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The Standard Curve - Density vs. Concentration of a Solution A. Overview of Concepts Recall the definition of density: mass/ volume When a solute is mixed with a solvent to make a homogenous, liquid solution, the density of the solution is directly proportional to the amount of solute in the solution. For example, the table summarizes the correlation between the concentrations of NaCl solutions and their densities: % NaCl (m/v) 1.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 Density of NaCl Solution (g/mL) A plot of the densities of these NaCl solutions against the concentrations of the NaCl solutions gives a line, thereby showing that densities and concentrations are directly proportional in this range of concentrations: 1.16 1.14 1.12 1.1 1.08 1.06 1.04 1.02 1 0.98 Density of NaCl (g/mL) O 1,00534 1.01246 1.02680 1.04127 1.05589 1.07068 1.08566 1.10085 1.11621 1.13190 1.14779 Densities of NaCl Solutions vs. Concentration of NaCl Solutions 5 10 15 Concentration of NaCl Solution (% m/v) 20 25

The plot "Density of NaCi Solution vs. Concentration of NaCl Solution" can serve as a standard curve. With a standard curve, one can measure the density of an NaCl solution with an unknown concentration and thereby, determine the density of that NaCl solution. Question: What is the concentration of an NaCl solution with a density measured to be 1.09 g/mL? Answer: Find 1.09 g/mL on the y-axis (vertical axis) and match it to the value on the x-axis (horizontal axis) that would give a point that falls on the line of the standard curve. 1.09 g/mL 12.5 % (m/v) B. Practical Applications for Generating and Using a Standard Curve In this exercise you will measure the densities of several sucrose (table sugar) solutions of known concentrations and using that data, construct a standard curve that correlates the densities of sucrose solutions with their concentrations. In addition you will measure the densities of two sucrose solutions of unknown concentrations and use the standard curve to determine their concentrations. Sucrose 0.00% 4.00 % Solutions (water) (m/v) Mass of empty 10.00 mL graduated cylinder Mass of graduated cylinder + 10.00 mL of solution Mass of solution Density of solution Procedure: 1. Measure and record the mass of a clean, dry 10.00 mL graduated cylinder. 2. Carefully fill the graduated cylinder to the 10.00 mL with a sucrose solution provided. 3. Measure and record the mass of the graduated cylinder + 10.00 mL of solution. 4. Repeat this procedure for each of the solutions provided and complete the table below: (Mass of solution/ 10.00 mL) 27.494 27. 9 8.00 % (m/v) 12.00 % (m/v) 16.00 % (m/v) 20.00 % (m/v) Unknown % Sucrose Solution Commercial Beverage

5.Using the grid below, construct a standard curve: of Density of Sucrose Solution vs. concentration of Sucrose Solution. 6. Use the standard curve to determine the sucrose concentration in your samples of unknown sucrose concentration. Unknown ID: Commercial Beverage: Sucrose % (m/v) Sucrose % (m/v)

C. Additional Exercises 1. What is the number of grams/serving of "sugars" indicated on the nutritional information on the can of commercial beverage you tested? (Hint: Look at the labeling on the beverage). Additionally, convert grams/serving from the label to % (m/v). 2. What is the % (m/v) of sugars in the commercial beverage as measured in your experiment? Additionally, convert % (m/v) from your experiment to grams/serving for one can of soda. When a concentration is expressed as X% (m/v) it means there are X grams of solute in 100 mL of solution. So a conversion factor you can use is: X grams= 100 mL. 3. Calculate the % difference between the mass percentage by volume of sugar that were experimentally determined and the mass percentage by volume of sugar reported by the producer of the beverage. You can get the same result by comparing grams/serving of your experimental results and those reported by the producer of the beverage. % difference= (%(m/v) of sugar on label -%(m/v) of sugar experimental) %6(m/v) of sugar on label x 100

Sucrose 0.00% 4.00% 8.00 % Solutions (water) (m/v) (m/v) Mass of empty 10.00 ml graduated cylinder Mass of graduated cylinder + 10.00 mL of solution Mass of solution Density of solution (Mass of solution/ 10.00 mL) 27.494 9 37.492 9 37.564 37.818 g 9 12.00% 16.00 % (m/v) (m/v) 37.979 9 38.144 g 20.00% (m/v) 38.312 9 Unknown % Sucrose Solution 37.677 g Commercial Beverage 38.064 g