It is important to note that the molarity is defined as moles of solute per liter of solution, not moles of solute per liter of solvent. This is because when you add a substance, perhaps a salt, to some volume of water, the volume of the resulting solution will be different than the original volume in some unpredictable way. To get around this problem chemists commonly make up their solutions in volumetric flasks. These are flasks that have a long neck with an etched line indicating the volume. The solute (perhaps a salt) is added to the flask first and then water is added until the solution reaches the mark. The flasks have very good calibration so volumes are commonly known to at least four significant figures. Show
Example #1 : Molarity Calculation The equation for calculating Molarity from the moles and volume is very simple. Just divide moles of solute by volume of solution. Molarity (M) = moles of solute / volume of solution (in liters) What is the molarity (with the correct numbers of significant figures) of a 0.40 moles of NaCl dissolved in 0.250 liters? Answer Example #2 : Making Dilutions
M1 V1 = M2 V2 Moles of solute in original solution 1 = Moles of solute in diluted solution 2 The volume units must be the same for both volumes in this equation. In general, M1 usually refers to as the initial molarity of the solution. V1 refers to the volume that is being transferred. M2 refers to the final concentration of the solution and V2 is the final total volume of the solution. Remeber that the number of moles of solute does not change when more solvent is added to the solution. Concentration, however, does change with the added amount of solvent. (illustration) Don't forget this concept. You will use it again in acidbase equilibrium. Dilution calculation example: How do you prepare 100ml of 0.40M MgSO4 from a stock solution of 2.0M MgSO4? Answer: There are two solutions involved in this problem. Notice that you are given two concentrations, but only one volume. Solution #1 is the one for which you have only concentration  the solution that is already sitting on the shelf. Solution #2 is the one for which you have both concentration and volume  the solution that you are going to prepare. At least until you are comfortable with this type of problem, it may be helpful to write out what numbers go with what letters in our equation. termdescriptionexamplesolute:substance which dissolvessolid sodium chloride, NaCl(s)solvent:substance which enables the solute to dissolveliquid water, H2O(l)solution:prepared by dissolving a solute in a solventNaCl(aq) is NaCl(s) dissolved in H2O(l) amount of solutevolume of solutionconcentrationunits of concentration of a stock solution in mol L1 = moles of solute ÷ volume of solution in litres c1 = n1 ÷ V1 The dilution equation (dilution formula or dilution expression) is: c1V1 = c2V2 The dilution equation (dilution formula or dilution expression) is: c1V1 = c2V2 Please do not block ads on this website. Dilution TechniqueDilution means to reduce the concentration of a solution.A solution can be diluted by adding solvent to a given volume of stock solution. In order to dilute a solution we need:
StepDescriptionCalculation1The solution to be diluted will be in a vessel such as a volumetric flask. This solution is referred to as the stock solution. 2You will need a clean, dry, pipette with a known volume. This will be printed on the pipette, for example 10.00 mL, 25.00 mL, etc Use the pipette filler (bulb) to draw up a small amount of stock solution from the conical flask, remove the pipette from the solution, swirl the solution in the pipette around to rinse it and then discard this solution suitably. DO NOT use water or any other solvent to rinse the pipette because you would be diluting the solution and we would no longer know what the concentration of this solution is. Place the rinsed pipette into the stock solution in the conical flask and draw up the solution until it is past the level marked on the pipette. Remove the pipette from the stock solution. Suspended the pipette within the confines of a beaker. Allow the solution to escape from the pipette drop by drop until the bottom of the meniscus (when viewed at eye level) sits just on the level marked on the pipette. You need to record the volume of this undiluted, stock solution, held in the pipette. It is a good idea to convert this volume in milliltres (mL) to a volume in litres (L) if your concentration is mol L1 (molarity): volume in L = volume in mL ÷ 1000 Record the volume of this pipette as V1, for example, V(NaCl)1 = 10.00 mL = 10.00/1000 = 0.0100 L V1 = [volume of undiluted solution in pipette] LV1 = V(undiluted solution) L 3Position the pipette so that the tip of the pipette meets the inside neck of the clean volumetric flask at an angle. Allow the solution in the pipette to escape and run down the neck of the volumetric flask into the body of the flask. Pipettes are usually designed to deliver a known volume, this means that the small drop of solution remaining in the tip of the pipette is supposed to be there, so don't try to blow it out. We now have a known volume of the undiluted stock solution, with a known concentration in this volumetric flask. Calculate the moles of solute, n(solute), contained in this volumetric flask. moles of solute (mol) = concentration of solution (mol L1) × volume of solution delivered from pipette (L) n(solute) = c1 × V1 Record the moles of solute, n(solute) in mol.n(solute) = c1 × V1 mol 4Place a glass funnel in the neck of the volumetric flask. As you pour your solvent, for example water, into the funnel, leave a small air gap between the stem of the funnel and the neck of the volumetric flask so that the solvent flows freely. When the solvent reaches the base of the neck of the volumetric flask, stop pouring and allow any solvent remaining in the funnel to flow through. Slowly, and carefully, add more solvent until the bottom of the meniscus is about 1 cm from the level marked on the neck of the volumetric flask when viewed at eye level. Use a clean pasteur pipette that has been rinsed with the solvent to add more solvent dropbydrop to the volumetric flask until the bottom of the meniscus sits exactly on the level marked on the neck of the flask when viewed at eye level. Stopper the volumetric flask. Record the volume of the diluted solution in this volumetric flask as V2 in mL Convert the volume in millilitres to a volume in litres dividing by 1000. Record this volume as V2 L.V2 = [dilute solution] L 5Calculate the concentration of the dilute solution, c2: concentration of dilute solution = moles of solute ÷ volume of dilute solution molarity of dilute solution (mol L1) = moles solute (mol) ÷ volume of dilute solution (L) c2 = n(solute) ÷ V2 Affix a label to the volumetric flask which states the date the solution was made, its formula and concentration.c2 = [dilute solution] mol L1 c2 = n(solute) ÷ V2 mol L1 Do you know this? Join AUSeTUTE! Play the game now! The Dilution Equation (dilution formula, or, dilution expression)We can summarise the process of diluting a stock solution as:undiluted solution→ pipette→ volumetric flask→ add solvent→ dilute solutionc(undiluted solution) mol L1V(pipette) in mL So we now have an equation (expression or formula) to calculate the concentration of a solution after it has been diluted: c2=c1 × V1 c1 = concentration of undiluted solution in mol L1 If we rearrange this equation (expression or formula) by multiplying both sides of the equation by V2 we get: c1V1 = c2V2 which simply means that the moles of solute transferred by pipette and placed in the volumetric flask (n1) equals the moles of solute present in the volumetric flask after more solvent was added during the dilution (n2). moles solute transferred by pipette to volumetric flask=moles solute in volumetric flask after solvent added (dilute solution)c1V1=c2V2n1=n2 This equation (formula or expression) is very useful because we can rearrange it find:
Do you understand this? Join AUSeTUTE! Take the test now! Examples of Dilucation Calculation Questions with Worked SolutionsCalculate concentration of solution after dilution: c2 = (c1V1) ÷ V2Calculate the new concentration in mol L1 (molarity) if enough water is added to 100.00 mL of 0.25 mol L1 sodium chloride solution to make up 1.5 L.
Calculate the volume of solution after dilution (V2 = (c1V1) ÷ c2)Calculate the volume in litres to which 500.00 mL of 0.020 mol L1 copper sulfate solution must be diluted to make a new solution with a concentration of 0.0010 mol L1.
Calculate the concentration in mol L1 of solution before dilution c1 = (c2V2) ÷ V1Calculate the concentration of the undiluted CuSO4(aq) if 10.00 mL of this solution was used to make 100.00 mL of dilute solution with a concentration of 0.20 mol L1.
Calculate the volume of the pipette used to dilute a solution (V2 = (c1V1) ÷ c2)Calculate the volume of the pipette in millilitres used to transfer a quantity of 0.15 mol L1 CuSO4(aq) to a 250.00 mL volumetric flask made up with enough water to produce a solution with a concentration of 0.012 mol L1.
Can you apply this? Join AUSeTUTE! Take the exam now! Problem SolvingThe Problem:Chris the chemist requires two aqueous solutions of sodium carbonate, Na2CO3(aq), of different concentrations for an analytical procedure. Solving the Problem Using the StoPGoPS model for problem solving: STOP!State the question.What is the question asking you to do? Calculate the concentration of the second solution in mol L1. What chemical principle will you need to apply? Apply stoichoimetry (chemical calculations) What information (data) have you been given?
Assume the Na2CO3 is 100% pure (no impurities) Step 2: Calculate concentration of the stock (undiluted) solution n(Na2CO3) from above Step 3: Calculate the moles of Na2CO3 in the pipette which is transferred to the second volumetric flask for dilution How is stock concentration calculated?The calculator uses the formula M_{1}V_{1} = M_{2}V_{2} where "1" represents the concentrated conditions (i.e., stock solution molarity and volume) and "2" represents the diluted conditions (i.e., desired volume and molarity).
How do you find the concentration of a diluted stock solution?Calculate concentration of solution after dilution: c_{2} = (c_{1}V_{1}) ÷ V. Calculate the new concentration in mol L^{}^{1} (molarity) if enough water is added to 100.00 mL of 0.25 mol L^{}^{1} sodium chloride solution to make up 1.5 L.
How do you find the percentage of a stock solution?This percentage can be determined in one of three ways: (1) the mass of the solute divided by the mass of solution, (2) the volume of the solute divided by the volume of the solution, or (3) the mass of the solute divided by the volume of the solution.
How do you calculate molarity of a stock?The equation for calculating Molarity from the moles and volume is very simple. Just divide moles of solute by volume of solution.
