1. BASIC GEOMETRY

 (0 points)How would you calculate:

1. The area of a circle2. The volume of a sphere3. The volume of a cube

Consider your answers, then click the Show Answer box to compare.

Area of a circle with radius  r :  A=πr2

Volume of a sphere with radius  r :  V=43πr3

Volume of a cube with side length  l :  V=l3

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2. LOGARITHMIC AND EXPONENTIAL FUNCTIONS

 (13 points possible)

log(100)=

10

2

log(10)=

1.0

1log(1)=

0

log(1/10)=

1

0 -1log(1/100)=

−2

-2

log(105)=

5

5log(10x)=

x

10log(x)=

xln(e)=

1

1

ln(300)=

5.7

5.7log(x)=7

What is x? 10000000

10000000

ex=1

What is x? 0

0e3.5=

33.12

33.12

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3. PERCENT

 (2 points possible)

You decide to make gels using the gelling agent gellan (you will learn more about this later in the course). If you use 2.5 g gellan in 200g water, what is the percentage of gellan in the solution?

2% 12% 1.2%  5%

Dave Arnold (visiting chef in Week 2) decides to make a gel of cranberry juice made with the thickener agar. If the gel has a 1.5% concentration of agar, what is the total amount needed to make 300 g of gel?

2% 4.5g 45g 12gEXPLANATION

The percentage of gellan is 2.5g/200g = 1.2%

The amount of agar needed to make the cranberry gel is 300g x 0.015 =

4.5 g

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4. PH REVIEW

 (10 points possible)What makes something acidic?

A lower pH means something is more:

acidicStatus: unsubmittedLemon juice has a low pH

TrueStatus: unsubmitted

What is the formula for calculating pH from proton concentration? What is the standard unit of [H+]? (Check your answer in the solutions.

How many molecules are there in a mole of molecules?

6.022e+23

If the pH = 4.0 what is the H+ concentration?

0.0001

If the pH = 5.0 what is the H+ concentration?

0.00001

How many-fold more H+ ions are there at pH 4 than pH 5?

10

If the H+ concentration is 10−4.3, what is the pH?

4.3

If the H+ concentration is 10−5.3, what is the pH?

5.3

What is fold difference in H+ ions for H+ concentration of 10−4.3 vs 10−5.3?

10

How many H+ ions are there in a glass of pure water (~0.3L)?

18100000000000000

pH=−log[H+]

The standard unit for concentration is mol/L (abbreviated M).

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5. GRAPHING PRACTICE (0 points)You measure the pH of 1 L of milk very carefully with a pH meter as vinegar is added, and get the following data.

Vinegar added pH

0 mL 6.5

1 mL 5.5

2.7 mL 5.1

7 mL 4.6

19 mL 4.2

50 mL 3.8

Plot pH vs. volume of vinegar added. Is this plot linear?

Plot [H+] vs. volume of vinegar added. Draw the best-fit line and calculate its slope. What is the pH of the vinegar?

(You will need to check your answers in the solutions as they cannot easily be entered here.)

The plot shows that the pH starts to change more slowly as more vinegar

is added. As more vinegar is added, the pH of the mixture will get closer to

the pH of vinegar, but more slowly than it did at first. Since the slope is

changing, this is not a linear plot.

This plot is fit very well by a line with slope 3.2 ⋅ 10 −6  M protons/mL

of vinegar. In other words, the number of moles of protons in our liter of

milk increases by 3.2 ⋅ 10 −6  every time one mL of vinegar is added.

This suggests that the concentration of protons in the vinegar is

3.2 ⋅ 10 −3  M, so the pH of vinegar is about 2.5.