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**Ch. 2: Measurement and Problem Solving**

Dr. Namphol Sinkaset Chem 152: Introduction to General Chemistry

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**I. Chapter Outline Introduction Scientific Notation**

Significant Figures Units of Measurement Unit Conversions Density as a Conversion Factor

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**I. Introduction Global warming measurement. Value? Method?**

Uncertainty?

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**II. Scientific Notation**

Science deals with the very large and the very small. Writing large/small numbers becomes very tedious, e.g. 125,200,000,000. Scientific notation is a shorthand method of writing numbers.

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**II. Scientific Notation**

Scientific notation consists of three different parts.

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**II. Converting to Scientific Notation**

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**II. Steps for Writing Scientific Notation**

Move decimal point to obtain a number between 1 and 10. Write the result of Step 1 multiplied by 10 raised to the number of places you moved the decimal point. If decimal point moved left, use positive exponent. If decimal point moved right, use negative exponent.

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**II. Practice with Scientific Notation**

Express the following in proper scientific notation. 3,677,000,000 93 0.004 0.0040

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**III. Measurement in Science**

Measurements are written to reflect the uncertainty in the measurement. A “scientific” measurement is reported such that every digit is certain except the last, which is an estimate.

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**III. Reading a Thermometer**

e.g. What are the temperature readings below?

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**III. Uncertainty in Measurement**

Quantities cannot be measured exactly, so every measurement carries some amount of uncertainty. When reading a measurement, we always estimate between lines – this is where the uncertainty comes in.

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**III. Significant Figures**

The non-place-holding digits in a measurement are significant figures (sig figs). The sig figs represent the precision of a measured quantity. The greater the number of sig figs, the better the instrument used in the measurement.

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**III. Determining Sig Figs**

All nonzero numbers are significant. Zeros in between nonzero numbers are significant. Trailing zeros (zeros to the right of a nonzero number) that fall AFTER a decimal point are significant. Trailing zeros BEFORE a decimal point are not significant unless indicated w/ a bar over them or an explicit decimal point. Leading zeros (zeros to the left of the first nonzero number) are not significant.

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III. Exact Numbers Exact numbers have no ambiguity and therefore, have an infinite number of sig figs. These include counts, defined quantities, and integers in an equation. e.g. 5 pencils, 1000 m in 1 km, C = 2πr.

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**III. Determining Sig Figs**

e.g. Indicate the number of sig figs in the following. 2.036 20 6.720 x 103 7920 135,001,000 820. 1.000 x 1021

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**III. Calculations w/ Sig Figs**

When doing calculations with measurements, it’s important that we don’t have an answer w/ more certainty (sig figs) than what we started with. Sig figs are handled based on what math operation is being performed.

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III. Multiplication The answer is limited by the number with the least sig figs.

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III. Division The answer is also limited by the number with the least sig figs.

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III. Addition The answer has the same number of PLACES as the quantity carrying the fewest places. *Note that the number of sig figs could increase or decrease.

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III. Subtraction The answer has the same number of PLACES as the quantity carrying the fewest places. *Note that the number of sig figs could increase or decrease.

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**III. Addition/Subtraction**

Addition and subtraction operations could involve numbers without decimal places. The general rule is: “The number of significant figures in the result of an addition/subtraction operation is limited by the least precise number.”

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III. Rounding When rounding, consider only the last digit being dropped; ignore all following digits. Round down if last digit is 4 or less. Round up if last digit is 5 or more. e.g. Rounding to the tenths place results in 2.3!

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III. Sample Problems Evaluate the following to the correct number of sig figs. 1.10 ´ ´ ´ = ? ¸ = ? = ? = ? – = ? 1252 – 360 = ?

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III. Mixed Operations In calculations involving both addition/subtraction and multiplication/division, we evaluate in the proper order, keeping track of sig figs. DO NOT ROUND IN THE MIDDLE OF A CALCULATION!! Carry extra digits and round at the end. e.g ´ (782.3 – ) = ?

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III. Sample Problems Evaluate the following to the correct number of sig figs. ( – 232.1) ¸ 5.3 = ? ( – 9.9) ´ 8.1 ´ 106 = ? (455 ¸ ) = ? (908.4 – 3.4) ¸ 3.52 ´ 104 = ?

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**IV. Units All measured quantities have a number and a unit!!!!**

Without a unit, a number has no meaning in science. e.g. The string was 8.2 long. ANY ANSWER GIVEN W/OUT A UNIT WILL BE GRADED HARSHLY.

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**IV. International System of Units**

More commonly known as SI units. Based on the metric system which uses a set of prefixes to indicate size. There are a set of standard SI units for fundamental quantities.

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IV. Prefix Multipliers

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IV. Derived Units Combinations of fundamental units lead to derived units. e.g. volume, which is a measure of space, needs three dimensions of length, or m3. e.g. speed, distance covered over time, m/s.

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**V. Unit Conversions Problem solving is a big part of chemistry.**

Converting between different units is the first type of problem we will cover. Problems in chemistry generally fall into two categories: unit conversions or equation-based.

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**V. Units in Calculations**

Always carry units through your calculations; don’t drop them and then add them back in at the end. Units are just like numbers; they can be multiplied, divided, and canceled. Unit conversions involve what are known as conversion factors.

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V. General Conversions Typically, we are given a quantity in some unit, and we must convert to another unit.

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V. Conversion Factors conversion factor: ratio used to express a measured quantity in different units For the equivalency statement “5280 feet are in 1 mile,” two conversion factors are possible. 1 mi 5280 ft 5280 ft 1 mi OR

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V. Conversion Example If 1 in equals 2.54 cm, convert 24.8 inches to centimeters.

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V. Conversion Factors

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**V. Sample Problems Perform the following multistep unit conversions.**

Convert 2400 cm to feet. Convert 10 km to inches. How many cubic inches are there in 3.25 yd3?

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VI. Density Density is a ratio of a substances mass to its volume (units of g/mL or g/cm3 are most common). To calculate density, you just need an object’s mass and its volume.

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VI. Density Problem Density differs between substances, so it can be used for identification. If a ring has a mass of 9.67 g and displaces mL of water, what is it made of?

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**VI. Density as a Conversion Factor**

Since density is a ratio between mass and volume, it can be used to convert between these two units. If the density of water is 1.0 g/mL, the complete conversion factor is:

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VI. Sample Problem If the density of ethanol is g/mL, how many liters are needed in order to have 1200 g of ethanol?

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