http://www.ck12.org Chapter 14. Thermodynamics
Check Your Understanding
1a. How many atoms of silver does one mole of silver contain?
Answer: One mole (abbreviated as mol), by definition, contains 6.022× 1023 particles. In this case, it is 6.022× 1023
atoms of silver.
1b. A United States silver dollar,Figure14.2, contains approximately 24.06 grams of silver. Themolecular mass
of silver is 107. (^87) molg. How many moles of silver are in a silver dollar?
Answer:n= 10724 .. 8706 gg
mol
= 0. 22304 → 0. 2230 mol
FIGURE 14.2
United States silver dollar, late 19thcentury2a. The mass of a United States penny (primarily zinc) is 2.50 grams. What is the molar mass of one mole of
pennies?
Answer: There are 6.022× 1023 particles in every mole. Therefore, one mole of pennies is 6.022× 1023 pennies.
(
- (^50) pennyg
)
( 6. 022 × 1023 pennies) = 1. 5055 × 1024 → 1. 51 × 1024 gramsor 1. 51 × 1021 kg. This is the mass ofPluto’s moon, Charon, seeFigure14.3. Clearly, a mole is a very large number.
By comparison, the amount of zinc in about 23 pennies is equivalent to one mole of zinc atoms.
Clearly, atoms are very small.
Three Laws
In the three laws that follow, we assume an ideal gas, as described by the Kinetic Theory. The mass of the gas is
held constant, and that the pressure of the gas remains fairly low.
Boyle’s Law
Robert Boyle (1627-1691), in theFigure14.4, is regarded as the first modern chemist. In the early 1660s he stated
what has become known asBoyle’s Law,which states that if the temperature of a gas is kept constant, then the
volumeVand pressurePform an inverse relationship.
→V∝^1 P,or PV=constant.
Figure14.5 shows the relationship as a graph. Notice that as the pressure increases, the volume decreases, if the
temperature remains constant. This may not seem obvious.
Let us try to understand why it happens. If the temperature does not increase, then the average velocity of the gas
molecules does not increase. As we showed earlier, a change in momentum(∆p=F∆t)is proportional to force.
Recall that pressure is force per unit area. If the volume decreases, then more molecules impact a smaller surface