Spud Lite?

"Spud Lite", the advertising poster said, "25% less carbs", followed in fine print by "than other potatoes".
"How strange", I thought, "I thought you ate potatoes for their carbohydrate (carbs) content so why would you want a potato with less carbohydrate?"
But then I started thinking about what this meant in terms of the chemical composition of the potato. If it contains 25% less carbohydrate, then surely that means something else must have been increased or added? Or are you just getting less potato for your money?

Typically, a traditional potato has the following approximate composition:

nutrient	% by mass
water	79
carbohydrate	17.5
protein	2
fat	0.1

 That is, 100 g of traditional potato contains about 79 g of water, 17.5 g of carbohydrate, 2 g of protein and 0.1 g of fat.

One way to reduce the percentage of carbohydrate in a potato would be to reduce the density of the potato.
If 100 g of a traditional potato had a volume of 92 mL, then the density of the potato would be 1.09 g/mL. 1 mL of traditional potato has a mass of 1.09 g and contains 17.5% by mass (0.19 g) of carbohydrate.
If "spud lite" has a lower density of potato "flesh", say 0.8 g/mL, then 1 mL of "spud lite" has a mass of 0.8 g and contains 17.5% by mass (0.14 g) of carbohydrate.
If we then compare equal volumes (sizes) of potatoes, say 1 mL of traditional potato and 1 mL of "spud lite" we find that "spud lite" contains 100 x (0.19 - 0.14)/0.19 = 26% less carbohydrate (by volume!).
But, if the density of "spud lite" is less, the % by mass composition remains the same, that is, for every 100 g of potato (traditional or "spud lite") there will be 17.5 g of carbohydrate (but the "spud lite" potato will be a bigger potato for your 100 g).

The nutrition label on a packet of "spud lite" potatoes gives the following masses per 100 g of potato:

• fat < 0.1 g
• protein 1.4 g
• carbohydrate: 8.9 g
• sugars: 1.1 g
• dietary fibre:  1.4 g

So, the total carbohydrate content is 8.9 + 1.1 + 1.4 = 11.4 g
(assuming the dietary fibre is cellulose which is also a carbohydrate).
This means that the actual mass of carbohydrate per 100 g of potato has been decreased. That is, "spud lites" are not just less dense than traditional potatoes.

 Another way to decrease the proportion of carbohydrate in your potatoes would be to increase their water content.
Imagine you have 100 g of traditional potato. This potato is made up of 79 g of water and 17.5 g of carbohydrate.
"Spud lite" contains 11.4 g of carbohydrate.

If all the lost mass of carbohydrate in the "spud lite" (17.5 - 11.4 = 6.1 g) was present as water, then the mass of water in "spud lite" = 6.1 + 79 = 85.1 g

And you, the consumer, is just paying for additional water in your potato!

Further Reading
 Experimental Design

 Carbohydrates
Proteins
Lipids (fats and oils) 
Percentage Composition
Density 

Suggested Study Questions:

1. Design an experiment to test the hypothesis that "spud lite" potatoes have a lower density than traditional potatoes.
2. Design an experiment to test the hypothesis that "spud lite" potatoes have a greater percentage by mass of water than traditional potatoes.
3.  For each serving of traditional potato given below, calculate the mass of carbohydrate consumed:
• 25 g of potato
• 75 g of potato
• 135 g of potato
4. Calculate the mass of "spud lite" you would have to consume in order to obtain
   • 1 g of carbohydrate
   • 7 g of carbohydrate
   • 21 g of carbohydrate
5. The density of potato changes as the potato ages on the shelf. The table below shows the results of an experiment in which the mass and volume of the same potato is measured and recorded every 3 days. Calculate the density of the potato on each day.

   Day	Mass (g)	volume (mL)
   1	142	130
   4	140	129
   7	138	128

6. Consider the results of the experiment above. Describe any trends that you see in the data and suggest reasons for these trends.
7. Explain what chemists mean when they refer to "carbohydrates".
8. The nutrition label on "spud lites" lists the mass of carbohydrate, sugars and dietary fibre separately. What do you think the "carbohydrate" is on this label?
9. Add together the percent by mass of all the components listed for a traditional potato.Suggest reasons for why the total percentage is less than 100%.
10. Potatoes are usually classified as high on the glycemic index (GI). What does this mean?