Measurement+In+Chemistry

When something is measured several times the results may vary. In science, for a certain measurement to be used there must be an indication of its reliability of uncertainty. 


 * Accuracy VS Precision **

In everyday life accuracy and precision are considered to have the same meaning, but in the world of science they are quite different. =Accuracy = =Correct =Precise = =Consistent

__Accuracy__ is the closeness of measurements to the actual or accepted value of the quantity measured. __Precision__ characterizes the degree of mutual agreement among a series of individual measurements or values. Values may be accurate but not precise, precise but not accurate, both or neither. 

Example: To help you better understand the difference between accuracy and precision you can think of them in term if throwing darts. 
 * Accurate** because the darts hit or hit close to the bull’s eye target.
 * Precise** because darts are grouped in a close cluster, which means they hit the same general spot (doesn't have to be the target spot).

= = When doing and experiment the percent error measures how innaccurate a measurement is from the correct, or accepted value. How to Calculate: **(experimental value) − (true value) % error = —―――――――――――――— × 100 true value**  Example: What is the percent error for a calculated mass measurement of 45g, given that the correct value is 50g? Answer: 10% __50g__  __-__ __45g__ * 100 = 10% 50g **Uncertainty in Measurements **
 * Percent Error **

Some type or error or uncertainty always exists in any measurement. The measuring instruments themselves place limitations on precision. Some balances can be read more precisley than others. The same is true for rulers, graduated cylinders, thermometers, and other measuring devices. Sometimes you may encounter a measurement that is inbetween values on your measuring device, which you will then have to estimate. Examples: What is the measurement of the object below? **Answer: 4.4 or 4.4 ± 0.1 cm ** We can estimate that the length is 4.4 cm but we might be off by 0.1 cm in either direction. So, we would record this measurement as: 4.4 ± 0.1 cm Temperature: What is the temperature of the thermometer below? **Answer: 78º ** __Measuring Liquids__- Measure the meniscus at eye level from the center of the meniscus. The meniscus is the curve seen at the top of a liquid in a container. Most liquids are concave so you take your measurement from the bottom of the. Examples: What is the volume of the liquid below? Answer: 38cm^3 =Significant Figures = Rules for Sig Figs in Measurements 1. Every nonzero digit in a reported measurement is assumed to be significant. The measurements **24**.**7** meters, 0.**743** meter, and **714** meters each express a measure of length to **//three//** significant figures.

2. Zeros appearing between nonzero digits are significant. The measurements 7**00**3 meters, 4**0**.79 meters, and 1.5**0**3 meters each have **//four//** significant figures.

3. The zeros furthest to the left appearing in front of nonzero digits are not significant. They act as placeholders. The measurements 0.00**71** meter, 0.**42** meter, and 0.0000**99** meter each have only **//two//** significant figures. The zeros to the left are **//NOT//** significant. If you can write the measurements in scientific notation and ignore the zeros than it isn’t significant In these three cases that would mean: 7.1 x 10-3 meter, 4.2 x 10-1 meter, and 9.9 x 10-5 meter

4. Zeros at the end of number and to the right of a decimal point are always significant. The measurements **43.00** meters, **1.010** meters, and **9.000** meters each have **//four//** significant figures.

5. Zeros the furthest to the right end of a measurement that lie to the left of an understood decimal point are not significant if they serve as placeholders to show the magnitude of the number. The zeros in the measurements **4**00 meters, **9**000 meters and 55,674, 000 meters are not significant. The numbers of significant figures in these values are **//one, one,//** and **//five//**, **respectively.** If such zeros were known and carefully measured values, however, then they would be significant.

For example, if the value of 300 meters resulted from a careful measurement rather than a rough, rounded measurement, the zeros would be significant. If all of the zeros in the measurement **//300//** meters were significant, writing the value in scientific notation as 3.00 x 102 meters makes it clear that these zeros **//are//** significant.

6. There are two situations in which measurements have an unlimited number of significant figures. One way is by counting for example if you carefully count that there are 5 coins in your pocket, then there are **//exactly//** 5 coins, not 4.99 or 5.01. This measurement can only be a whole number and has an unlimited number of significant figures, because of all of the zeros to the right, you can re-write the 5 to look like 5.00000000000…

The second situation where you can have an unlimited number of significant figures is exactly defined quantities, which can include those within a system of measurement. For example there are 12 inches in 1 foot; both of these quantities have an unlimited amount of sig figs like the one above. Rules for the Answers When using: // Addition and Subtraction // The answer to an addition or subtraction calculation should be rounded to the same number of decimal places **//(NOT DIGITS)­­­­­//** as the measurement with the **// __least__ //** number of decimal places.

Examples:

a. 12.52 cm + 349.0 cm + 8.24 cm

b. 74.626 cm – 28.34 cm

a. Line up the decimal points and add the numbers. 12.52 cm Where’s the ** least ** number of decimal places? 349.**0** cm 349.0 cm + 8.24 cm It has only **//__ONE__//** digit to the right of the decimal point.

369.76 cm à Round the answer to 369.**//8 //** cm or 3.698 x 102 cm

b. Line up the decimal points and subtract the numbers. 74.636 cm Once again, where’s the ** least ** number of decimal places? - 28.34 cm 28.34 cm __It has__ **//TWO//** digits to the right after the decimal point 46.286 cm à Round the answer to 46.29 cm or 4.629 x 101 cm

// Multiplication and Division // In calculations involving multiplication and division, you need to round the answer to the same number of significant figures as the measurement with ** least ** number of **SIGNIFICANT FIGURES**. // (Note: The position of the decimal point has NOTHING to do with the rounding. ONLY the number of SIG FIGS!) // Examples:

a. 7.55 cm x 0.34 cm

b. 0.365 cm / 0.0200

a. 7.55 cm x 0.34 cm = 2.567 square cm = 2.6 square cm (0.34 cm has the least number of sig figs with **two** significant figures so the answer has **two** sig figs or **2.6** sq cm.)

b. 0.365 cm / 0.0200 = 18.25 cm = 18.3 cm (**Both** numbers have **three** sig figs so the answer should be rounded to have **three** sig figs also i.e. **18.3** cm)

=<span style="font-size: 200%; color: rgb(227, 108, 10);">Dimensional Analysis = SI Unit Conversion

// SI Units // are an abbreviation for the **International System of Units**, a revised version of the metric system. The SI base units are the meter, kilogram, Kelvin, second, mole, candela, and ampere.

// Dimensional Analysis // is a way to analyze and solve problems using the units, or dimensions, of the measurements.

First, draw a long line with the initial unit on the left and the target units of what you’re trying to find on the right.

Second, Leave space underneath the line to write down the conversion equations that you will need in order to do the conversions

Third, fill in the known information making sure to put the initial starting point over **1** and lining up all of the other fractions so that the unit diagonal from it is the same so that they can be crossed out.

Last, cross out all of the same units and solve for the unknown given the equations. Simple math, divide diagonal and multiply to the right.

Confused? Let’s start with some //very// BASIC problems.

1. 2.5 **ft** = how many **inches**?

<span style="margin-top: 12px; z-index: 251659264; margin-left: 83px; width: 3px; position: absolute; height: 92px;"> ** Step 1: **


 * || [[image:file:///C:/DOCUME~1/ABISOL~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image002.gif width="3" height="58"]] ||
 * || [[image:file:///C:/DOCUME~1/ABISOL~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image002.gif width="3" height="58"]] ||

2.5 **feet** ** ? **** ? inches **

**<span style="font-size: 14pt; color: rgb(112, 48, 160);">Step 2: ** <span style="font-size: 14pt; color: rgb(112, 48, 160);">12 **inches** = 1 **foot**

<span style="margin-top: 12px; z-index: 251662336; margin-left: 83px; width: 3px; position: absolute; height: 92px;"> **<span style="font-size: 14pt; color: rgb(0, 112, 192);">Step 3: **

<span style="font-size: 12pt; color: rgb(0, 112, 192);">
 * || [[image:file:///C:/DOCUME~1/ABISOL~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image002.gif width="3" height="58"]] ||
 * || [[image:file:///C:/DOCUME~1/ABISOL~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image002.gif width="3" height="58"]] ||

<span style="font-size: 14pt; color: rgb(0, 112, 192);">2.5 **__feet__ 12 //inches// ? //inches//** <span style="font-size: 12pt; color: rgb(0, 112, 192);"> <span style="font-size: 22pt; color: rgb(0, 112, 192);">1 <span style="font-size: 14pt; color: rgb(0, 112, 192);">1 **__foot__** <span style="font-size: 12pt; color: rgb(0, 112, 192);">

<span style="margin-top: 12px; z-index: 251665408; margin-left: 83px; width: 3px; position: absolute; height: 92px;"> ** Last Step: **

2.5 **__feet__ 12 //inches// 30 //inches//** <span style="margin-top: 4px; z-index: 251667456; margin-left: 282px; width: 40px; position: absolute; height: 38px;"> 1 1 **__foot__**

** (2.5 x 12)/1 = **** 30 inches* ** Example:

1.609 **km** is how many **miles**?

<span style="font-size: 12pt; color: rgb(0, 112, 192);">If you follow all the steps your answer should look like this:

<span style="font-size: 16px; color: rgb(0, 112, 192); line-height: 24px;">

<span style="font-size: 12pt; color: rgb(0, 112, 192);"> <span style="font-size: 14pt; color: rgb(0, 112, 192);">1.609 **<span style="font-size: 16pt; color: rgb(13, 13, 13);">km **<span style="font-size: 14pt; color: rgb(0, 112, 192);"> 1000 **<span style="font-size: 16pt; color: rgb(148, 54, 52);">m **<span style="font-size: 14pt; color: rgb(0, 112, 192);"> 100 **<span style="font-size: 16pt; color: rgb(0, 32, 96);">cm **<span style="font-size: 14pt; color: rgb(0, 112, 192);"> 1 <span style="font-size: 16pt; color: rgb(148, 138, 84);">in <span style="font-size: 14pt; color: rgb(0, 112, 192);"> 1 <span style="font-size: 16pt; color: rgb(227, 108, 10);">feet **<span style="font-size: 14pt; color: rgb(0, 112, 192);"> 1 **** mi ** <span style="font-size: 14pt; color: rgb(0, 112, 192);"> **// .9998 //****// mi //** <span style="margin-top: 3px; z-index: 251685888; margin-left: 497px; width: 24px; position: absolute; height: 34px;"> <span style="margin-top: 3px; z-index: 251683840; margin-left: 386px; width: 25px; position: absolute; height: 34px;"> <span style="margin-top: 12px; z-index: 251681792; margin-left: 320px; width: 24px; position: absolute; height: 34px;"> <span style="margin-top: 0px; z-index: 251679744; margin-left: 228px; width: 24px; position: absolute; height: 34px;"> <span style="margin-top: 0px; z-index: 251677696; margin-left: 150px; width: 25px; position: absolute; height: 34px;"> <span style="font-size: 12pt; color: rgb(0, 112, 192);"> <span style="font-size: 22pt; color: rgb(0, 112, 192);">1 <span style="font-size: 14pt; color: rgb(0, 112, 192);"> <span style="font-size: 16pt; color: rgb(0, 112, 192);">1 <span style="font-size: 14pt; color: rgb(0, 112, 192);"> **<span style="font-size: 16pt; color: rgb(13, 13, 13);">km **<span style="font-size: 22pt; color: rgb(13, 13, 13);"> <span style="font-size: 14pt; color: rgb(0, 112, 192);"> <span style="font-size: 16pt; color: rgb(0, 112, 192);">1 **<span style="font-size: 16pt; color: rgb(148, 54, 52);">m **<span style="font-size: 14pt; color: rgb(0, 112, 192);"> <span style="font-size: 16pt; color: rgb(0, 112, 192);">2.54 <span style="font-size: 16pt; color: rgb(0, 32, 96);">cm <span style="font-size: 14pt; color: rgb(0, 112, 192);"> <span style="font-size: 16pt; color: rgb(0, 112, 192);">12 <span style="font-size: 14pt; color: rgb(0, 112, 192);"> <span style="font-size: 16pt; color: rgb(148, 138, 84);">in <span style="font-size: 14pt; color: rgb(0, 112, 192);">. <span style="font-size: 16pt; color: rgb(0, 112, 192);">5,280 <span style="font-size: 16pt; color: rgb(227, 108, 10);">feet <span style="font-size: 14pt; color: rgb(0, 112, 192);"> <span style="font-size: 12pt; color: rgb(112, 48, 160);"> <span style="font-size: 14pt; color: rgb(112, 48, 160);">1 **km** = 1000 **m** 1 **m** = 100 cm 2.54 **cm** = 1 in 12 **in** = 1 **ft** 5280 **feet** = 1 **mi**

(**1.609 x 1000 x 100) / (2.54 x 12 x 5280) = .9998**

<span style="color: rgb(227, 108, 10); font-family: 'Comic Sans MS',cursive;">** The Mole ** ** Average Atomic Mass of Elements ** The average atomic mass of elements is determined by the result of the atomic masses of each isotope in the element being multiplied by their ratio of abundance in the element and then added together. The average atomic mass unit is simplified to //amu//.

To find the total atomic mass of an element, the following process can be used:

** amu of isotope x relative abundance (isotope mass) ** **// Example: //** To find the Average Atomic Mass of Carbon, the following data must be used: Isotopes Present: Carbon-12 (Percent abundance: 98.9) Carbon-13 (Percent abundance: 1.1) AMU of Isotopes: Carbon-12 : 12 Carbon-13 : 13.003355
 * + any other isotopes’ masses__**
 * = TOTAL Average Atomic Mass of Element **

STEP 1: Multiply percent abundances by amu of isotopes; 98.9 x 12=1186.8 1.1 x 13.003355=14.3036905

STEP2 : Add mass of isotopes; 1186.8 + 14.3036905=1201.103691

STEP 3: Divide total by 100; 1201.03691/100 = 12.011

Average Atomic Mass of Carbon is **12.011**

** Mole Concept ** The mole is commonly used scientific unit for amount of substance, and is based off of how many particles are in 12 grams of carbon-12. This number is **Avogadro’s number** and is currently accepted at 6.0221415 x 10^23. This means that there are that many particles of carbon-12 in 12 grams of carbon. Thus, a single mole of any element is the amount of that substance that has 6.0221415 x 10^23 particles. The mole is the standard SI unit for amount of substance, and is a //quantitative measurement//.

** Molar Mass ** The molar mass of a substance is //the mass of the same amount of particles// (of carbon-12) //in 12 grams of carbon that are in a substance//. So, the mass attained by Avogadro’s number of particles for a substance is the molar mass of that substance. **// Example: //** Copper’s molar mass is 63.54 g/mol (mol is the abbreviation of mole), which means that the mass of 6.0221415 x10^23 particles of copper is 63.54 grams.

Molar mass is a unit commonly used in chemistry, and it allows for easy conversion to other units and tells a lot about a substance and can be used in many equations that help discover more about a substance or compound.

=<span style="font-size: 24pt; color: rgb(255, 0, 0); font-family: 'Comic Sans MS',cursive;">Percent Composition: = = = Percent composition is basically the percentage there is of each element present in a compound based on the mass of the elements and the compound. How much of each element is in a compound.

H2O (empirical formula for water) The molar mass of Hydrogen, H, is about 1 and the molar mass for oxygen is about 16. By looking at the empirical formula you can see that there are two hydrogen molecules and one oxygen molecule. <span style="color: rgb(128, 0, 128); font-size: 12pt;">So the total mass of all the hydrogen in the molecule is: 2⋅1= 2 <span style="color: rgb(128, 0, 128); font-size: 12pt;">The total mass of all the oxygen in the molecule is: 1⋅16=16 <span style="color: rgb(128, 0, 128); font-size: 12pt;">To find the total mass of the entire compound, the formula mass, add the two masses together: 16+2=18 <span style="color: rgb(128, 0, 128); font-size: 12pt;">Now you divide each part of the formula mass by the formula mass: <span style="color: rgb(128, 0, 128); font-size: 12pt;">You divide the Hydrogen part by 18: 2/18= 0.11111111111 <span style="color: rgb(128, 0, 128); font-size: 12pt;">And you divide the Oxygen part by 18: 16/18= 0.888888888888

<span style="color: rgb(29, 43, 201); font-size: 12pt;">//*Make sure that the parts of your formula add up to the formula mass so in this case 16+2 must be equal to 18 and 0.1111111111+0.8888888888 must be equal to 1 (or almost equal since the decimal repeats)//

<span style="color: rgb(128, 0, 128); font-size: 12pt;">After dividing the parts you multiply each quotient by 100 (because percents are out of 100): 0.11111111111⋅100= 11.111111

<span style="color: rgb(29, 43, 201); font-size: 12pt;">//*Remember to use 3 significant figures when writing the percent composition// 0.88888888888⋅100= 88.8888 <span style="color: rgb(128, 0, 128); font-size: 12pt;">So, the percent composition of H2O is approximately 11.1% Hydrogen and approximately 88.9% Oxygen.

Taurine (the stuff in Red Bull) C2H7NO3S Carbon: 12⋅2= 24 Hydrogen: 1⋅7= 7 Nitrogen: 14⋅1= 14 Oxygen: 16⋅3= 48 Sulfur: 32⋅1= 32 24+7+14+48+32= 125 Carbon: 24/125 ⋅ 100= 19.2% Hydrogen: 7/125 ⋅100= 5.60% Nitrogen: 14/125 ⋅ 100= 11.2% Oxygen: 48/125 ⋅ 100= 38.4% Sulfur: 32/125 ⋅ 100= 25.6%

=<span style="font-size: 24pt; color: rgb(255, 0, 0); font-family: 'Comic Sans MS',cursive;">**Determining the Formula of a Compound:** = = = When determining the empirical formula of a compound you will be given the percent composition instead of the empirical formula.

The mystery compound contains 32.38% Na, 22.65% S, and 44.99% O, find the empirical formula for this compound.

<span style="color: rgb(29, 43, 201); font-size: 12pt;">//*The easiest way to do these calculations is by assuming you have 100g of compound since the percents are out of 100//

<span style="color: rgb(128, 0, 128); font-size: 12pt;">First convert the formula to grams: 33.38 g Na, 22.65g S, and 44.99g O <span style="color: rgb(128, 0, 128); font-size: 12pt;">Next divide each of the values by the grams per mole of that element: 33.38g/ 23g/mol= 1.45 mol 22.65g/32g/mol= 0.708 mol 44.99g/16g/mol= 2.81 mol <span style="color: rgb(128, 0, 128); font-size: 12pt;">So now you have: Na1.45 S0.708 O2.81 <span style="color: rgb(128, 0, 128); font-size: 12pt;">Divide each of the mol values by the smallest value: in this case it is 0.708 1.45/0.708= about 2 2.81/0.708= about 4 <span style="color: rgb(128, 0, 128); font-size: 12pt;">Your formula is: Na2SO4

Lets say you are given 10.150g of a mystery compound that contains only P and O and all you know is that it contains 4.433g of P. <span style="color: rgb(128, 0, 128); font-size: 12pt;">First you subtract the mass of the P in the sample from the mass of the total sample: 10.150g – 4.433g = 5.717g <span style="color: rgb(128, 0, 128); font-size: 12pt;">Now you know you have: 4.433g P and 5.717g O <span style="color: rgb(128, 0, 128); font-size: 12pt;">Now you just follow the steps like you did before: Divide each mass by the element’s molar mass 4.433g/31g/mol= 0.143 mol 5.717g/16g/mol= 0.357 mol <span style="color: rgb(128, 0, 128); font-size: 12pt;">Now divide each molar value by 0.143 and you get: 0.357mol/0.143mol= about 2.5 <span style="color: rgb(29, 43, 201); font-size: 12pt;">//*2.5 is not a whole number and only whole numbers can be in the Empirical formula so you must multiply 2.5 by two to get 5 and you must also multiply the 1 P by two to get two.// <span style="color: rgb(128, 0, 128); font-size: 12pt;">Your empirical formula is: P2O5

=<span style="font-size: 24pt; color: rgb(255, 0, 0); font-family: 'Comic Sans MS',cursive;">Molecular Formula: = = = <span style="color: rgb(0, 0, 0); font-size: 12pt;">The molecular formula is basically the unreduced version of the Empirical formula so lets say you did your calculations and ended up with 4 Phosphorous instead of 2 and 10 Oxygen instead of five. Your molecular formula would be P4O10 because it tells you how many atoms of each molecule are in your compound. However the empirical formula still is P2O5 because the empirical formula tells you the ratio of different atoms in a compound. <span style="font-size: 12pt; color: rgb(0, 255, 0);">

<span style="font-size: 150%; color: rgb(0, 128, 128);"> Helpful Links: http://www.wwnorton.com/college/chemistry/gilbert/concepts/chapter4/ch4_3.htm <span style="font-size: 90%; color: rgb(0, 128, 128);"> <span style="color: rgb(255, 255, 255); font-family: ArialMT;"> http://www.tutor.com/Resources/SubTopic.aspx?id=471 <span style="color: rgb(0, 128, 128);">