Chapter 2 Homework

Measurements and Calculations

2.1 Scientific Method

1. What is the scientific method?

2. Which of the following are quantitative?

a) the liquid floats on water

b) the metal is malleable

c) the liquid has a temperature of 55.6^{o}C

3. How do hypotheses and theories differ?

4. How are models related to theories and hypotheses?

5. What are the components of the system in the graduated cylinder shown on page 38?

6. How does quantitative information differ from qualitative information?

7. Define hypothesis.

2.2 Units of Measurement

1. Why are standards needed for measured quantities?

2. Label each of the following measurements by the quantity each represents. For instance, a measurement of 10/6 kg/m^{3} represents density.

a) 5.0 g/mL

b) 37 s

c) 47 J

d) 39.56 g

e) 25.3 cm^{3}

f) 325 ms

g) 500 m^{2}

h) 30.23 mL

i) 2.7 mg

j) 0.005 L

3. Convert the following showing all work, conversion factors and cancellation of units:

a) 10.5 g into kg (0.0105 kg ) soln

b) 1.57 km into m ( 1570 m ) soln

c) 3.54 microg into g ( 0.000 003 54 g ) soln

d) 3.5 mol into micromol ( 3 500 000 micromol ) soln

e) 1.2 L into mL ( 1200 mL ) soln

f) 548.6 mL into cm3 ( 548.6 cm^{3} ) soln

4. Write the conversion factors to represent the following equalities:

a) 1 in = 2.54 cm

b) 1 microg = 0.000 001g

c) 1 Mm = 1 000 000 m

5. For each of the following show given information, conversion factors, set up, unit cancellation and the answer boxed.

a) What is the density of an 84.7 g sample of an unknown substance if the sample occupies 49.6 cm^{3}? (1.71 g/cm^{3}) soln

b) What volume would be occupies by 7.75 g of this same substance? ( 4.53 cm^{3}) soln

6. a) Express 16.45 m in cm showing given information, conversion factors, set up, unit cancellation and the answer boxed. soln

b) Express 16.45 cm in km given information, conversion factors, set up, unit cancellation and the answer boxed. soln

7. Express the mass of 0.014 mg in g, showing given information, conversion factors, set up, unit cancellation and the answer boxed. soln

8. Define conversion factor.

9. A sample of a substance that has a density of 0.824 g/mL has a mass of 0.451 g. Calculate the volume of the sample, showing given information, conversion factors, set up, unit cancellation and the answer boxed. ( 0.547 mL ) soln

10. Convert 882 microg to g showing given information, conversion factors, set up, unit cancellation and the answer boxed. ( 8.82 x 10^{-4} g ) soln

11. Convert 92.25 m to km showing given information, conversion factors, set up, unit cancellation and the answer boxed. ( 9.225 x 10^{-2} km ) soln

12. Convert 9.225 x 10^{-2} km to cm showing given information, conversion factors, set up, unit cancellation and the answer boxed. ( 9.225 x 10^{3} cm ) soln

2.3 Using Scientific Measurements

1. The density of copper is listed as 8.94 g/cm^{3}. Two students each make three density determinations of samples of the substances. Student A's results are 7.3 g/mL, 9.4 g/mL, and 8.3 g/mL. Student B's results are 8.4 g/cm^{3}, 8.8 g/cm^{3}, and 8.0 g/cm^{3}. Compare the two sets of results in terms of precision and accuracy.

2. How many significant figures are there in each of the following measured values and circle each significant figure in each measurement: soln

a) 6.002 cm

b) 0.0020 m

c) 10.0500 g

d) 7000 kg

e) 7000. kg

3. Round 2.6765 to two significant figures. soln

4. Carry out the following calculations using the rules of significant figures:

a) 52.13 g + 1.7502 g soln

b) 12 m x 6.41 m soln

c) 16.25 g / 5.1442 mL soln

5. Perform the following operations. Express each answer in scientific notation.

a) (1.54 x 10^{-2} g) + (2.86 x 10^{-1} g) soln

b) (7.023 x 10^{9} g) - (6.62 x 10^{7} g) soln

c) (8.99 x 10^{-4} m) x (3.57 x 10^{4} m) soln

d) (2.17 x 10^{-3} g) / (5.022 x 10^{4} mL) soln

6. Write the following numbers in scientific notation: soln

a) 560 000

b) 33 400

c) 0.000 4120

7. A student measures the mass of a beaker filled with corn oil. The mass reading averages 215.6 g. The mass of the beaker is 110.4 g. Show given information, all work and your answer boxed. soln

a) What is the mass of the corn oil?

b) What is the density of the corn oil if its volume is 114 cm3?

8. Calculate the mass of a sample of gold that occupies 5.0 x 10^{-3} cm^{3}. The density of gold is 19.3 g/cm^{3}. Show given information, all work and your answer boxed. soln

9. a) What is the difference between a graph representing data that are directly proportional and a graph of data that are inversely proportional?

b) Sketch each graph on a set of axes.

10. Contrast accuracy and precision.

11. a) Write the equation that is used to calculate percent error.

b) Under what conditions will percent error be negative?

12. What is meant by a mass measurement expressed in this form: 4.6 g +/- 0.2 g?

13. Round each of the following measurements to the number of significant figures indicated:

a) 67.029 g to three significant figures

b) 0.15 L to one significant figure

c) 52.800 5 mg to five significant figures

d) 3.174 97 mol to three significant figures

14. State the rules governing the number of significant figures that result from each of the following operations:

a) addition and subtraction

b) multiplication and division

15. What is the general form for writing numbers in scientific notation.

16. a) State the general equation for quantities that are directly proportional.

b) For two directly proportional quantities, what happens to one variable when the other increases?

17. a) State the general equation for quantities that are inversely proportional.

b) For two inversely proportional quantities, what happens to one variable when the other increases?

18. What is the volume, in cubic meters, of a rectangular solid that is 0.25 m long, 6.1 m wide, and 4.9 m high?

19. A student measures the mass of a sample as 9.67 g. Calculate the percent error, given that the correct mass is 9.82 g. Show given information, formula, plug into formula, unit cancellation and answer boxed.

20. A handbook gives the density of calcium as 1.54 g/cm^{3}. What is the percent error of a density calculation of 1.25 g/cm^{3} based on lab measurements? Show given information, formula, plug into formula, unit cancellation and answer boxed.

21. The following numbers are in scientific notation. Write them in ordinary notation.

a) 7.050 x 10^{-3} g

b) 4.000 05 x 10^{7} mg

c) 2.350 0 x 10^{4} mL