Page 253 - Schaum's Outline of Theory and Problems of Applied Physics

238 KINETIC THEORY OF MATTER [CHAP. 20

SOLVED PROBLEM 20.10
Find the mass of 75 mol of uranium (U).
The atomic mass of uranium is 238.03 u, which means that a mole of U has a mass of 238.03 g. Hence

Mass of U = (moles of U)(atomic mass of U)
4
= (75 mol)(238.02 g/mol) = 1.785 × 10 g = 17.85 kg
SOLVED PROBLEM 20.11

How many moles of Cu are present in 100 g of copper?
The atomic mass of Cu is 63.54 u = 63.54 g/mol. Hence
mass of Cu 100 g
Moles of Cu = = = 1.574 mol
atomic mass of Cu 63.54 g/mol

SOLVED PROBLEM 20.12
(a) Find the mass of 9.4 mol of ethylene (C 2 H 4 ). (b) How many carbon atoms are present?

(a) The molecular mass of ethylene is
2(C) = (2)(12.01) u = 24.02 u
4(H) = (4)(1.008) u = 4.03 u
28.05 u = 28.05 g/mol

The required mass is
Mass of C 2 H 4 = (moles of C 2 H 4 ) (molecular mass of C 2 H 4 ) = (9.4 mol)(28.05 g/mol) = 264 g
(b) Two moles of carbon are present in each mole of C 2 H 4 . Hence there is (2) (9.4 mol) = 18.8 mol of carbon
present in 9.4 mol of C 2 H 4 . The number of carbon atoms is

Atoms of C = (moles of C)(Avogadro’s number)
23
25
= (18.8 mol)(6.023 × 10 atoms/mol) = 1.13 × 10 atoms

MOLAR VOLUME
Equal volumes of all gases, under the same conditions of temperature and pressure, contain the same number
of molecules and therefore the same number of moles. This observation is most useful stated in reverse: Under
given conditions of temperature and pressure, the volume of a gas is proportional to the number of moles present.
2
2
5
◦
For convenience, a temperature of 0 C (273 K) and a pressure of 1 atm (1.013 ×10 N/m = 14.7 lb/in. ) are
taken as the standard temperature and pressure (STP); Charles’s and Boyle’s laws permit measurements made at
other temperatures and pressures to be reduced to their equivalents at STP. Experimentally it is found that 1 mol
of any gas at STP occupies a volume of 22.4 L. Thus the molar volume of a gas is 22.4 L at STP. This observation
makes it possible to deal with gas volumes in chemical reactions. If a certain reaction is known to produce 2.5
mol of a gas, for instance, we know that at STP the volume of the gas will be
V = (moles of gas)(molar volume) = (2.5 mol)(22.4 L/mol) = 56 L

UNIVERSALGAS CONSTANT
According to the ideal gas law (Chapter 19), the pressure, volume, and temperature of a gas sample obey the
relationship pV/T = constant. We can find the value of the constant in terms of the number of moles n of gas in
◦
the sample by making use of the fact that the molar volume at STP is 22.4 L. At STP we have T = 0 C = 273 K,