### introduction

I set this up and critiqued it in this blog before teaching it. The basic idea is that I needed a way into logarithms with my College Algebra students.

### The questions

I have two question videos. I debated which to use in class and ultimately chose the first option below.

#### Option Number 1

In this option, we measure the pH of water and the pH of pure orange juice concentrate.

#### Option Number 2

In this option, we measure the pH of water and the pH of 100 ml of water mixed with 1 ml of orange juice concentrate.

I imagine that Option 1 will prompt questions such as, “What is the pH of regular orange juice?” and “What if we mix it 50-50?”

I imagine that Option 2 will also prompt the question, “What is the pH of the straight-up concentrate?”

In fact, this last question is the one that motivated this project. I was expecting (as will my students) that the difference between the pH of juice and the pH of concentrate will be quite large.

### answers

#### Juice (20 ml)

This actually doesn’t demonstrate juice (see post where I regret this oversight in my data collection). But it’s pretty close. Real OJ should be 3:1 water to concentrate. This is 5:1.

Note: For a number of technical reasons, these observed pH values do not perfectly match the theoretically computed ones.

Nonetheless, the basic operation of the pH scale is wildly different from our gut instincts about measurement. Even the most chemistry savvy among my College Algebra students were off by orders of magnitude on their guesses. The discrepancy tends to prove so surprising that our curiosity is piqued; how could one ml of concentrate change the pH

so much?Even if our computations don’t match the observations in these videos, the results are close enough to explain what is going on, and close enough to motivate further study of logarithms.