?!?!?! three three 1.17 x 10 9 seconds 1.17 x 10 9 seconds

Objective 5-6 cont... v Practice... How many weeks are equivalent to 4.6 x 10 8 seconds? 4.6 x 10 8 seconds 60 seconds 1 minute 60 minutes 1 hour 24 hours 1 day 7 days 1 week = ** how many sig. digs. should be in your answer?!?!?! two two 760 weeks 760 weeks

= Objective 5-6 cont... v Practice... Convert 302 km/hr to m/min. 302 km 1 hour 1 km 1000 m1 hour 60 minutes ** how many sig. digs. should be in your answer?!?!?! three three 5030 m/min 5030 m/min

Objective 5-6 cont... v Common conversion factors... 1 pound (lb) = 454 grams 1 quart = 946 mL 1 inch = 2.54 cm 1 calorie (cal) = joules (j) 12 inches = 1 foot 3 feet = 1 yard 2 pints = 1 quart 4 quarts = 1 gallon 1 mL = 1 cm 3 1 L = 1 dm 3