Page 53 - Physical Chemistry

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1.8 A solution of HCl in water is 12.0% HCl by mass. Find 1.16 (a) What is the pressure exerted by 24.0 g of carbon
the mole fractions of HCl and H O in this solution. dioxide in a 5.00-L vessel at 0°C? (b) A rough rule of thumb is
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that 1 mole of gas occupies 1 ft at room temperature and pres-
1.9 Calculate the mass in grams of (a) one atom of carbon;
sure (25°C and 1 atm). Calculate the percent error in this rule.
(b) one molecule of water.
One inch 2.54 cm.
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1.10 The room-temperature density of Po is 9.20 g/cm and 1.17 A sample of 65 mg of an ideal gas at 0.800 bar pressure
its longest-lived isotope has mass number 209. The structure of has its volume doubled and its absolute temperature tripled.
solid Po can be described as follows. Imagine a layer of cubes Find the final pressure.
like Fig. 23.8 but with many more cubes; the edge length of
each cube is taken as equal to the diameter of a Po atom; then 1.18 For a certain hydrocarbon gas, 20.0 mg exerts a pressure
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place another cube directly over each cube in the first layer and of 24.7 torr in a 500-cm vessel at 25°C. Find the molar mass
aligned with that cube, thereby forming a second layer; then and the molecular weight and identify the gas.
add cubes directly over the second-layer cubes to form a third 1.19 Find the density of N at 20°C and 0.667 bar.
layer; and so on. If one Po atom is put into each cube with 2
the atomic nucleus at the center of the cube, we have the Po 1.20 For 1.0000 mol of N gas at 0.00°C, the following vol-
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structure. (a) Find the volume of one mole of Po. (b) Find umes are observed as a function of pressure:
the volume of the cube that surrounds one Po atom in the solid. P/atm 1.0000 3.0000 5.0000
(c) Find the diameter of a Po atom. (d) For a spherical nanopar-
ticle of Po whose diameter is 2 nm, find the number of Po V/cm 3 22405 7461.4 4473.1
atoms present. (e) Repeat (d) for a Po spherical nanoparticle of
diameter 100 nm. (f) For a cubic nanoparticle of Po whose edge Calculate and plot PV/nT versus P for these three points and ex-
length is 2 nm, calculate the percentage of Po atoms that are at trapolate to P 0 to evaluate R.
the surface of the particle. (g) Repeat (f ) for a Po cubic particle 1.21 The measured density of a certain gaseous amine at 0°C
of edge length 100 nm. (The increasing percentage of atoms at as a function of pressure is
the surface as the particle size decreases is one reason the prop-
erties of nanomaterials change with size.) P/atm 0.2000 0.5000 0.8000
r/(g/L) 0.2796 0.7080 1.1476
Section 1.5 Plot P/r versus P and extrapolate to P 0 to find an accurate
1.11 True or false? (a) On the Celsius scale, the boiling point molecular weight. Identify the gas.
of water is slightly less than 100.00°C. (b) Doubling the ab-
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solute temperature of an ideal gas at fixed volume and amount 1.22 After 1.60 mol of NH gas is placed in a 1600-cm box
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of gas will double the pressure. (c) The ratio PV/mT is the same at 25°C, the box is heated to 500 K. At this temperature, the
for all gases in the limit of zero pressure. (d) The ratio PV/nT is ammonia is partially decomposed to N and H , and a pressure
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the same for all gases in the limit of zero pressure. (e) All ideal measurement gives 4.85 MPa. Find the number of moles of
gases have the same density at 25°C and 1 bar. ( f) All ideal each component present at 500 K.
gases have the same number of molecules per unit volume at 1.23 A student attempts to combine Boyle’s law and Charles’
25°C and 10 bar.
law as follows. “We have PV K and V/T K . Equals mul-
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1.12 Do these conversions: (a) 5.5 m to cm ;(b) 1.0 GPa to bar tiplied by equals are equal; multiplication of one equation by
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(where 1 GPa 10 Pa); (c) 1.000 hPa to torr (where 1 hPa the other gives PV /T K K . The product K K of two con-
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1 2
1 2
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10 Pa); (d) 1.5 g/cm to kg/m . stants is a constant, so PV /T is a constant for a fixed amount of
ideal gas.” What is the fallacy in this reasoning?
1.13 In Fig. 1.2, if the mercury levels in the left and right
arms of the manometer are 30.43 and 20.21 cm, respectively, 1.24 Prove that the equations PV/T C for m constant and
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above the bottom of the manometer, and if the barometric pres- V/m C for T and P constant lead to PV/mT a constant.
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sure is 754.6 torr, find the pressure in the system. Neglect tem- 1.25 A certain gas mixture is at 3450 kPa pressure and is
perature corrections to the manometer and barometer readings. composed of 20.0 g of O and 30.0 g of CO . Find the CO par-
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tial pressure.
1.14 (a) A seventeenth-century physicist built a water barom-
eter that projected through a hole in the roof of his house so that 1.26 A 1.00-L bulb of methane at a pressure of 10.0 kPa is
his neighbors could predict the weather by the height of the connected to a 3.00-L bulb of hydrogen at 20.0 kPa; both bulbs
water. Suppose that at 25°C a mercury barometer reads 30.0 in. are at the same temperature. (a) After the gases mix, what is the
What would be the corresponding height of the column in a total pressure? (b) What is the mole fraction of each component
water barometer? The densities of mercury and water at 25°C in the mixture?
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are 13.53 and 0.997 g/cm , respectively. (b) What pressure in 3
atmospheres corresponds to a 30.0-in. mercury-barometer read- 1.27 A student decomposes KClO and collects 36.5 cm of
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ing at 25°C at a location where g 978 cm/s ? O over water at 23°C. The laboratory barometer reads 751 torr.
The vapor pressure of water at 23°C is 21.1 torr. Find the vol-
1.15 Derive Eq. (1.17) from Eq. (1.18). ume the dry oxygen would occupy at 0°C and 1.000 atm.