How sweet Is It?

Introduction

The density of a sample is defined as

density = (mass of sample)/(volume of sample)

The density of an aqueous solution at constant temperature depends upon the concentration and nature of the solute. For example, increasing the concentration of a sucrose-water solution causes the density to increase, whereas an increase in the concentration of an ethyl alcohol-water solution results in a decrease in density. This connection between density and concentration is used in the wine industry to determine the concentration of sugar in grape juice. The purpose of today’s experiment is to determine the concentration of sugar in several commercial drinks from measurements of their densities.

In this experiment, the measurement of a physical property, the density, is being used to determine the sample concentration. The first step in the procedure is to establish a relationship between the measured property and the concentration. This is accomplished, in this case, by preparing several sucrose -water solutions of known concentration , measuring their densities, and preparing a graph of density versus concentration. Such a graph, illustrated in Figure 1, below, is called a calibration curve.

Figure 1: calibration curve

The calibration curve can now be used to determine the sugar concentration of an unknown solution such as a soft drink. Suppose that you find that the density of a soda pop is 1.016 g/mL. What is the concentration of sugar? From the graph in Figure 1, we see that this density corresponds to a concentration of 5.04 mass percent. In constructing a calibration curve it is necessary to draw the "best" straight line through the data points.This is accomplished mathematically by the method of Linear regression. A linear regression analysis of the calibration data points results in an equation of the best straight line through the points.The equation has the form

where m and b are the slope and intercept, respectively. Equation (1) can then be used to plot the best line through the points and the density of the unknown solution read directly from the graph. An alternative procedure, which is the one used in this experiment, is to substitute the density of the unknown solution into the regression equation, (equation (1)), and calculate the percent sugar. You will be using the Excel spreadsheet program to perform the regression analysis of your data. The instructions are provided in the "Conclusion" section below.

A potential source of error in this procedure is that the calibration curve is constructed using solutions of pure sugar in water, whereas a soft drink contains,in addition to sugar, other solutes such as dyes, flavorings and preservatives. The assumption in this analysis is that these other solutes are present in much lower concentrations than the sugar and have a negligible effect on the density. The validity of this assumption can be checked by measuring the density of the "normal", sugar-containing version of a particular soft drink and its "diet" version. The diet version differs from the normal version only in the fact that it contains an artificial sweetener rather than sugar. Artificial sweeteners such as saccharin and aspartame, are many times sweeter than sucrose and fructose, the sugars commonly found in soft drinks. See the table below:

Therefore, in a diet soda containing aspartame the percentage aspartame will be less than one-one hundredth the percentage of sucrose in the normal soda. The effect of the other solutes on the density can be determined by comparing the density of the diet soda with that of water.

Procedure

Calibration curve: The sugar to be used in the standard solutions is table sugar or sucrose. Prepare about 50 mL each of at least five standard aqueous sugar solutions in the range 0 to 17 percent by mass sugar. Do this by weighing the appropriate amounts of sugar and water in beakers. Weigh to 0.001 g. Thoroughly stir each solution to insure that the sugar is dissolved. Use a class A transfer pipet to transfer 10.00 mL of each solution to a clean, dry, preweighed beaker. Consult your instructor about the proper use of the pipet. Weigh the beaker plus solution and calculate the solution density. Since density depends on temperature you should measure and record the temperature of each sample.

Analysis of Drinks: Select two commercial, sugar-containing drinks, and measure the density of each one using the procedure used for the calibration curve. If the drink is carbonated it will be necessary to degas the solution by stirring it with a magnetic stirrer until the evolution of bubbles stops. Make at least four complete measurements of the density of each drink. Note the temperature of each sample. It should be the same as that of the standard solutions used to construct the calibration curve.

Repeat the density measurement with the diet version of one of the drinks analyzed above.

Conclusion

1. Prepare a calibration curve of density plotted versus mass percent sugar using Excel. For a review of how to prepare a graph using Excel, click here.

2. Perform a regression analysis of the calibration data, again using Excel, and obtain the equation of the best straight line through the calibration data points.

1. Calculate the average density of each drink. If any of your density values appears to be questionable you may be justified in rejecting it, and calculating the average from the remaining values. To decide whether or not a suspicious value should be rejected use the Q test. A measure of the precision of your measurements is the standard deviation. Calculate the standard deviation of each of your three density values.

2. Substitute the average density of each drink into the regression equation to calculate the percentage sugar.

3. Do the other solutes- dyes, flavorings and preservatives, etc.- have a significant effect on the density of a soft drink? Please explain.