Q: You are given a length of $$10\ \mathrm{m}$$ and asked to convert it to decimeters (dm). Which calculation correctly performs this conversion?

$$10\ \mathrm{m} \times \frac{10\ \mathrm{dm}}{1\ \mathrm{m}} = 100\ \mathrm{dm}$$

Q: Convert $$1$$ short ton to kilograms using the provided conversion factor.

$$1\ \text{short ton} = 907.2\ \mathrm{kg}$$

Q: Given the volume of the oceans is $$1.35 \times 10^9$\ \mathrm{km}^3$$, convert this to liters ($$\mathrm{L}) $$using scientific notation.

$$1.35 \times 10$$^{21}$$\ \mathrm{L}$$

Q: Given the current value of gold is $$14 \times 10$$^{15}$$ dollars, what is the value of all the gold in the ocean?

$$14\ \text{Quadrillion dollars}$$

Question 1

Which of the following statements best describes a unit conversion factor?

Accepted Answer

A ratio relating two equivalent quantities, allowing conversion between units without changing the measured value.

Question 2

You are given a length of $$10\ \mathrm{m}$$ and asked to convert it to decimeters (dm). Which calculation correctly performs this conversion?

Accepted Answer

$$10\ \mathrm{m} 	imes \frac{10\ \mathrm{dm}}{1\ \mathrm{m}} = 100\ \mathrm{dm}$$

Question 3

Which of the following is an exact unit conversion factor?

Accepted Answer

$$1\ \mathrm{in} = 2.54\ \mathrm{cm}$$

Question 4

If $$1\ \mathrm{m} = 10\ \mathrm{dm}$$, what is the conversion factor for $$1\ \mathrm{m}^2 to$$ $$\mathrm{dm}^2$$?

Accepted Answer

$$1\ \mathrm{m}^2 = 100\ \mathrm{dm}^2$$

Question 5

A cube with sides of $$1\ \mathrm{m}$$ contains how many $$1\ \mathrm{dm}$$ cubes?

Accepted Answer

$$1000$$

Question 6

Convert $$1$$ short ton to kilograms using the provided conversion factor.

Accepted Answer

$$1\ 	ext{short ton} = 907.2\ \mathrm{kg}$$

Question 7

Given the volume of the oceans is $$1.35 	imes 10^9$\ \mathrm{km}^3$$, convert this to liters ($$\mathrm{L}) $$using scientific notation.

Accepted Answer

$$1.35 	imes 10$$^{21}$$\ \mathrm{L}$$

Question 8

If there is $$1.8 	imes 10$$^{13}$$\ \mathrm{g} of $$gold in the ocean, what is the concentration in $$\mathrm{ng}/\mathrm{mL}$$?

Accepted Answer

$$0.013\ \mathrm{ng}/\mathrm{mL}$$

Question 9

If all the gold in the ocean ($$1.8 	imes 10$$^{13}$$\ \mathrm{g}) $$were formed into a perfect sphere, what would be its radius in meters?

Accepted Answer

$$61\ \mathrm{m}$$

Question 10

Given the current value of gold is $$14 	imes 10$$^{15}$$ dollars, what is the value of all the gold in the ocean?

Accepted Answer

$$14\ 	ext{Quadrillion dollars}$$

Question 11

The density of a hydrogen atom is calculated using its mass ($$1.67 	imes 10$$^{-24}$$\ \mathrm{g}) $$and volume ($$7.2 	imes 10$$^{-24}$$\ \mathrm{cm}^3). $$What does this calculation reveal about atomic structure?

Accepted Answer

Atoms are mostly empty space; most mass is in the nucleus.

Question 12

A sample of sulfur contains isotopes with mass numbers 32, 33, 34, and 36. If $$^{32}\mathrm{S}$$ and $$^{34}\mathrm{S}$$ have abundances of $$79.99\%$$ and $$4.25\%$$ respectively, what is the abundance of $$^{36}\mathrm{S}$$?

Accepted Answer

$$5.01\%$$

Question 13

Which isotope of iron ($$^{54}\mathrm{Fe}$$, $$^{55}\mathrm{Fe}$$, $$^{56}\mathrm{Fe}$$, $$^{57}\mathrm{Fe}) $$has the highest percent abundance in the extraterrestrial sample described?

Accepted Answer

$$^{54}\mathrm{Fe}$$

Question 14

If a neutral $$^{56}\mathrm{Fe}$$ atom is converted to a $$+1$$ cation, does its mass change significantly for most chemical calculations?

Accepted Answer

No, the change is negligible for most chemical calculations.

Question 15

Which of the following best explains why the energy of interaction between two point charges approaches zero as their separation becomes infinite?

Accepted Answer

The electric field lines no longer interact, so the potential energy goes to zero.

Question 16

Using Coulomb's Law, what is the electrostatic potential energy between a proton and an electron separated by $$52.9\ \mathrm{pm}$$? ($$k = 8.99 	imes 10^9$\ \mathrm{N}\cdot\mathrm{m}^2/\mathrm{C}^2$$, $$e = 1.602 	imes 10$$^{-19}$$\ \mathrm{C})$$

Accepted Answer

$$-4.36 	imes 10$$^{-18}$$\ \mathrm{J}$$

Question 17

Which of the following is true about the energy levels predicted by the Bohr model for the hydrogen atom?

Accepted Answer

Energy levels are discrete and become closer together as $$n$$ increases.

Question 18

A cubic unit cell of a metal has an edge length of $$0.3925\ \mathrm{nm}$$ and contains $$4$$ atoms per cell. If the density is $$21.45\ \mathrm{g}/\mathrm{cm}^3$$, what is the molar mass of the metal?

Accepted Answer

$$195\ \mathrm{g}/\mathrm{mol}$$

Dimensional Analysis, Unit Conversions, and Atomic Structure in General Chemistry

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