Regents Chemistry - Commack Schools



Pre-IB Chemistry Dr. Kramer

Chapter 3 ________________________

SCIENTIFIC MEASUREMENT

Define measurement (hint, a measurement has two parts; we’re only dealing with one to start):

Scientific Notation

How many atoms are in one gram of hydrogen?

602,000,000,000,000,000,000,000!!!!!!

So, how can we easily write this?

One atom of gold weighs 0.000 000 000 000 000 000 000 327 grams. Write this in scientific notation:

Rule: A x 10b A is ALWAYS:

Some examples:

3,000,000,000

6,780

35,760

0.0001345

0.00256

Let’s go the other way!

1.08 x 105

3.4 x 10-3

7.2387 x 103

9.8 x 1011

3.143 x 10-7

Brief discussion of inputting numbers in scientific notation into graphing calculators: Use of EE button.

Try these:

(2 x 105)(3 x 10-4)

(3.6 x 1034)/(4.2 x 107)

Now, let’s discuss how good our measurements are.

Accuracy and Precision

Precise:

Accurate:

Error:

Percent Error:

Water is supposed to boil at 100.00 oC. The thermometer that Jenny is using reads 99.00 oC, and the water is boiling. What is the error in the thermometer’s reading? What is the percent error?

Ricki weighs 60.9 kg on scale #1, and 58.6 on scale #2. If scale #2 is found to be correctly calibrated, what is the error and percent error of scale #1?

Significant Figures (this is a biggie…pay attention to this one!!)

Demo with electric balance:

How many decimal places do you see? Is there anything on the balance to tell you how accurate it is?

If we had an electric balance that had 4 decimal places, but it was so bouncy that the last two digits were always changing, how confident would we be in the number? Which decimal places would you believe?

Rule for Significant Figures

Take the number of digits and/or decimal places you are sure about, and throw in a somewhat ‘guessed’ number, this is your last significant digit. So, how many significant figures (digits) are there in the measurement on the bouncy balance?

Always assume that a number your given in a problem has already been evaluated to give you the right number of digits (i.e. all of the certain ones plus one ‘guessed’ digit)

What does count as a significant digit?

What does not count as a significant digit?

OK. Let’s try this out.

As a class, let’s do these exercises. How many significant digits are there in each of these numbers?

4 4.2 23.562 1.08 x 106

4.0005 2.0 4.87 x 10-5 5 x 102045

OK…let’s get a little tricky

How many sig figs in 100? What about 40?

What’s the problem?

How do we clarify this? How can we tell? How can a measurement tell us?

OK…now that you are armed, try these trickier ones!

300. 100 4.0 x 102 400

300.0 1000 1.0 x 103 5270

5270. 43210 43210.0 76000.

Excellent Work!! (

Adding and Subtracting Measurements

How do we decide how many significant figures are in the result of calculations involving measurements? Let’s start with addition and subtraction.

Rule:

Let’s try these as a class, then.

4 + 2 =

4.0 + 2 =

4.0 + 2.0 =

4.00 - 2.0 =

4.00 + 12.0 =

Individually:

5 + 4.00 =

3.0 + 2.52 =

7.53 – 6.9 =

Multiplication and Division

What if we need to multiply to measurements together (remember the formula for area?)?

Rule:

Class Examples:

4.0 x 3.00 =

2.00 x 100 =

2.00 x 100. =

50.0/25 =

(1.0 x 103) x (4.3 x 108) =

(3.01 x 10-4)(2.000 x 107) =

In Pairs (express answer in scientific notation):

(4.65 x 1010)/(2.59 x 107) =

3.99/100. =

3.65 – (3.75)(4.2)

9 x 80 =

9 x 80. =

4.00 x 55 =

CHEMICAL BINGO

Questions (answer with proper significant figures!!):

1. 4 x 3.0

2. 3 + 12

3. 3 x 12

4. (4.0 x 106)(3.0 x 10-2)

5. (4.0 x 106)(2 x 106)

6. 3.05 + 4.375

7. 4.18 + 7.820

8. 3.7 x 190

9. 3 + 100.0

10. 4.0 + 100.

11. 4.0 x 100.

12. (4.0)(1.0 x 103)

13. 12.75 – 3.75

14. 4.5 x 2.0

15. 1.0 + (1.00 x 4.0)

Answers:

1. 7.0 x 102

2. 103

3. 1.2 x 105

4. 9.0

5. 5.0

6. 4.0 x 103

7. 15

8. 104

9. 8 x 1012

10. 10

11. 40

12. 4.0 x 102

13. 9.00

14. 12.00

15. 7.43

We’ve discussed a lot about measurements and even done a lab with them. However, we have not talked a lot about units. So…

Fill in this table (first two columns only)

|Type |Examples |SI Unit |

| | | |

|Mass | | |

| | | |

|Volume | | |

| | | |

|Time | | |

| | | |

|Distance | | |

| | | |

Metric units: prefixes

tera |giga |mega |kilo |hecto |deca | |deci |centi |milli |micro |nano | | | | | | | |1 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

How many millimeters in 1 meter?

How many millimeters in 3.5 cm?

How many kiloliters in 25 liters?

How can we do the examples above using the factor label method (the art of multiplying by 1)?

See cancellation of labels worksheet handed out separately.

Uncertainties in Calculations

Sig figs are nice and everything, but they’re kind of weird. Let’s look at our original example of the centigram balance reading we used at the beginning of our sign fig talk.

What was that reading?

OK. So, if you had to express an uncertainty of that measurement, you would need to know the range of possible values.

Which digit in this reading has uncertainty in it?

How much do you think it could possibly be off by?

So, how could we express our reading of 3.00 g, showing the uncertainty?

Great! What about an analog instrument like a graduated cylinder? How well do you think you could read it?

OK. So, the rule for uncertainties in analog instruments is…

And the rule for digital instruments is…

Adding and Subtracting Measurements With Uncertainties

So, there may be situations in which we’d like to manipulate measurements, like in a perimeter calculation, or a final-initial calculation in a graduated cylinder or burette (see demo). How do we calculate the uncertainty in the answer?

Let’s try one:

What is the volume of water placed in a beaker if the initial reading in a burette was 3.70 ± 0.05 mL and the final reading was 13.20 ± 0.05 mL?

Now you:

Find the perimeter of a rectangle with sides measuring 14.7 ± 0.1 m and 4.5 ± 0.3 m.

One more example: How much longer is a 5.40 ± 0.01 km run than a 2.47 ± 0.02 km run?

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download