Week 32 – Comparing Amounts

For our final section of this week’s lesson, we need to connect back with the theme of toxicity.  Simply stated, too much of anything can be toxic.  For example, caffeine is toxic (LD50 = 150 mg/kg).  One cup of strong coffee has about 150 mg of caffeine.  Two cups of strong coffee would have about 300 mg of caffeine.  Therefore, two cups of coffee (300 mg of caffeine) is more toxic than 1 cup of coffee (1 cup of caffeine).  Thankfully, for most people, it takes a whole lot more than a couple of cups of coffee to be lethal.  For this example, since the LD50 for caffeine is the same as the amount of caffeine per cup of coffee, you can figure out how many cups of coffee it would take to reach the LD50 for you by converting your weight in pounds to mass in kg (weight in pounds divided by 2.2 = mass in kg).  A 180 pound person has a mass of about 82 kg, so drinking 82 cups of coffee would result in a 50% chance of death.

Fun fact: A cup of coffee is nearly 8 ounces of water, and there are about 30 mL per ounce.  Therefore, drinking a cup of coffee means drinking about 240 mL of water.  The LD50 for water is 90 mL/kg.  For that 82 kg person in the coffee example, drinking 7380 mL of water (90 mL/kg x 82 kg) would result in a 50% chance of death.  How many cups of water are in 7380 mL?  Divide 7380 mL by 240 mL / cup and that comes out to 30.75 cups of water.  So for all you coffee haters out there…go easy on your delicious water!  Turns out water is more toxic than coffee.  Sorry.

When comparing substances to determine which is more toxic, the key point is you must convert LD50 values to mol/kg.  When you convert from mass to moles, you remove the impact of molecule size and instead normalize the data on a per molecule basis.  When we ask whether one substance is more toxic than another, we want to be able to compare the toxicity of the molecules, irrespective of the mass of those molecules.  In Lesson 79 of the textbook, there is a table comparing the sweeteners fructose (fruit sugar) and aspartame (artificial sweetener).  Fructose is commonly found in regular soda, while aspartame is found in some diet sodas.  The molecules have different molecular formulas, which means they have different molar masses.  Converting the LD50 values to mol/kg shows that aspartame is more toxic than fructose.  That’s an important finding, but doesn’t address the real-world question: how much of each sweetener is added to regular (fructose) or diet (aspartame) soda?  How many cans of regular or diet soda does it take to reach the LD50 for fructose and aspartame?  Read through Lesson 79 in the textbook and find out – the answer might surprise you!

For your final piece of chemistry work this week, complete the Week 32 Exit Task.