Problem 28
Nitrogen and hydrogen gases react to form ammonia gas as follows: $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ At a certain temperature and pressure, \(1.2 \mathrm{~L}\) of \(\mathrm{N}_{2}\) reacts with \(3.6 \mathrm{~L}_{2}\) of \(\mathrm{H}_{2}\). If all the \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) are consumed, what volume of \(\mathrm{NH}_{3}\), at the same temperature and pressure, wi
Problem 29
(a) What conditions are represented by the abbreviation STP? (b) What is the molar volume of an ideal gas at STP? (c) Room temperature is often assumed to be \(25^{\circ} \mathrm{C}\). Calculate the molar volume of an ideal gas at \(25^{\circ} \mathrm{C}\) and 1 atm pressure. (d) If you measure pressure in bars instead of atmospheres, calculate the corresponding value of \(R\) in L-bar/mol-K.
Problem 30
To derive the ideal-gas equation, we assume that the volume of the gas atoms/molecules can be neglected. Given the atomic radius of neon, \(0.69 \AA\), and knowing that a sphere has a volume of \(4 \pi \mathrm{r}^{3} / 3\), calculate the fraction of space that Ne atoms occupy in a sample of neon at STP.
Problem 31
Suppose you are given two 1-L flasks and told that one contains a gas of molar mass 30 , the other a gas of molar mass 60 , both at the same temperature. The pressure in flask A is \(\mathrm{X}\) atm, and the mass of gas in the flask is \(1.2 \mathrm{~g}\). The pressure Which flask contains the gas of molar mass 30 , and which contains the gas of molar mass 60 ?
Problem 34
Calculate each of the following quantities for an ideal gas: (a) the volume of the gas, in liters, if \(1.50 \mathrm{~mol}\) has a pressure of \(1.25 \mathrm{~atm}\) at a temperature of \(-6^{\circ} \mathrm{C}\) (b) the absolute temperature of the gas at which \(3.33 \times 10^{-3} \mathrm{~mol}\) occupies \(478 \mathrm{~mL}\) at 750 torr; (c) the pressure, in atmospheres, if \(0.00245 \mathrm{~mol}\) occupies \(413 \mathrm{~mL}\) at \(138^{\circ} \mathrm{C}\); (d) the quantity of gas, in moles, if \(126.5 \mathrm{~L}\) at \(54^{\circ} \mathrm{C}\) has a pressure of \(11.25 \mathrm{kPa}\)
Problem 35
The Goodyear blimps, which frequently fly over sporting events, hold approximately \(175,000 \mathrm{ft}^{3}\) of helium. If the gas is at \(23^{\circ} \mathrm{C}\) and \(1.0 \mathrm{~atm}\), what mass of helium is in a blimp?
Problem 36
A neon sign is made of glass tubing whose inside diameter is \(2.5 \mathrm{~cm}\) and whose length is \(5.5 \mathrm{~m}\). If the sign contains neon at a pressure of \(1.78\) torr at \(35^{\circ} \mathrm{C}\), how many grams of neon are in the sign? (The volume of a cylinder is \(\pi r^{2} h\).)
Problem 37
(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 735 torr. (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 \(1.00 \mathrm{~atm}\), assuming the air behaves ideally.
Problem 38
(a) If the pressure exerted by ozone, \(\mathrm{O}_{3}\), in the stratosphere is \(3.0 \times 10^{-3}\) atm and the temperature is \(250 \mathrm{~K}\), how many ozone molecules are in a liter? (b) Carbon dioxide makes up approximately \(0.04 \%\) of Earth's atmosphere. If you collect a \(2.0-\mathrm{L}\) sample from the atmosphere at sea level ( \(1.00\) atm) on a warm day \(\left(27^{\circ} \mathrm{C}\right)\), how many \(\mathrm{CO}_{2}\) molecules are in your sample?
Problem 39
A scuba diver's tank contains \(0.29 \mathrm{~kg}\) of \(\mathrm{O}_{2}\) compressed into a volume of \(2.3 \mathrm{~L}\) (a) Calculate the gas pressure inside the tank at \(9^{\circ} \mathrm{C}\). (b) What volume would this oxygen occupy at \(26^{\circ} \mathrm{C}\) and \(0.95 \mathrm{~atm}\) ?
