Have you ever wondered why a can of Diet Coke floats in water, while a can of regular Coca-Cola sinks? This seemingly simple observation is a fantastic demonstration of density differences and Archimedes' principle. This article delves into the science behind this phenomenon, exploring the factors that influence the density of these popular beverages.
Archimedes' Principle and Buoyancy
The foundation of understanding why objects float or sink lies in Archimedes' principle. This principle states that a body wholly or partly immersed in a fluid experiences an upward force, known as the buoyant force. This buoyant force is equal to the weight of the fluid displaced by the body.
Whether an object floats or sinks depends on the relationship between gravity and the buoyant force. If the immersed object is denser than the fluid, the force of gravity exceeds the buoyant force, causing the object to sink. Conversely, if the object is less dense than the fluid, the buoyant force is greater than gravity, and the object floats. The object will float to a level where the buoyant force balances gravity.
The Density Difference: Sugar vs. Aspartame
The key to the Diet Coke and regular Coke mystery lies in their different sweetening agents. Regular Coca-Cola contains a significant amount of sugar, typically around 39 grams per 355 ml serving. Diet Coke, on the other hand, uses aspartame, an artificial sweetener, instead of sugar.
Aspartame, commonly known as Nutrasweet or Equal, is intensely sweeter than sugar. As a result, a much smaller mass of aspartame is needed to achieve the desired level of sweetness in Diet Coke compared to the amount of sugar in regular Coke. This difference in mass significantly impacts the overall density of the two beverages.
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Real sugar has a high molecular density. In other words you can think of sugar molecules as being thickly packed together. This also means sugar molecules themselves will be relatively heavy, even when dissolved in solution.
Quantifying the Density
To understand the density difference more concretely, let's consider some measurements and calculations:
Regular Coke: A can of regular Coke contains approximately 39 g of sugar in 355 ml of soda. The can itself weighs about 13 g. The 39 g of sugar in 355 ml Coke is about 11%. According to the tables in the 51st edition of the CRC Handbook of Chemistry and Physics, an 11% solution of either fructose or sucrose has a density of slightly greater than 1.04 g/ml (1.045 for fructose and 1.044 for sucrose). We may reasonably expect that the sugars in Coke should bring its density near this. If we use a density of 1.045 g/ml for the Coke, 355 ml has a mass of 371 g. Adding 13 g for the can brings this to 384 g, for an overall density of 1.01 g/ml, enough to sink the can. (Any mass over about 380 g will sink the can, as noted above.)
Diet Coke: Diet Coke uses a much smaller mass of aspertaine (Nutrasweet/Equal) to flavor the diet soda. Our own rough experiment-weighing different volumes of liquid in a graduated cylinder-gives an average density of 0.911 g/mL for Diet Coke, and 1.026 g/mL for regular Coke. The can of Diet Coke shown above has a mass of about 370 g, as does a second spare can. Its overall density is 370 g/380 cm3, or 0.97 g/cm3.
These measurements demonstrate that regular Coke has a higher density than Diet Coke due to the presence of a significant amount of sugar. The density of water is approximately 1.0 g/mL. Since the density of regular Coke is greater than 1.0 g/mL, it sinks. Conversely, since the density of Diet Coke is less than 1.0 g/mL, it floats.
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Factors Affecting Density
Several factors can influence the density of soda cans, leading to variations in whether they float or sink:
- Sugar Concentration: The amount of sugar in regular Coke can vary slightly, affecting its density.
- Can Material: The mass of the aluminum can itself can vary slightly (the ones I measured were somewhere between 12 and 13 g).
- Volume Delivered: There is some variation in either the density of the Coca-Cola itself, or the volume delivered to each can.
- Dissolved Carbon Dioxide: Dissolved carbon dioxide, in both Diet and regular Coke, probably also changes the density.
- Temperature: The temperature of the water in which the cans are placed can also affect their buoyancy.
Demonstrating the Density Difference
The floating Diet Coke and sinking regular Coke phenomenon makes for a dramatic display of density differences. Here's how you can easily demonstrate it:
- Gather Materials: You'll need a tank of water, a can of Diet Coke, and a can of regular Coca-Cola.
- Setting it up: Use the smallest available tank. If unopened cans are not already in the Prep Room, they can be procured from one of the vending machines near the elevators in the basement of the Science Center. Put everything on a small A/V cart near the audience so everyone can see directly. Start with both cans out of the water so that the audience has a chance to predict the outcome. Have towels ready.
- Submerge the Cans: Place both unopened cans of soda in a large container of water. Turn the can sideways to make certain no air bubbles are trapped beneath the soda can.
- Observe: You'll find the can of Diet Coke rises to the top, while the Classic Coke stays sunk.
Fooling the Audience
It is fairly easy to fool the audience into thinking that both float on their own. The bottoms of each can are concave, so if one holds the Coke can perfectly upright when lowering it into the tank, enough air can be trapped under the can to make it buoyant. To debunk the prank, give the can a slight nudge and the air bubble will surface.
Manipulating Density with Salt
You can further enhance the demonstration by manipulating the density of the water. By adding salt to the tank, you can increase the density of the water (which is now salt water). A 1.5% (wt/wt) salt solution has a density of 1.0107 g/cm3. For the 15-liter tank, this would be approximately 225 g of salt. So any salt concentration greater than this should be enough to raise the can of regular Coke. To be safe, the beaker contains about 275 grams of salt, which is more than enough to raise the heaviest Coke can listed above.As the dissolved salt raises the density of the water, the regular Coke can will rise to the top of the water. little stirring may bring about the change.
Quantitative Analysis
An analysis of whether an unopened can will float or sink can be made quantitatively. The entire can includes the aluminum can itself, the beverage contained in the can, and the gas in the headspace of the soda. Each contributes to the overall density.Finding the volume of the unopened can is a bit trickier. The total mass of the unopened can is easy enough to find: just place the unopened can on a balance!
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Vi is the sum of the beverage volume and the gas headspace in the enclosed can. can be estimated by first finding the mass of water (mw) required to completely fill the empty space in the can. It is possible to find Vcan in a similar manner. First, the mass of the completely emptied can (mcan) is found.