Chapter 2

Write two conversion factors that express the relationship between: (a) Grams and kilograms, using 1 and 1000 (b) Kilograms and grams, using 1 and \(0.001\) (c) Yards and feet (d) Meters and centimeters, using 1 and 100 (e) Meters and centimeters, using 1 and \(0.01\)

The recommended tire pressure in a bicycle is 125 pounds \(/ \mathrm{in}^{2}\). What is this tire pressure in atmospheres? \(\left(1 \mathrm{~atm}=14.70\right.\) pounds \(\left./ \mathrm{in} .^{2}\right)\)

Do the following calculations and express each answer to the correct number of significant figures. (All values are measurements.) (a) \(\frac{5.03+7.2}{0.003}\) (b) \(\frac{8.93 \times 0.054}{1.32}\) (c) \((6.23 \times 0.042)+9.86\)

You overhear a classmate telling another student that \(1 \mathrm{ft}\) equals \(12 \pm 0.5 \mathrm{in}\). Is this statement correct or incorrect? Why?

Indicate the correct number of significant figures for each answer, given that all values are measurements: (a) \(\left(6.350 \times 10^{-8}\right) \times(0.0080)\) (b) \(\left(5.30 \times 10^{2}\right)+\left(22.1 \times 10^{2}\right)\) (c) \(\left(5.830 \times 10^{2}\right)+\left(22.100 \times 10^{2}\right)\) (d) \(\frac{100.0 \times 0.1500}{58.443}\) (e) \(\frac{100.0 \times 0.15}{58.4}\)

If 1 U.S. dollar is worth \(0.690\) English pounds, how many U.S. dollars are needed to purchase an item that costs 350 pounds?

The density of water at \(4.00^{\circ} \mathrm{C}\) is \(1.00 \mathrm{~g} / \mathrm{mL}\). The density of ice at \(0{ }^{\circ} \mathrm{C}\) is \(0.917 \mathrm{~g} / \mathrm{mL}\). Water is different from most other substances in that the solid phase (ice) is less dense than the liquid phase. Explain why this characteristic makes ice fishing possible.

How many significant figures are there in each number: (a) \(5.300 \times 10^{-2}\) (b) \(3.2 \times 10^{5}\) (c) \(0.00890 \times 10^{-4}\) (d) \(7.9600000 \times 10^{10}\) (e) \(8.030 \times 10^{21}\)

The speed limit on some interstate highways is 70 miles \(/ \mathrm{h}\). What is this speed limit in (a) kilometers per hour, (b) kilometers per second, (c) meters per hour, (d) meters per second? \((1\) mile \(=1.61 \mathrm{~km}\) )

Explain what effect compressing a gas has on the density of the gas.

Calculate the amount of heat energy in joules required to heat \(50.0 \mathrm{~g}\) of each substance from \(25.0^{\circ} \mathrm{C}\) to \(37.0^{\circ} \mathrm{C}\). (specific heats shown in parentheses): (a) Iron \(\left(0.449 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\) (b) Aluminum (0.901 J/g \(\cdot{ }^{\circ} \mathrm{C}\) ) (c) Mercury \(\left(0.14 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\) (d) Water \(\left(4.18 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\)

Shooters \(\mathrm{A}\) and \(\mathrm{B}\) each shoot three arrows at their target, aiming for a bull's-eye. Which shooter is more precise? Which shooter is more accurate? Explain.

A rock is experimentally determined to be \(3.5\) billion years old, with an uncertainty of plus on minus 100,000 years. Write the age of this rock in scientific notation.

A microscopic particle is measured and found to have a \(40.2\) micron diameter. What is its diameter in meters? What is its diameter in nanometers?

\(10.6 \mathrm{~g}\) of a substance was burned in an insulated calorimeter that contained \(1.00 \times 10^{4} \mathrm{~g}\) of water and a bomb made of \(9.00 \times 10^{1} \mathrm{~g}\) of aluminum. The initial temperature inside the calorimeter was \(25.0^{\circ} \mathrm{C}\). After the burning, the temperature inside the calorimeter was \(45.0^{\circ} \mathrm{C}\). How many kilojoules per gram of energy is released upon burning this substance?

A student uses a digital balance to determine the mass of an object. Its digital display reads \(2.635 \mathrm{~g}\). He keeps looking at the balance and it stays fixed at \(2.635 \mathrm{~g}\) for half an hour. He then states, "The mass of the object is \(2.635 \mathrm{~g}\) exactly. There is no uncertainty in this measurement because the last digit '5' stayed constant and did not change over time." Is he right? Is the mass of the object exactly known with no uncertainty? Explain.

Without doing any numerical calculations, determine which would have the smallest volume: (a) \(50 \mathrm{~g}\) of water (density \(=1.0 \mathrm{~g} / \mathrm{mL}\) ) (b) \(50 \mathrm{~g}\) of salt water (density \(=2.3 \mathrm{~g} / \mathrm{mL}\) ) (c) \(50 \mathrm{~g}\) of mercury (density \(=13.6 \mathrm{~g} / \mathrm{mL}\) ) (d) \(50 \mathrm{~g}\) of alcohol (density \(=0.89 \mathrm{~g} / \mathrm{mL}\) ) Explain your reasoning.

A physician has ordered \(325 \mathrm{mg}\) of atropine to be given to a patient intramuscularly. If atropine were available as a solution that contained \(5000 \mu\) \(\mathrm{g} / \mathrm{mL}\), how many milliliters would you need to give the patient?