0 WS-R Sig Fig Units Dimensional Analysis Based on Review Chapter - Zumdahl Chemistry Atoms First PDF

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WS-R Significant Figures - the number of significant figures (sig. fig.) is a measure of the degree of uncertainty in a measurement. There is experimental uncertainty in the last significant figure of a measurement. The rules for sig. fig. are provided in the textbook as well as presentations. All non-zero numbers are significant. Zeros between numbers are significant. Zeros to the left of numbers are not significant. Zeros to the right of numbers are significant in the presence of a decimal point.

1. Express each of the following numbers in scientific notation and decide the number of significant figures. Scientific notation Sig. fig. 409.10

_________________________

______

4091.00

_________________________

______

0.004091

_________________________

______

308,000

_________________________

______

30,860

_________________________

______

0.00056030

_________________________

______

Calculations with significant figures: Significant Figure Rules with Same Type of Operations On a series of calculations that only involve multiplication and/or division; 1. Identify exact numbers and measurements. 2. Identify how many significant figures each value has. 3. Determine the number of significant figures in the value with the least number of significant figures. 4. Complete the entire calculation without rounding-off as you go. 5. Round-off the final answer to the same number of significant figures as the value with the least number of significant figures. On a series of calculations that only involve addition and/or subtraction; 1. 2. 3. 4. 5.

Identify exact numbers and measurements. Identify how many decimal places each value has. Determine the number of decimal places in the value with the least number of decimal places. Complete the entire calculation without rounding-off as you go. Round-off the answer to the same number of decimal places as the value with least number of decimal places.

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WS-R Significant Figure Rules with Mixed Operations On a series of calculations that involve multiplication/division and addition/subtraction; 1. Apply PEMDAS rule to complete calculation in steps. Calculate one step at a time. 2. Round-off at the end of a step if the next step involves a different category of operations to the one you performed. If the next step involves the same type of operation you just did, proceed without rounding off. Note: Try to understand the significant figure rules and rounding off methods in terms of error analysis. Questions to ponder: Are the chances of errors compounding higher in calculations with same type of operations or mixed operations? Will rounding-off at each step and rounding-off at the end will make a difference? Additional information (not covered in CHEM 102) Significant Figure Procedure in Logarithmic Calculations 1. Count the number of significant figures in the value given. 2. Calculate the logarithm. 3. In the final answer, keep the same number of decimal places as there were significant figures in the original number. Example 1: log10(6.500×103 ) [four significant figures] = 3.8129133566428… rounds-off to 3.8129 [four decimal places] In acid base calculations it is typical for pH to be reported with one decimal place. This is in keeping with a concentration measurement with a precision at least to one significant figure.

Examples of calculations with significant figures: In multiplication or division, the number of sig. fig. in the final answer has only as many sig. fig. as the value with the smallest number of sig. fig.’s.

(0.46307)( 0.0805) =0.004016430 (63.54 )(0.052 )(2.809) 2 sig. fig. (Deciding factor) Final answer 0.0040 or 4.0 x 10-3 (2 sig. fig.) In addition and subtraction, the answer should be reported to the same number of decimal places as the value with the least number of decimal places.

37.598−36.76 =0.838 2 decimal places (Deciding factor) Final answer 0.84 or 8.4 x 10-1

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WS-R 

Rules of rounding of; o If the number to round-off is 6 or more, add one to the number left of it. o If the number to round-off is 4 or less, keep the number left of it the same. o If the number to round-off is 5;  If there are ‘any’ numbers after 5, treat it as 6  If there are zeroes or no numbers after 5;  Add one to the number left of 5 if the number to the left is odd.  Keep the number left of it the same if the number is even

2. Do the following calculations and express the answers to the correct number of sig. fig. (show intermediate steps)

29.837 −29.241 =¿ 32.064

752.12+ 26.3 =¿ 1.024236842

Dimensional Analysis - This technique can be used to change units (K → oC) and also as an aid in solving problems, by carefully keeping track of units. SI Units and conversion factors are listed in textbook as well as presentation slides. A certain process yields 4.85 x 10-2 g of a chemical product per second. How many kilograms will be produced in five days of continuous reaction?

¿ ¿ 4.85 ×10−2 g /s=¿ ¿

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WS-R

¿ ¿ ¿ ¿ ¿ ¿ ¿ ¿ ¿ ¿ ¿ 5 day (s) 24¿ ¿ ¿ day (s)× ❑ =¿ ❑❑ kg 60¿ ¿¿ hour (s)׿ −2 ¿ s 4.85 ×10 g × ¿ ׿ s ¿¿ min

Finally, determine the number of sig. fig. The first term has 3 sig. fig. All of the other factors are definitions, and have ꝏ sig. fig.’s. Therefore the answer will be limited to 3 sig. fig.’s. In the conversion factors the value of the numerator and denominator are the same; 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day. The final conversion unit illustrates the use of metric prefixes; 1000 grams = 1 kilogram. It is important to know these commonly used prefixes.

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WS-R 3. Fill in the missing information in the following chart. Metrix Prefix

Symbol

Exponent

M −9

10 deci

−6

10 p kilo m

10−2 4. A volume of 520 cm3 is equivalent to: ______________ mL

______________ dL

______________ L

5. Make the following conversions (Express your answer in scientific notation.) a. 0.0024 km to nm

b. 3.5 g/dm3 to mg/mm3

c. 95 yards to cm ( 3 feet in a yard; 2.54 cm in 1 inch)

Work on the following problems, paying attention to sig. fig.’s Page 5 of 6

WS-R

6. You feel a bit feverish and take your temperature with a lab thermometer, marked in degrees kelvin. It reads 310 K. What is your Fahrenheit temperature? [(oF) = 1.8 (oC) + 32o and K = oC +273]

7.

Write down your height.

_____ ft.

_____ in.

Convert it to meters (m.)

8. A child's sandbox is 4.0 feet wide, 4.0 feet long and 9.0 inches deep. If there are, on the average, 55 grains of sand per mm3, how many grains of sand are there in the sandbox?

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