The Gas Laws

1. **Charles'Law**: applies to ideal gases under constant pressure.

If you heat a gas, its volume, V, will expand at a rate that is directly proportional to its absolute temperature measured in Kelvin.

T (

^{o}C)

-273

Notice that a plot of volume versus temperature in degrees
Celsius (^{o}C) leads to an x-intercept of about -273. To obtain an
x-intercept of 0, we add 273 to the Celsius temperature to obtain the absolute
temperature measured in Kelvin. This leads to a simpler relationship known as
Charles' Law:

_{} at constant pressure
with T in Kelvin

**Example**: A 250 mL balloon is warmed under constant
atmospheric pressure from 0.00 C to 20.0 C. Find its final volume.

(Assume that the rubber does not offer less resistance as it stretches: in reality it may and pressure would not be constant.)

Using Charles' Law:

_{}

*V*_{2}
= 268 mL

2 **Avogadro's
Law**: Under the same conditions of pressure and temperature, equal volumes
of different gases have the same number of molecules, or in other words the
same number of moles.

If the above are all at, say for example, room temperature and at atmospheric pressure, if the containers they are in are all of the same volume, then they all have the same number of moles. The size of the individual molecules is irrelevant. Conversely, if you were told that under certain conditions 10 moles of Ar occupied 224 L, then 10 moles of oxygen would also take up 224 L.

**At O ^{o}C and under 101.3
kPa of pressure , one mole of any ideal gas occupies 22.4 L.**

** **

** **

** Example 1**: At STP, how many litres of hydrogen gas
would you collect by reacting 0.10 g of Na?

2 Na + 2 HCl --> 2 NaCl + H_{2(g)}

First convert the Na to moles. 0.10g/23g/mole = 0.00435 moles of Na

Consider the ratio between Na and H_{2(g)}
in the equation and write a proportion.

2/0.00435 = 1/x

x = 0.00217
moles of H_{2(g)}

Since conditions are STP, we can convert to L using 22.4 L/mole( the molar volume)

Answer =0.00217 moles of H_{2(g) }(22.4L/mole)
= 0.0487 L or 48.7 mL

**Example 2: **Find the density of Ar at STP and at -20 C and 101.3 kPa.

Consider 1 mole of Ar = 40 g/mole. At STP, the volume of 1 mole= 22.4 L, so its density becomes:

40 g /22.4 L = **1.8g/L**

At -20 C, we need Charles Law to get its volume:

22.4/(0+273) = V_{2}/-20+273

V_{2} = 20.8 L; so the
density increases to 40g /20.8 L = **1.9 g/L**

3. **Boyle's
Law**: applies to ideal gases at
constant temperature. The product of a gas' pressure and volume are constant,
implying that

P_{1}V_{1}
= P_{2}V_{2}. at constant temperature.

The relation is an inverse one: if you double pressure, the volume becomes half of the original.

The curve is known as a hyperbola, and it reveals how volume decreases as more pressure is applied.

**Example**: At constant
temperature, the pressure of a gas is increased threefold. The final volume of
the gas is 36 L. what was the original volume?

P_{1}V_{1}
= P_{2}V_{2}. at constant temperature.

P_{2}_{ }= 3 P_{1}.

Substitute: P_{1}V_{1}
= 3 P_{1}(36 L)

Since P_{1}
cancels, V_{1} = 3 (36) = 108 L.

4. **Gay-Lussac's Law**: applies to ideal gases at constant volume. In a container of
constant volume, the pressure is directly proportional to its absolute
temperature (K).

P(kPa)_ T (K)

_{} under constant
volume. Temp in K.

The graph reveals how increasing the temperature will cause the molecules to move faster, and since they are not permitted extra room for maneuvering, they collide more often, resulting in more pressure.

**Example 1**:
At 300K, what pressure would be
exerted by hydrogen gas if it exerts 200 kPa at 100 K?

200/100 = x/300

x = 600 kPa.