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Chapter 10: Problem 14

(a) Are you more likely to see the density of a gas reported in \(\mathrm{g} / \mathrm{mL}, \mathrm{g} / \mathrm{L},\) or \(\mathrm{kg} / \mathrm{cm}^{3} ?(\mathbf{b})\) Which units are appropriate for expressing atmospheric pressures, \(\mathrm{N}, \mathrm{Pa}, \mathrm{atm}, \mathrm{kg} / \mathrm{m}^{2} ?\) (c) Which is most likely to be a gas at room temperature and ordinary atmospheric pressure, \(\mathrm{F}_{2}, \mathrm{Br}_{2}, \mathrm{~K}_{2} \mathrm{O}\)

Short Answer

Expert verified
(a) \(\text{g/L}\). (b) \(\text{Pa}\) or \(\text{atm}\). (c) \(\text{F}_2\).

Step by step solution

01

Understanding Gas Density Units

Gases have densities much lower than liquids and solids, usually expressed in larger volumes. In chemistry, the density of a gas is commonly reported in \(\text{g/L}\) because gases are typically measured in liters at standard conditions. \(\text{g/mL}\) is more common for liquids, and \(\text{kg/cm}^3\) is not practical for gases because it involves very small values.
02

Units for Atmospheric Pressure

Atmospheric pressure is commonly expressed in \(\text{atm}\) and \(\text{Pa}\). The Pascal \((\text{Pa})\) is the SI unit for pressure, while \(\text{atm}\) is useful for practical, everyday measures. \(\text{N}\) (newtons) is a force unit, not a pressure unit, and \(\text{kg/m}^2\) is incorrect because it doesn't have time in the units to constitute pressure.
03

Identifying Gaseous Substance

Under normal conditions (room temperature and atmospheric pressure), \(\text{F}_2\) (Fluorine) is a gas, \(\text{Br}_2\) (Bromine) is a liquid, and \(\text{K}_2\text{O}\) (Potassium Oxide) is a solid. Therefore, \(\text{F}_2\) is the choice most likely to be a gas under these conditions.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atmospheric Pressure Units
Atmospheric pressure is the pressure within the earth's atmosphere. It's important to understand the units used to express atmospheric pressure in order to properly interpret scientific data.
  • The most common units for expressing atmospheric pressure are atmospheric pressure (atm) and Pascal (Pa).
  • Pascals are the SI units for pressure, making it essential for scientific applications. This is because it uses meters, kilograms, and seconds鈥攖he fundamental SI units.
  • Atmosphere (atm) is often used in everyday contexts and practical applications, measuring pressure in terms we can easily observe at sea level.
  • While newtons (N) and kilograms per square meter ( kg/m^2 ) might seem relevant, they lack the necessary time component that pressure units require. This is why they're not typically used to express atmospheric pressure.
Understanding these units can help you grasp how atmospheric conditions affect various phenomena, such as weather patterns and breathing effectiveness.
Gaseous State at Room Temperature
Certain substances are more likely to be in a gaseous state at room temperature and atmospheric pressure. This is important for understanding and predicting how substances behave in different environments.
  • F_2 , or Fluorine, is a diatomic gas under normal conditions, making it a frequent example of a gaseous element at room temperature.
  • Br_2 (Bromine), on the other hand, is a liquid, highlighting how similar elements can exist in different states due to variations in molecular interactions and atomic weight.
  • K_2O (Potassium Oxide) is a solid, demonstrating how compounds, especially ionic ones, tend to be solids due to strong ionic bonds that require higher temperatures to break.
By recognizing patterns in the periodic table and molecular structure, the state of compounds and elements can often be predicted at room temperature. Such knowledge is crucial in chemical reactions and industrial applications.
SI Units for Pressure
The SI unit for pressure is the Pascal (Pa), which is vital for scientific work. Understanding SI units ensures precision and universal understanding in measurements. Here are some important points:
  • The Pascal is defined as one newton per square meter (1 Pa = 1 N/m^2), reflecting how pressure is calculated as force per unit area.
  • SI units enable international consistency, especially in scientific research, as they are universally accepted and standardized.
  • Pascal units can also be converted to kilopascals (kPa) for larger pressures, which is useful in scientific and engineering contexts.
Using SI units, such as Pascals, ensures your measurements are both accurate and universally understood. This fundamental understanding aids in the accurate interpretation and execution of scientific studies, engineering designs, and various technical fields.

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Most popular questions from this chapter

(a) How high in meters must a column of ethanol be to exert a pressure equal to that of a \(100-\mathrm{mm}\) column of mercury? The density of ethanol is \(0.79 \mathrm{~g} / \mathrm{mL}\), whereas that of mercury is \(13.6 \mathrm{~g} / \mathrm{mL}\). (b) What pressure, in atmospheres, is exerted on the body of a diver if she is \(10 \mathrm{~m}\) below the surface of the water when the atmospheric pressure is \(100 \mathrm{kPa}\) ? Assume that the density of the water is \(1.00=1.00 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\). The gravitational constant is \(9.81 \mathrm{~m} / \mathrm{s}^{2}\), and \(1 \mathrm{~Pa}=1 \mathrm{~kg} / \mathrm{ms}^{2}\).

(a) Calculate the number of molecules in a deep breath of air whose volume is \(2.25 \mathrm{~L}\) at body temperature, \(37^{\circ} \mathrm{C},\) and a pressure of \(97.99 \mathrm{kPa} .(\mathbf{b})\) The adult blue whale has a lung capacity of \(5.0 \times 10^{3} \mathrm{~L}\). Calculate the mass of air (assume an average molar mass of \(28.98 \mathrm{~g} / \mathrm{mol}\) ) contained in an adult blue whale's lungs at \(0.0^{\circ} \mathrm{C}\) and \(101.33 \mathrm{kPa}\), assuming the air behaves ideally.

Which of the following statements best explains why a closed balloon filled with helium gas rises in air? (a) Helium is a monatomic gas, whereas nearly all the molecules that make up air, such as nitrogen and oxygen, are diatomic. (b) The average speed of helium atoms is greater than the average speed of air molecules, and the greater speed of collisions with the balloon walls propels the balloon upward. (c) Because the helium atoms are of lower mass than the average air molecule, the helium gas is less dense than air. The mass of the balloon is thus less than the mass of the air displaced by its volume. (d) Because helium has a lower molar mass than the average air molecule, the helium atoms are in faster motion. This means that the temperature of the helium is greater than the air temperature. Hot gases tend to rise.

Nickel carbonyl, \(\mathrm{Ni}(\mathrm{CO})_{4},\) is one of the most toxic substances known. The present maximum allowable concentration in laboratory air during an 8 -hr workday is \(1 \mathrm{ppb}\) (parts per billion) by volume, which means that there is one mole of \(\mathrm{Ni}(\mathrm{CO})_{4}\) for every \(10^{9}\) moles of gas. Assume \(24^{\circ} \mathrm{C}\) and 101.3 kPa pressure. What mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\) is allowable in a laboratory room that is \(3.5 \mathrm{~m} \times 6.0 \mathrm{~m} \times 2.5 \mathrm{~m}\) ?

Determine whether each of the following changes will increase, decrease, or not affect the rate with which gas molecules collide with the walls of their container: (a) increasing the volume of the container, \((\mathbf{b})\) increasing the temperature, (c) increasing the molar mass of the gas.
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