Question

My cousin was interested in reactions that produce carbon dioxide gas. She wondered if there was some way to predict how much gas a reaction would produce. She did a series of seven experiments and measured the amount of carbon dioxide released by each one. Baking soda (spoons) Calcium chloride (spoons) Carbon dioxide (milliliters) 1 1 800 1 2 1600 1 3 1600 2 1 800 2 2 1600 2 3 2400 3 1 800 Based on my cousin’s experimental results,answer these questions. 1. How many mL of gas would be produced if 3 spoons of baking soda reacted with 3 spoons of calcium chloride? 2. How many mL of gas would be produced if 2 spoons of baking soda reacted with 1.5 spoons of calcium chloride? 3. My cousin wanted to produce exactly 2000 mL of carbon dioxide. How much baking soda and calcium chloride should she use?

Answer 1

1.)2240

2.)1173.33334

3) soda = 3, calcium chloride = 2.625

Explanation:

Baking soda (spoons)

1 - 1 - 1 - 2 - 2 -2 - 3

Calcium chloride (spoons)

1 - 2 - 3 - 1 - 2 - 3 - 1

Carbon dioxide (milliliters)

800 - 1600 - 1600 - 800 - 1600 - 2400 - 800

Modeling the above using a multiple regression technique:

ŷ = ax1 + bx2 + c

Where ŷ is the predicted value

x1 and x2 are the first and second predictor variable.

ŷ = 106.66667X1 + 640X2 - 0

1.) How many mL of gas would be produced if 3 spoons of baking soda reacted with 3 spoons of calcium chloride?

ŷ = 106.66667(3)+ 640(3) - 0

320.00001 + 1920 - 0 = 2240

2.) How many mL of gas would be produced if 2 spoons of baking soda reacted with 1.5 spoons of calcium chloride?

ŷ = 106.66667(2)+ 640(1.5) - 0

213.33334 + 960 + 0 = 1173.33334

C.) To produce 2000mL of gas

It could be achieves a a number of ways

ŷ = 106.66667X1 + 640X2 - 0

For instance if she opts to use 3 spoons of soda

2000 = 106.66667(3) + 640x2

2000 = 320.00001 + 640x2

2000 - 320 = 640x2

x2 = 1680/640

x2 = 2.625 spoons