13.3 The Ideal Gas Law

The active ingredient in a Tylenol pill is 325 mg of acetaminophen $\left(\text{C}_{8} \text{H}_{9} \text{NO}_{2}\right)$. Find the molar mass of acetaminophen, and from this, the number of moles and the number of molecules of acetaminophen in a single pill.

The density of air at standard conditions $\left(\right. P = 1 \text{atm}$ and $T = \text{20} º \text{C} \left.\right)$ is $1.20 \text{ kg}/\text{m}^{3}$. At what pressure is the density $0.60 \text{kg}/\text{m}^{3}$ if the temperature and number of molecules are kept constant?

Liquids and solids have densities about 1000 times greater than gases. Explain how this implies that the distances between atoms and molecules in gases are about 10 times greater than the size of their atoms and molecules.

A fixed amount of ideal gas is kept in a container of fixed volume. The absolute pressure P, in pascals, of the gas is plotted as a function of its temperature T, in degrees Celsius. Which of the following are properties of a best fit curve to the data? Select two answers.

1. Having a positive slope
2. Passing through the origin
3. Having zero pressure at a certain negative temperature
4. Approaching zero p…

The gauge pressure in your car tires is $2 . \text{50} \times \text{10}^{5} \text{ N}/\text{m}^{2}$ at a temperature of $\text{35} . 0 º \text{C}$ when you drive it onto a ferry boat to Alaska. What is their gauge pressure later, when their temperature has dropped to $– \text{40} . 0 º \text{C}$?

Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of $\text{20} . 0 º \text{C}$. (a) Find the gauge pressure inside such a bulb when it is hot, assuming its average temperature is $\text{60} . 0 º \text{C}$ (an approximation) and neglecting any change in volume due to thermal expansion or gas leaks. (b) The actual final pressure for the light bul…

Confirm that the units of $\text{nRT}$ are those of energy for each value of $R$: (a) $8 . \text{31} \text{ J}/\text{mol} \cdot \text{K}$, (b) $1 . \text{99 cal}/\text{mol} \cdot \text{K}$, and (c) $0 . \text{0821 L} \cdot \text{atm}/\text{mol} \cdot \text{K}$.

Calculate the number of moles in the 2.00-L volume of air in the lungs of the average person. Note that the air is at $\text{37} . 0 º \text{C}$ (body temperature).

(a) What is the volume (in $\text{km}^{3}$) of Avogadro’s number of sand grains if each grain is a cube and has sides that are 1.0 mm long? (b) How many kilometers of beaches in length would this cover if the beach averages 100 m in width and 10.0 m in depth? Neglect air spaces between grains.

The number density of gas atoms at a certain location in the space above our planet is about $1 . \text{00} \times \text{10}^{\text{11}} \text{m}^{- 3} ,$ and the pressure is $2 . \text{75} \times \text{10}^{– \text{10}} \text{ N}/\text{m}^{2}$ in this space. What is the temperature there?

A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of $1 . \text{40} \times \text{10}^{7} \text{ N}/\text{m}^{2}$ and a temperature of $\text{25} . 0 º \text{C}$. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature $\left(– \text{78} . 5 º \text{C}\right)$ to reduce the leak rate and pressure so that it can be safely repaired. (a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase…

Calculate the depth to which Avogadro’s number of table tennis balls would cover Earth. Each ball has a diameter of 3.75 cm. Assume the space between balls adds an extra 25.0% to their volume and assume they are not crushed by their own weight.

(a) In the deep space between galaxies, the density of atoms is as low as $\text{10}^{6} \text{ atoms}/\text{m}^{3} ,$ and the temperature is a frigid 2.7 K. What is the pressure? (b) What volume (in $\text{m}^{3}$) is occupied by 1 mol of gas? (c) If this volume is a cube, what is the length of its sides in kilometers?