Vitamin C Some people belicve that large doses of vitamin C...

Vitamin C Some people belicve that large doses of vitamin C can cure the common cold. One commercial over-thecounter product consists of $500.0 \mathrm{mg}$ tablets that are 20% mass vitamin C. How many tablets are needed for a $1.00 \mathrm{g}$ dose of vitamin C?

Key Concepts

Proportional Reasoning

This key concept involves setting up and solving proportions, which is necessary to extrapolate the amount of product needed based on a known ratio of active ingredient to the total product quantity.

Dosage Calculation

Dosage calculation is the process of determining the number of product units required to deliver a specified amount of an active ingredient. This involves using the percentage of the active ingredient and the total weight per unit to scale up to the desired dose.

Unit Conversion

This concept involves converting quantities from one unit to another, such as milligrams to grams, which is essential when working with different measurement units in chemical and biological contexts.

Percentage Composition

Understanding percentage composition is crucial when determining the amount of a particular component in a mixture. It allows one to calculate the actual mass of an active ingredient when given the total mass of the product and its percent composition.

Transcript

00:01 Okay, so in this problem, we know that there are, one tablet is 500 .0 milligrams.

00:09 So to write that in a more useful way, maybe, is to say that there are 500 .0 milligrams per one tablet.

00:18 That way we can use this as a conversion factor.

00:21 Additional information that we're given is that the pills are 20 %, 20 % by mass vitamin c, which i'm going to call a vitc.

00:40 Another way to write that is a more useful way is to say 20 % by vitamin c.

00:46 We can write that as a conversion factor by saying that there are 20 milligrams of vitamin c for every 100 milligrams within the tablet.

01:00 So that way we can use these both as conversion factors.

01:04 So then the question is, how many tablets do we need if what we want is 1 .0 grams of vitamin c? that's what we want, and we want to know how many tablets.

01:20 So let's do some conversion factors.

01:23 First of all, we've been working in milligrams, all the given information to milligrams.

01:27 So it would be nice to convert this first one to milligrams.

01:30 So i know one milligram, miligram, there we go, is 10 to the negative third grams.

01:41 Again, there's other ways you can write this.

01:43 This is the way i'm choosing to write it.

01:45 But pick your own.

01:46 Maybe you should come to the same answer.

01:48 Try picking a different conversion factor, see if it comes out the same.

01:51 If it does, that's a good sign.

01:53 It means you're a little bit flexible with the way you do your arithmetic, but it kind of makes sense in your head, hopefully.

01:57 So that gets rid of grams.