- WELCOME TO THE DILUTION CALCULATION VIDEO TUTORIAL.
THERE ARE A LOT OF GOOD REASONS
TO USE DILUTIONS, ESPECIALLY IN THE--HEALTH FIELD.
MANY PHARMACEUTICALS ARE
PREPARED IN A HIGHLY CONCENTRATED STOCK SOLUTION.
AND THEN IT'S UP TO THE NURSE TO DO THE DILUTION
SO THAT WE HAVE THE CORRECT DOSAGE FOR THE PATIENT.
SO ALL OF THESE DILUTION CALCULATIONS,
YOU CAN SEE THE FORMULA ON YOUR HANDOUT.
C1V1=C2V2.
SOME TEXTBOOKS WILL DESCRIBE IT AS M1V1=M2V2.
AND I THINK THAT USING M IS FOR MOLARITY
AND THAT'S SOMETHING CHEMISTS LOVE
BUT THIS CALCULATION WORKS FOR ALL DIFFERENT TYPES
OF CONCENTRATION UNITS.
SO I PREFER THE MORE GLOBAL C1V1=C2V2.
SO HOW DID WE END UP
NEEDING TO HAVE THESE DILUTION CALCULATIONS?
WELL, LET'S COME OVER HERE.
AND MOST DRUGS AND MANY COMPOUNDS ARE SOLIDS.
AND SO IF WE'RE WEIGHING OUT THE SOLIDS
WE HAVE TO WEIGH OUT ENOUGH THAT WE TRUST THE WEIGHT.
IT WOULD BE HARD TO JUST NEED ONE CRYSTAL
AND TRY TO LOOK FOR THE PERFECT CRYSTAL.
SO WE END UP MAKING A CONCENTRATED STOCK SOLUTION.
SO WE WOULD CALL THIS C1.
AND THEN WE WANT TO MAKE A DILUTION.
SO HERE IS GOING TO BE OUR NEW SOLUTION.
IT WILL HAVE A NEW CONCENTRATION C2
AND WHATEVER VOLUME WE NEED TO MAKE WOULD BE OUR V2.
SO IN MOST CASES
THE CALCULATION WE'RE TRYING TO SOLVE IS WHAT IS THE VOLUME
WE WOULD NEED OF OUR CONCENTRATED STOCK SOLUTION
TO MAKE A DILUTE SOLUTION?
SO FOR EXAMPLE,
IF I TAKE THIS BULB AND I PULL OUT FIVE MILLILITERS
OF OUR CONCENTRATED STOCK SOLUTION
AND WE TRANSFER THAT TO OUR FLASK
AND THEN WE'LL DILUTE WITH WATER.
OKAY. SO YOU CAN ALREADY SEE--
YOU CAN ALREADY START TO COMPARE THE INTENSITY,
OF COURSE WE AREN'T ALWAYS LUCKY ENOUGH
TO HAVE BEAUTIFULLY COLORFUL SOLUTIONS.
MANY SOLUTIONS ARE CLEAR.
AND WE DON'T EVEN KNOW THAT A SOLUTE HAS BEEN DISSOLVED.
OKAY. JUST A FEW MORE SQUIRTS HERE.
THEN WE'LL HAVE OUR DILUTE SOLUTION.
SO THEN IF--
AND OF COURSE WE ALWAYS WANT TO MIX-- OH,
OOPS, THERE WE GO. OKAY.
AND SO NOW IF WE LOOK AT THE COLOR
OF THESE TWO SOLUTIONS,
WE CAN SEE THE VIBRANT BRIGHT BLUE
OF OUR CONCENTRATED STOCK SOLUTION
AND THEN THE LOVELY PALE BLUE OF OUR DILUTE SOLUTION.
SO NOW LET'S CONNECT THIS TO THE CALCULATIONS.
ALL RIGHT.
SO TO HAVE SOME NOTES HERE, RIGHT,
WE HAVE OUR CONCENTRATED STOCK SOLUTION.
AND THEN WE HAVE OUR NEW--
THIS WILL BE OUR DILUTE SOLUTION. OKAY.
AND SO THEY'LL BE SOME SORT
OF VOLUME HERE AND THEN THIS IS THE CONCENTRATION.
SO IN MANY APPLICATIONS THIS WOULD BE THE DOSAGE
THAT WAS NEEDED FOR THE PATIENT TO RECEIVE THE DRUG.
AND THEN TYPICALLY
THE MAIN QUESTION WE'RE LOOKING AT IS HOW MUCH
OF THIS CONCENTRATED SOLUTION IS NEEDED.
SO WE'LL JUST START WITH A REGULAR--
MORE LIKE A IV SOLUTION TYPE QUESTION.
HOW MANY LITERS OF A 0.025% MASS OVER VOLUME KCL SOLUTION,
POTASSIUM CHLORIDE,
CAN BE PREPARED FROM 200 MILLILITERS OF A 4.5% MASS
OVER VOLUME STOCK SOLUTION, RIGHT?
BECAUSE WE NOTICE HERE WE CAN USE THESE CALCULATIONS
WITH ANY TYPE OF CONCENTRATION UNIT.
SO THE KEY HERE IS TO MAKE SURE
THAT WE'VE LINKED THE CONCENTRATION AND VOLUMES
TOGETHER APPROPRIATELY.
THAT SEEMS TO BE THE BIGGEST CHALLENGE
BECAUSE THEN SOLVING IT WILL BE--
JUST SIMPLE ALGEBRA.
SO IF WE LOOK HERE, RIGHT?
HOW ANY LITERS OF--
SO HOW MANY LITERS OF--
WE CAN SEE THAT THIS INFORMATION IS ALL LINKED TOGETHER.
WE'RE TRYING TO FIND THIS VOLUME AND THIS IS OUR CONCENTRATION.
NOW, WE COULD CALL THESE ONES OR TWOS.
BUT I NOTICED THAT THIS CONCENTRATION
IS MUCH SMALLER THAN THIS ONE.
SO I'M GOING TO CALL THIS V2 AND C2
TO KEEP IT IN ALIGN WITH OUR DIAGRAM.
AND NOW WE HAVE--
HERE'S OUR V1, RIGHT?
THE MILLILITERS, WE RECOGNIZE THAT AS A VOLUME
AND THEN THERE'S OUR CONCENTRATION UNITS.
SO WE'VE CORRECTLY LINKED THE CONCENTRATIONS
AND THE VOLUMES TOGETHER.
NOW, WE LOOK AND WE SEE THAT WE'RE TRYING TO SOLVE FOR V2.
WHEN WE SOLVE THIS EXPRESSION FOR V2,
RIGHT, SO V2 IS GOING TO BE C1V1/C2.
AT THIS POINT IT BECOMES WHAT WE CALL PLUG-AND-CHUG.
WE'VE IDENTIFIED ALL THE VARIABLES
AND WE'VE SOLVED THE ALGEBRAIC EXPRESSION.
SO NOW WE CAN COMPLETE THE CALCULATION.
SO 200 MILLILITERS
AND 4.5% MASS VOLUME DIVIDED BY 0.025% MASS VOLUME.
SO NOTICE HOW THE UNITS ARE HELPFUL, RIGHT?
THE PERCENT MASS VOLUMES CANCEL AND WE'RE LEFT WITH MILLILITERS
WHICH WE'RE TRYING TO CALCULATE A VOLUME,
SO THAT WORKS OUT PERFECTLY.
ALL RIGHT.
SO NOW WE TAKE AND WE PUNCH THOSE NUMBERS
INTO OUR CALCULATOR.
AND THE CALCULATOR TELLS US THAT WE WOULD BE ABLE
TO PRODUCE 3600 MILLILITERS
OF A 0.025% MASS VOLUME POTASSIUM CHLORIDE SOLUTION.
AND THEN OF COURSE LAST BUT NOT LEAST,
ONCE WE FINISHED THE CALCULATION,
TAKE A BREATH, SAVOR THE MOMENT
AND THEN CHECK FOR SIG FIGS. RIGHT.
IN THIS EXAMPLE WE HAVE THREE SIG FIGS HERE,
TWO SIG FIGS HERE,
SIG FIGS HERE, RIGHT?
BECAUSE LEADING ZEROS NEVER COUNT.
THE DECIMAL POINT IS HERE, SO WE COUNT THE TRAILING ZEROS.
SO OUR FINAL ANSWER SHOULD BE TWO SIG FIGS
WHICH IS WHAT WE'RE SHOWING.
SO WE HAVE SOLVED OUR FIRST PRACTICE PROBLEM.
ALL RIGHT.
NOW, LET'S TRY ANOTHER ONE.
HYDROCORTISONE IS USED AS AN ANTI-INFLAMMATORY
FOR LOCALIZED PAIN.
YOU NEED TO PREPARE A 50 MILLIGRAM
PER MILLILITER SOLUTION OF HYDROCORTISONE FOR AN INJECTION.
YOU HAVE FIVE MILLILITERS OF A TWO HUNDRED MILLIGRAM
PER MILLILITER STOCK SOLUTION.
HOW MANY MILLILITERS OF THE 50 MILLIGRAM
PER ML SOLUTION CAN YOU PREPARE?
THIS ONE IS VERY SIMILAR TO THE ONE UP ABOVE.
WE'RE WANTING TO KNOW HOW MUCH SOLUTION WE CAN PREPARE.
SO LET'S DISSECT IT LIKE WE DID THE FIRST ONE.
ALL RIGHTY.
HOW MANY MILLILITERS, THERE IT IS AGAIN.
THERE IS THE VOLUME WE'RE NOT SURE ABOUT.
THIS IS THE CONCENTRATION WE NEED TO PREPARE.
WHAT DO WE HAVE?
WE HAVE FIVE MILLILITERS,
THERE'S OUR V1 AND THEN THERE'S OUR C1.
OKAY. SO THE ALGEBRA HASN'T CHANGED.
V2 IS STILL CALCULATED THE SAME WAY.
SO WE'RE BACK TO PLUG-AND-CHUG,
200 MILLIGRAMS PER MILLILITER.
THERE'S OUR C1 AND OUR VOLUME.
FIVE MILLILITERS AND THEN OUR--
THE DESIRED CONCENTRATION IS FIFTY.
NOW, NOTICE WE'VE USED VERY DIFFERENT CONCENTRATION UNITS
FROM THE LAST ONE
BUT THIS CALCULATION WORKS REGARDLESS, RIGHT?
BECAUSE THE MILLIGRAMS PER ML
ALL CANCEL AND ONCE AGAIN WE'RE LEFT WITH MILLILITERS
WHICH IS A VOLUME UNIT.
SO NOW WE TAKE THE TIME TO PLUG IT IN TO OUR CALCULATOR.
AND WE SEE THAT WE HAVE THE ABILITY
TO PRODUCE 20 MILLILITERS OF THIS SOLUTION
OF THE HYDROCORTISONE. OKAY.
AND WE'RE BACK TO SIG FIGS AGAIN, RIGHT?
TO CLEAN UP THOSE LAST BIT OF DETAILS.
AND WE SEE HERE,
THIS ONE IS PRETTY STRAIGHTFORWARD,
ALL OF OUR VALUES ARE ONLY ONE SIGNIFICANT FIGURE
AND OUR ANSWER HAS ONE SIGNIFICANT FIGURE.
SO WE'RE DONE.
AND THEN WE BOX THE ANSWER
SO IT'S EASY TO GRADE. ALL RIGHTY.
SO THESE TWO QUESTIONS HAVE BEEN VERY SIMILAR.
AND SO LET'S TRY--
JUST MIX IT UP A LITTLE BIT.
SO ON THE NEXT PAGE OF YOUR HANDOUTS,
WE WILL--
THERE WE GO.
WE'LL LOOK AT INTRAVENOUS SOLUTION OF SODIUM LACTATE.
LET'S SEE. RIGHT.
IT CONTAINS 1.72% WEIGHT OVER VOLUME.
NOW, I DID THIS ON PURPOSE, RIGHT.
SO REMEMBER THAT NOT EVERYONE IS GOING TO USE MASS OVER VOLUME
EVEN THOUGH THAT WOULD BE THE MOST CORRECT EXPRESSION.
IT'S VERY COMMON TO ALSO SEE WEIGHT OVER VOLUME.
SO DON'T LET THAT FOOL YOU OR GET YOU OFF TRACK.
ALL RIGHTY.
SO WE HAVE OUR SODIUM LACTATE SOLUTION AT THIS CONCENTRATION,
IT'S IN WATER.
SO WE HAVE A HUNDRED AND TWENTY MLS OF A FIVE PERCENT SOLUTION.
OH, THIS IS JUST--
THERE WE GO, THIS IS JUST LIKE THE PREVIOUS ONE.
YOU GUYS SHOULD BE GETTING GOOD AT THESE NOW.
OH, HOW MUCH WATER DO WE ADD?
ALL RIGHT. SO THIS ONE HAS A LITTLE BIT OF A TWIST TO IT.
DO YOU SEE-- HOPEFULLY YOU SEE WHERE WE'RE GOING WITH THIS.
ALL RIGHT.
SO THERE'S OUR VOLUME,
OUR INITIAL VOLUME AND OUR INITIAL CONCENTRATION.
WE RECOGNIZED THOSE AS THE V1 AND THE C1
BECAUSE WE HAVE THE HIGHER CONCENTRATION
AND THEY'RE LINKED BY THE WORD OF.
AND THEN THIS IS THE CONCENTRATION
THAT WE WANT TO MAKE.
AND SO HOW MUCH OF OUR MATERIALS DO WE HAVE?
LIKE HOW MUCH CAN WE MAKE?
SO WE'RE BACK TO V2 AGAIN
FROM THE PREVIOUS PAGE.
SO WE'LL GO AHEAD AND DO THE CALCULATION.
SO WE WOULD HAVE FIVE PERCENT WEIGHT OVER VOLUME
AND THEN WE WOULD HAVE A HUNDRED AND TWENTY MLS
AND WE WANT TO MAKE A 1.72 SOLUTION.
ALL RIGHT.
SO WE PUNCH THIS RESULT INTO OUR CALCULATOR.
AND WE GET--
YEAH, THAT LOOKS RIGHT.
LET ME DO THAT ONE AGAIN. OKAY.
SO WE WOULD GET 348.8 MILLILITERS.
ALL RIGHTY.
SO NOW THIS ONE IS GOING TO GIVE US A LITTLE MORE WORK.
SIG FIGS, WE HAVE THREE SIG FIGS, TWO AND THREE.
SO THE TWO SIG FIG DATA IS GOING TO LIMIT OUR RESULT
AND SO WE'RE GOING TO END UP NEEDING 350 MILLILITERS
WILL BE THE VOLUME OF SOLUTION. OKAY.
BUT NOW LET'S THINK BACK TO THE BEGINNING, RIGHT?
HOW WE ACTUALLY PHYSICALLY DO THIS SOLUTION.
WE WILL HAVE A HUNDRED AND TWENTY MILLILITERS
OF THE FIVE PERCENT.
AND THEN WE WANT TO HAVE A FINAL VOLUME OF THE 1.72%.
ALL RIGHTY.
SO HOW MUCH WATER DO WE ADD, RIGHT?
SO WE ALREADY HAVE A HUNDRED AND TWENTY MLS
AND WE WANT OUR FINAL VOLUME TO BE THREE-FIFTY.
SO IF WE LOOK THERE WE SEE
WE'RE GOING TO HAVE TO ADD 230 MILLILITERS OF WATER.
SO THIS ONE IS ONE STEP INTO A MORE PRACTICAL SETTING,
THE TYPE OF CALCULATION THAT WOULD BE DONE IN A--
IN A REAL CONTEXT. OKAY.
AND THEN LAST BUT NOT LEAST
LET'S TRY THIS LAST PRACTICE PROBLEM HERE.
IF WE MIX A HUNDRED AND TWENTY-FIVE MLS OF WATER
WITH TWENTY-FIVE MLS OF 4.45% MASS OVER VOLUME GLUCOSE,
WHAT WILL BE THE RESULTING CONCENTRATION?
SO THIS ONE IS SLIGHTLY DIFFERENT.
LET'S LOOK HERE.
THESE ARE--
THERE IS OUR INITIAL VOLUME AND OUR INITIAL CONCENTRATION
OF GLUCOSE AND NOW WE'RE GOING TO DO A DILUTION, RIGHT?
WE'RE GOING TO ADD WATER.
BUT THIS IS NOT V2.
ALL RIGHT.
REMEMBER V2 IS GOING TO BE THE HUNDRED AND TWENTY-FIVE MLS
OF WATER THAT WE ADD PLUS THE TWENTY-FIVE MLS
OF THE GLUCOSE SOLUTION.
SO V2 IS GOING TO BE A HUNDRED AND FIFTY MILLILITERS. RIGHT?
AND THEN WHAT'S THE RESULTING CONCENTRATION?
THAT'S WHAT WE'RE TRYING TO CALCULATE.
SO THIS ONE WILL BE SOLVING FOR C2.
SO WE'RE BACK TO OUR ORIGINAL EQUATION.
WE JUST REARRANGE IT ALGEBRAICALLY
TO SOLVE FOR THE NEW CONCENTRATION.
AND NOW WE PLUG IN THE VALUES FROM THE QUESTION.
SO THERE'S OUR INITIAL CONCENTRATION
AND THERE IS OUR VOLUME AND THEN OUR ULTIMATE VOLUME
WHEN WE'VE MIXED EVERYTHING TOGETHER,
IT WILL BE A HUNDRED AND FIFTY MILLILITERS.
SO WE PUNCH THIS DATA INTO OUR CALCULATOR.
AND WE SEE THAT THE NEW CONCENTRATION,
OUR CALCULATOR TELLS US WOULD BE 0.7417% MASS OVER VOLUME, RIGHT?
BECAUSE IN THIS CASE NOW,
THE MILLILITERS CANCEL AND WE'RE LEFT WITH CONCENTRATION UNITS.
ONCE WE FINISHED THE CALCULATION,
BIG BREATH, LOOK BACK,
COMPARE THE SIG FIGS OF OUR DATA.
THREE SIG FIGS, TWO SIG FIGS,
AND THIS WOULD ACTUALLY BE THREE SIG FIGS.
ALL RIGHT.
BECAUSE THE UNCERTAINTY WAS HERE AND HERE.
SO I SHOULD HAVE PUT A DECIMAL THERE.
ALL RIGHTY.
BUT REMEMBER THAT OUR DATA IS ALWAYS LIMITED BY THE WORD--
THE LEAST ACCURATE AND PRECISE.
SO WE WOULD ROUND OUR ANSWER TO TWO SIG FIGS,
LEADING ZEROS NEVER COUNT, SO 0.74% MASS
OVER VOLUME GLUCOSE WOULD BE THE SOLUTION WE PREPARED.
ALL RIGHTY.
SO I HOPE THAT YOU FIND THESE PRACTICE PROBLEMS HELPFUL
AND NOW YOU WANT TO GO AND WORK A FEW HOMEWORK PROBLEMS
TO REINFORCE WHAT WE JUST PRACTICED TOGETHER.