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Ch. 2: Measurement and Problem Solving
Dr. Namphol Sinkaset Chem 152: Introduction to General Chemistry

I. Chapter Outline Introduction Scientific Notation
Significant Figures Units of Measurement Unit Conversions Density as a Conversion Factor

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

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.

II. Scientific Notation
Scientific notation consists of three different parts.

II. Converting to Scientific Notation

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.

II. Practice with Scientific Notation
Express the following in proper scientific notation. 3,677,000,000 93 0.004 0.0040

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.

III. Reading a Thermometer
e.g. What are the temperature readings below?

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.

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.

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.

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.

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

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.

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

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

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.

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.

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.”

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!

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

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 – ) = ?

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 = ?

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.

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.

IV. Prefix Multipliers

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.

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.

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.

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

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

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

V. Conversion Factors

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?

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.

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?

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:

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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