Chapter 1

Which of these uncertain values has the largest number of significant figures? (a) \(1 / 545 ;\) (b) \(1 / 6.4 \times 10^{-3} ;\) (c) \(1 / 6.50\) (d) \(1 / 1.346 \times 10^{2}\)

Which of these uncertain values have four significant figures? (a) \(0.0592 ;\) (b) \(0.08206 ;\) (c) \(8.314 ;\) (d) 5420 (e) \(5.4 \times 10^{3}\)

Which of these uncertain values have only three significant figures? (a) \(7.02 ;\) (b) \(6.452 ;\) (c) \(6.02 \times 10^{23}\) (d) \(302 ;\) (c) 12.77

Perform each of the following calculations, and express the answer with the correct number of significant figures (only the highlighted values are exact): a. \(0.6274 \times 1.00 \times 10^{3} /\left[2.205 \times(2.54)^{3}\right]=\) b. \(6 \times 10^{-18} \times\left(1.00 \times 10^{3}\right) \times 12=\) c. \((4.00 \times 58.69) /\left(6.02 \times 10^{23} \times 6.84\right)=\) d. \([(26.0 \times 60.0) / 43.53] /\left(1.000 \times 10^{4}\right)=\)

Perform each of the following calculations, and express the answer with the correct number of significant figures (only the highlighted values are exact): a. \([(12 \times 60.0)+55.3] /\left(5.000 \times 10^{3}\right)=\) b. \((2.00 \times 183.9) /\left[\left(6.02 \times 10^{23}\right) \times\left(1.61 \times 10^{-8}\right)^{3}\right]=\) c. \(0.8161 /\left[2.205 \times(2.54)^{3}\right]=\) d. \((9.00 \times 60.0)+(50.0 \times 60.0)+\left(3.00 \times 10^{1}\right)=\)

Diabetes Test Glucose concentrations in the blood above \(110 \mathrm{mg} / \mathrm{dL}\) can be an early indication of several medical conditions, including diabetes. Suppose analyses of a series of blood samples from a patient at risk of diabetes produce these results: \(106,99,109,108,\) and \(105 \mathrm{mg} / \mathrm{dL}\) a. What are the mean and the standard deviation of the data? b. Patients with blood glucose levels above \(120 \mathrm{mg} / \mathrm{dL}\) are considered diabetic. Is this value within the \(95 \%\) confidence interval of these data?

Use Grubbs' test to decide whether the value 3.41 should be considered an outlier in the following data set from analyses of portions of the same sample conducted by six groups of students: \(3.15,3.03,3.09,3.11,3.12,\) and 3.41.

Use Grubbs' test to decide whether any one of the values in this set of replicate measurements should be considered an outlicr: \(61,75,64,65,64,\) and 66.

Can a temperature in "C ever have the same value in "F?

What is meant by an absolute temperature scale?

Radiator Coolant The coolant in an automobile radiator freezes at \(-39^{\circ} \mathrm{C}\) and boils at \(110^{\circ} \mathrm{C} .\) What are these temperatures on the Fahrenheit scale?

Silver and gold melt at \(962^{\circ} \mathrm{C}\) and \(1064^{\circ} \mathrm{C},\) respectively. Convert these two temperatures to the Kelvin scale.

Critical Temperature The discovery of new "high temperature" superconducting materials in the mid-1980s spurred a race to prepare the material with the highest superconducting temperature. The critical temperatures (T_)- the temperatures at which the material becomes superconducting - of three such materials are \(93.0 \mathrm{K}\) \(-250.0^{\circ} \mathrm{C},\) and \(-231.1^{\circ} \mathrm{F} .\) Convert these temperatures into a single temperature scale, and determine which superconductor has the highest \(T_{\mathrm{c}}\) value.

As air is cooled, which gas condenses first: \(\mathrm{N}_{2}, \mathrm{He},\) or \(\mathrm{H}_{2} \mathrm{O} ?\)

Liquid helium boils at \(4.2 \mathrm{K}\). What is the boiling point of He in "C?

Liquid hydrogen boils at \(-253^{\circ} \mathrm{C} .\) What is the boiling point of \(\mathrm{H}_{2}\) on the Kelvin scale?

A person has a fever of \(102.5^{\circ} \mathrm{F}\). What is this temperature in \(^{\circ} \mathrm{C} ?\)

Physiological temperature, or body temperature, is considered to be \(37.0^{\circ} \mathrm{C} .\) What is this temperature in ' \(\mathrm{F} ?\)

Record High The highest temperature ever recorded in the United States is \(134^{\circ} \mathrm{F}\) at Greenland Ranch, Death Valley, CA, on July \(13,1913 .\) What is this temperature on the Celsius and Kelvin scales?

Sodium chloride (NaCl) contains 1.54 g of Cl for every \(1.00 \mathrm{g}\) of \(\mathrm{Na} .\) Which of the following mixtures would react to produce sodium chloride with no Na or Cl left over? a. \(11.0 \mathrm{g}\) of \(\mathrm{Na}\) and \(17.0 \mathrm{g}\) of \(\mathrm{Cl}\) b. \(6.5 \mathrm{g}\) of \(\mathrm{Na}\) and \(10.0 \mathrm{g}\) of \(\mathrm{Cl}\) c. \(6.5 \mathrm{g}\) of \(\mathrm{Na}\) and \(12.0 \mathrm{g}\) of \(\mathrm{Cl}\) d. \(6.5 \mathrm{g}\) of \(\mathrm{Na}\) and \(8.0 \mathrm{g}\) of \(\mathrm{Cl}\)

Gasoline and water do not mix. Regular grade ( 87 octane) gasoline has a lower density \((0.73 \mathrm{g} / \mathrm{mL})\) than water \((1.00 \mathrm{g} / \mathrm{m})\) \(\mathrm{mL}) .\) A \(100 \mathrm{mL}\) graduated cylinder with an inside diameter of \(3.2 \mathrm{cm}\) contains \(34.0 \mathrm{g}\) of gasoline and \(34.0 \mathrm{g}\) of water. What is the combined height of the two liquid layers in the cylinder? The volume of a cylinder is \(\pi r^{2} b,\) where \(r\) is the radius and \(b\) is the height.

Ms. Good son's geology classes are popular because of their end-of-the-year field trips. Some last several days, but all involve exactly eight hours of hiking per day. On one three-day trip the class's average hiking speeds were \(1.6 \mathrm{mi} / \mathrm{h}, 1.4 \mathrm{mi} / \mathrm{h},\) and \(1.7 \mathrm{mi} / \mathrm{h}\) each day. What was the length of their trip in miles and kilometers?

Toothpaste Chemistry Most of the toothpaste sold in the United States contains about 1.00 mg of fluoride per gram of toothpaste. The fluoride compound that is most often used in toothpaste is sodium fluoride, NaF, which is \(45 \%\) fluoride by mass. How many milligrams of NaF are in a typical 8.2 -ounce tube of toothpaste?

Test for HIV Tests called ELISAs (enzyme-linked immunosorbent assays) detect and quantify substances such as HIV antibodies in biological samples. A "sandwich" assay traps the HIV antibody between two other molecules. The trapping event causes a detector molecule to change color. To make a sandwich assay for HIV, you need the following components: one plate to which the molecules are attached; a 0.550 mg sample of the recognition molecule that "recognizes" the HIV antibody; 1.200 mg of the capture molecule that "captures" the HIV antibody in a sandwich; and \(0.450 \mathrm{mg}\) of the detector molecule that produces a visible color when the HIV antibody is captured. You need to make 96 plates for an assay. You are given the following quantitics of material: 100.00 mg of the recognition molecule; 100.00 mg of the capture molecule; and \(50.00 \mathrm{mg}\) of the detector molecule. a. Do you have sufficient material to make 96 plates? b. If you do, how much of each material is left after 96 sandwich assays are assembled? If you do not have sufficient material to make 96 assays, how many assays can you assemble?

Vitamin C Some people belicve that large doses of vitamin C can cure the common cold. One commercial over-thecounter product consists of \(500.0 \mathrm{mg}\) tablets that are 20% mass vitamin C. How many tablets are needed for a \(1.00 \mathrm{g}\) dose of vitamin C?