Transcript of Chemical Quantities, Moles, and Stoichiometry Part 1 (English)

welcome to the first of two videos that will introduce unit conversions followed by conversions between chemical quantities with the aid of the triangle which will allow the beginning student to convert between moles grams and particles of a substance this review will help the beginning student to develop essential skills for more advanced concepts found in the next video for example introductory stoichiometric calculations as well as more advanced limiting reactant stoichiometric calculations to understand concepts within chemical quantity conversions such as converting moles of a substance to grams of a substance it is best to take a step back and review the concepts within basic unit conversions which is sometimes called dimensional analysis or unit transposition to do this we will begin with a simple conversion [Music] given 42 centimeters we are asked how many inches is this given 2.54 centimeters equals one inch while the author realizes there are many shortcuts and even websites that will perform any conversion we need to develop this imperative skill so we can apply it to more complicated chemistry exercises so let's begin with the following premise if i multiply the 42 centimeters by one then the value is still the same but what if i could derive a new definition for the numerical value of one for example if i divide both sides of this equality by 2.54 centimeters or divide both sides of this equality by one inch the equalities will still hold after simplification we have now derived two new expressions for the numerical value of one [Music] if the newly derived expression for the value of one is substituted the centimeter units will cancel and the desired unit of inches will remain after simple division we get a suggestion on our calculator which is rounded to two significant figures 17 inches at this point it is worth reviewing the significant figure rule for multiplication and division the least number of sig figs within your arithmetic manipulation must be reflected in your final answer thus two sig figs divided by infinite sig figs is two sig figs remember if a numerical value is within a definition it is assumed to have infinite sig figs we have now demonstrated that the derived expression on the left allows one to convert from centimeters to inches and we can assume the derived expression on the right allows one to convert from inches to centimeters let's prove this hypothesis to convert inches to centimeters then the same problem-solving strategy exists simply multiply the given quantity by 1 which was derived to be 2.54 centimeters over one inch after substitution the inch units cancel affording the desired unit of centimeters with the correct number of sig figs for after rounding regardless of what values n units are part of a definition one can derive two conversion factors one side of the definition can be in the numerator and the other side can be within the denominator or vice versa which is mathematically proven here the key is the numerator must equal what is in the denominator which means we do not have to derive the two resultant conversion factors from any definition we can simply write them by inspection remember that whatever is in the numerator has to equal what is in the denominator when writing a conversion factor so let's do a conversion that many may not be familiar with and apply this same approach pascals to millimeters mercury given 101 325 pascals equals 760 millimeters mercury simply write the given quantity then your units will guide you for example write the unit to cancel in the denominator and the desired unit in the numerator as shown now simply write the numerical values that equate these units from the given definition and complete the arithmetic manipulation and round to correct sig figs which is three sig figs here notice that the conversion factor that allows this unit transposition was written by inspection and it was not necessary to derive it [Music] to further review and reinforce unit conversions let's convert 1182 meters to miles using only the given definitions from the given definitions we see that we can convert meters to centimeters and centimeters to inches and inches to feet and feet to miles our plan has a total of four arrows which means the employment of four conversion factors let's use the units of our plan to guide the execution of this exercise so first write down what is given then place the unit to be canceled in the denominator and the desired unit in the numerator for each conversion factor as shown meters to centimeters centimeters to inches inches to feet feet to miles and the desired unit of miles is obtained now simply go back and add the numerical values that allow the units in the numerator to equal the units in the denominator for example 100 centimeters equals one meter which are all supplied within the given definitions finally solve the problem and round to the correct number of sig figs which is four now let's try an abstract example of converting pence to skits given the following abstract definitions from the given definitions we see that we can convert pence to draggles and draggles to gigs and gigs to munchknowns and munchknowns to skits our plan has a total of four arrows which means the employment of four conversion factors let's use the units of our plan to guide the execution of this exercise first write down what is given then place the unit to be cancelled in the denominator and the desired unit in the numerator for each conversion factor pence to draggles draggles to gigs gigs to munchknowns munchknowns to skits which is the final desired unit now simply go back and add the numerical values that allow the units in the numerator to equal the units in the denominator for example 2.5 draggles equals 1.8 pence which are all supplied within the definitions finally solve the problem and round to the correct number of sig figs which in this case is 2. now let's try unit conversion where we have to convert the numerator and the denominator the numerator is a distance conversion feet to inches inches to centimeters and the denominator is a time conversion hours to minutes minutes to seconds again there are four arrows in our plan which abstractly represents the employment of four conversion factors so write down what is given then place the unit to be cancelled in the numerator and the desired unit in the denominator hours to minutes and minutes to seconds to afford the desired unit of seconds in the denominator now convert feet to inches and inches to centimeters which completes the desired units of centimeters per second now write the numerical values that allow these sets of units to be equated 60 minutes and one hour 60 seconds and one minute twelve inches in one foot two point five four centimeters and one inch finally solve the problem and round the three sig figs to afford the final answer so now let's try one more conversion that may again seem like an abstract exercise converting 89.5 grams of gold to moles of gold given 196.97 grams of gold equal one mole of gold no matter what equality is given we can always write two conversion factors one to convert from grams to moles and one to convert from moles to grams in this example we will need the grams to moles conversion factor grams gold cancel giving the desired units of moles gold and correcting for sig figs we have the final answer in moles gold while the given definition of 196.97 grams of gold equals one mole of gold may have seemed odd at first the equality is not made up or something random in fact one mole of x equals its molar mass in grams of x the value of 196.97 grams of gold came from the periodic table which is the atomic mass for gold thus one mole of whatever element we are talking about is equal to its atomic mass in grams which is often called its molar mass with this knowledge let's convert 82.1 mole of silver to gram silver first we need to write our definition 107.87 grams of silver equal one mole of silver and again no matter what equality is given we can always write two conversion factors one to convert from grams to moles and one to convert from moles to grams again 107.87 grams came from the periodic table the atomic mass of silver in this example we will need the moles to grams conversion factor moles silver cancel giving the desired unit of gram silver and correcting for sig figs we have our final answer in grams silver in the next example we have to convert 32.9 grams of ethanol to moles of ethanol recall one mole of x is equal to the molar mass of x we need to develop a new scale calculating the molar mass of any compound with the a to the periodic table ethanol has two carbons six hydrogens and one oxygen in the formula now multiply the molar mass of each element which was found on the periodic table and add this up to afford the molar mass of ethanol which is 46.07 grams after rounding to the hundredths place thus 46.07 grams of ethanol equal one mole of ethanol now two conversion factors can be imagined starting from the given grams of ethanol we will need the conversion factor that converts grams to moles grams ethanol cancel giving the desired units of moles of ethanol and correcting for sig figs we have our final answer now let's try one more conversion that may again seem like an abstract exercise converting 2.82 moles of gold to atoms of gold given 6.02 times 10 to the 23rd atoms of gold equal one mole of gold recall no matter what equality is given we can always write two conversion factors in this case want to convert from number of atoms to moles and the other to convert from moles to numbers of atoms so write down the given quantity we will need the moles to number of atoms conversion factor here moles cancel giving the desired unit of number of atoms of gold and correcting for sig figs we have our final answer in number of atoms of gold while the given definition of 6.02 times 10 to the 23rd atoms of gold equal one mole of gold may have seemed odd this equality is not fictitious in fact one mole of x equals 6.02 times 10 to the 23rd particles of x where particles can be atoms molecules ions etc whatever it is we are talking about as defined by x the value of 6.02 times 10 to the 23rd is a special value and it's called avogadro's number which is the number of particles in one mole this is similar to the phrase one dozen eggs equals 12 eggs or simply one dozen of x equals 12 of x the word doesn't is in fact a number 12. similarly mol is a number 6.02 times 10 to the 23rd so let's review all of these concepts by converting moles to grams and moles to molecules for c7h14o2 isopentyl acetate recall one mole of x is equal to the molar mass of x thus we need to first calculate the molar mass of c7h14o2 with the aid of our periodic table there are seven carbons 14 hydrogens and two oxygens within the molecule and we can glean the atomic masses or molar masses for each element from the periodic table and multiply the molar mass of each element and add this up to afford the molar mass of the compound which is 130.18 after rounding to the hundredths place thus one mole equals 130.18 grams now two conversion factors can be imagined that allow for either conversion starting with the given value in moles we will need the conversion factor that converts moles to grams moles cancel giving the desired unit of grams and correcting for sig figs we have our final answer in grams of isopentyl acetate now let's convert the same number of moles of c7h14o2 to number of molecules of c7h14o2 first we need to write our definition that will allow us to convert between moles and number of molecules 6.02 times 10 to the 23rd molecules of c7h14o2 equal one mole of c7h14o2 no matter what equality is given we can always write two conversion factors one to convert from number of particles to moles and one to convert from moles to number of particles starting with the given quantity we will need the moles to number of molecules conversion factor moles cancel giving the desired unit of number of molecules and correcting for sig figs we have our final answer in the previous exercises one mole of whatever we are talking about is equal to its mass in grams which can be calculated with the eight of the periodic table in addition one mole of whatever we are talking about is also equal to avogadro's number of particles again once x is defined we can be more specific by using molecules atoms or ions instead of particles employing the transitive property we can also equate number of particles and molar mass as shown which now completes our triangle being able to zip around the triangle will be an imperative skill when we tackle even more challenging exercises in chemistry such as stoichiometric exercises and limiting reactant exercises in the next [Music] video [Music] you