Chemistry 1.4, 1.5

Multiplication and division Significant numbers

-The answer can be no more precise than the least precise number from which the answer is derived -The least precise number is the one with the fewest SIGNIFICANT figures Example: (4.2X10^3)(15.94)/ 2.255x10^4 =2.96886918 *4.2x10^3 has the fewest significant figures (it only has 2) So the ANSWER will be 3.0

Rules for addition and subtraction (significant figures)

-The result in calculation cannot have greater significance than any of the quantities that produced the result Example: Consider adding 37.68 liters, 6.71862 liters, and 108.428 1) line up with decimal places 2) find which value has the least amount of decimal places (in this case 2) 3) answer cannot have more than 2 decimal places On the calculator we get 152.82662 So we round it to where there will only be 2 decimal places which equals = 152.83

Scientific Notation

-Used to express very large or very small numbers easily and with the correct number of significant figures -Represents a number as a power of ten Example: 4,300= 4.30X1,000=4.30X10^3 *must be used to input large numbers into the calculator

Rules for rounding numbers

-When the number to be dropped is less than 5, the preceding number is not changed -When the number to be dropped is 5 or larger, the preceding number is increased by one unit -Round the following number to 3 significant figures: 3.34966x10^4 = 3.35x10^4

On the Celsius temperature scale, water freezes at _____ degree C and boils at _______ C

0 , 100

Practice adding significant figures 1) 4.26 + 3.831 2) 8.321 - 2.4

1) 8.09 2) 5.9

Rules for Significant Figures

1) All nonzero digits are significant 7.314 has four significant digits * The number of significant digits is independent (doesn't matter) of the decimal point 2) Zeros located between nonzero digits are significant 60.052 has five significant numbers 3) Zeros at the end of a number are(trailing zeros) are significant if the number contains a decimal point. 4.70 has three significant digits *If the number does NOT contain a decimal point the digits are insignificant 100 has one digit 100. has three. Zero to the left of the first nonzero integer are not significant like 0.0032 only has 2 significant digits

Scientific Notation Examples 1) 0.00018 2) 3004 3) 300. 4) 0.00304

Answer: 1) 1.8x10^-4 2) 3.004x10^3 3) 3.00X10^2 4) 3.04x10^-3 *remember to use negative with small numbers!

How many significant figures are in the following? 1) 3.400 2) 3004 3) 300. 4)0.003040

Answer: 1) 4 2) 4 3) 3 4) 4

Examples for rounding numbers: Round off each number to three significant figures 1) 61.40 2) 6.171 3) 0.066494

Answers: 1) 61.4 2)6.17 3)0.0665 or 6.65x10-2

what is defined as the amount of heat required to raise 1 gram of water 1 degree

Calorie

Exact (counted) and inexact numbers

Inexact numbers have uncertainty (degree of doubt in final significant digit) Exact numbers are a consequence of counting -A set of counted items (beakers on a shelf) has no uncertainty -Exact numbers by definition have an infinite number of significant figures

Adding and subtracting in Scientific Notation

There are two ways to solve the following: 9.47X10^-6 + 9.3X10^-5 *Solution 1: convert both numbers to standard form and add 0.00000947 0.000093 =0.00010247 = 1.02X10^-4 Or you can change one of the exponents so that they have the same exponents 9.47x10^-6 becomes 0.0947x10^-5 (we moved the decimal to the left so that the exponent could become more positive) 0.947x10^-5 9.3x10^-5 =10.247x10^-5 =10.2x10^-5 which is also 1.02x10^-4 (proper scientific notation)

Converting into Scientific Notation (LARGE numbers)

To convert a number greater than 1 to scientific notation, the original decimal point is moved x places to the left, and the resulting number is multiplied by 10^x *That power is equal to the times that the decimal has been moved Example: 6,200 = 6.2X10^3 To express the above number with significan figures: =6.20X10^3

Converting to Scientific Notation (small numbers)

To convert a number less than 1 to a scientific notation, the original decimal point is moved x places to the right, and the resulting number is multiplied by 10^-x *The exponent x is a negative number equal to the number of places the decimal point moved Example: 0.0062 = 6.2X10^-3

Factor-Labeled Method (Dimensional Analysis)

Uses Conversion Factors to: -Convert from one unit to another within the same system -Convert units from one system to another

Precision

a measure of the agreement of replicate measurements (like repeated measurements that are close together so you know you're getting a precise result but it's not the result that it should be) *Deviation- amount of variation present in a set of replicate measurements. Large amount of variability.

Significant figures

all digits in a number representing data or results that are known with certainty plus one uncertain digit

Potential energy

can be defined as stored energy

Conversion factor

converting from one unit to another you need to know the Conversion factor which is the relationship between the two units. Example: The relationship: 1 gal=4qt The conversion factor: 1gal/4qt or 4qt/1gal (need to re-write into a fraction

Conversion factor examples Convert 12 gallsons to quarts

relationship: 1gal=4qt conversion factor 1gal/4qt or 4qt/1gal Data given: 12 gal use conversion factor with gal in denominator : 12X 4/1gal = 48

Accuracy

the degree of agreement between the true value and the measured value *ERROR- the difference between the true value and our estimation -random -systemic

Convert 360 feet to miles

the relationship: 5280ft = 1mi the conversion factor: 5280ft/1mi or 1mi/5280ft Data given: 360ft Data given is in feet so you want to use the conversion factor with feet in the denominator so that it can cancel out: 360x 1mi/5280 =0.068