2.1 Molecular Model of an Ideal Gas

The recommended daily amount of vitamin $\text{B}_{3}$ or niacin, $\text{C}_{6} \text{NH}_{5} \text{O}_{2} ,$ for women who are not pregnant or nursing, is 14 mg. Find the number of molecules of niacin in that amount.

The density of air in a classroom $\left(\right. p = 1.00 \text{atm}$ and $T = 20 ° \text{C})$ is $1.28 \text{kg}/\text{m}^{3}$. At what pressure is the density $0.600 \text{kg}/\text{m}^{3}$ if the temperature is kept constant?

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

Two $\text{H}_{2}$ molecules can react with one $\text{O}_{2}$ molecule to produce two $\text{H}_{2} \text{O}$ molecules. How many moles of hydrogen molecules are needed to react with one mole of oxygen molecules?

A constant-volume gas thermometer contains a fixed amount of gas. What property of the gas is measured to indicate its temperature?

In the last chapter, free convection was explained as the result of buoyant forces on hot fluids. Explain the upward motion of air in flames based on the ideal gas law.

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 $20.0 ° \text{C}$. (a) Find the gauge pressure inside such a bulb when it is hot, assuming its average temperature is $60.0 ° \text{C}$ (an approximation) and neglecting any change in volume due to thermal expansion or gas leaks. (b) The actual final pressure for the light bul…

How many moles are there in (a) 0.0500 g of $\text{N}_{2}$ gas $\left(M = 28.0 \text{g}/\text{mol}\right) ?$ (b) 10.0 g of $\text{CO}_{2}$ gas $\left(M = 44.0 \text{g}/\text{mol}\right) ?$ (c) How many molecules are present in each case?

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 $37.0 ° \text{C}$ (body temperature) and that the total volume in the lungs is several times the amount inhaled in a typical breath as given in the example.

A company advertises that it delivers helium at a gauge pressure of $1.72 \times 10^{7} \text{Pa}$ in a cylinder of volume 43.8 L. How many balloons can be inflated to a volume of 4.00 L with that amount of helium? Assume the pressure inside the balloons is $1.01 \times 10^{5} \text{Pa}$ and the temperature in the cylinder and the balloons is $25.0 °\text{C}$.

An expensive vacuum system can achieve a pressure as low as $1.00 \times 10^{−7} \text{N}/\text{m}^{2}$ at $20.0 ° \text{C} .$ How many molecules are there in a cubic centimeter at this pressure and temperature?

A bicycle tire contains 2.00 L of gas at an absolute pressure of $7.00 \times 10^{5} \text{N}/\text{m}^{2}$ and a temperature of $18.0 ° \text{C}$. What will its pressure be if you let out an amount of air that has a volume of $100 \text{cm}^{3}$ at atmospheric pressure? Assume tire temperature and volume remain constant.

A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of $1.40 \times 10^{7} \text{N}/\text{m}^{2}$ and a temperature of $25.0 °\text{C}$. The cylinder is cooled to dry ice temperature $\left(−78.5 ° \text{C}\right)$ 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 change? (b) What is the final pressure if one-t…

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.