The document discusses the combined gas law, which incorporates Charles' law, Boyle's law, and Gay-Lussac's law. It provides the equations for each individual gas law and the combined gas law. Two examples are shown applying the combined gas law to calculate changes in pressure, temperature, and volume. The final activity asks how many 5L balloons can be filled from a starting gas quantity.

1. (Charles’ Law, Boyle’s Law, and
Gay-Lussac’s Law)
Ms. G. Martin

2. Lets Learn
The combined gas law is a gas law that combines Charles’
law, Boyle’s law. And Gay-Lussac’s Law. Recall that:
• Boyle’s Law P1V1 = P2V2
• Charles’ Law
𝑽𝟏
𝑻𝟏
=
𝑽𝟐
𝑻𝟐
• Gay-Lussac’s Law
𝑷𝟏
𝑻𝟏
=
𝑷𝟐
𝑻𝟐
Combined Gas Law
𝑷𝟏𝑽𝟏
𝑻𝟏
=
𝑷𝟐𝑽𝟐
𝑻𝟐

3. Combined Gas Law
𝑷𝟏
𝑽𝟏
𝑻𝟏
=
𝑷𝟐
𝑽𝟐
𝑻𝟐
; T2P1V1 = T1P2V2
Example 1.
A 25.0 mL bubble is released from a driver’s air tank at a
pressure of 5.50 atm and temperature of 25° C . What is the volume of
the bubble when it reaches the ocean surface where the pressure is 1.00
atm and the temperature is 20°C?
Given:
P1 = 5.50 atm P2 = 1.00 atm
T1 = 25°C or 298 K T2 = 20°C or 293 K
V1 = 0.025 L V2 = ?

4. Analysis:
To find for the volume of V2, we use the formula:
𝑷𝟏
𝑽𝟏
𝑻𝟏
=
𝑷𝟐
𝑽𝟐
𝑻𝟐
; T2P1V1 = T1P2V2
Solution:
V2 =
𝑷𝟏
𝑽𝟏
𝑻𝟐
𝑷𝟐
𝑻𝟏
=
(5.50 𝑎𝑡𝑚)(0.025 𝐿)(293 𝐾)
(1.00 𝑎𝑡𝑚)(298 𝐾)
V2 =
40.2875 𝑎𝑡𝑚 . 𝐿. 𝐾
298 𝑎𝑡𝑚 . 𝐾
V2 = 0.14 L
Interpretation: Using combined gas law, the volume produced is 0.14 L from 0.025 L.
This is due to a decrease in pressure and temperature.

5. Example 2.
A weather balloon is filled with 20.0L of helium at a temperature
of 30°C and a pressure of 750 mmHg. What is the pressure of the
Helium in the balloon in the upper atmosphere when the temperature
is -33°C and the volume becomes 45L?
Given:
P1 = 750 mmHg P2 =
T1 = 30°C or 303 K T2 = -33°C or 240 K
V1 = 20 L V2 = 45 L

6. Solution:
P2 =
𝑷𝟏
𝑽𝟏
𝑻𝟐
𝑽𝟐
𝑻𝟏
P2 =
(𝟕𝟓𝟎 𝒎𝒎𝑯𝒈)(𝟐𝟎.𝟎 𝑳)(𝟐𝟒𝟎 𝑲)
(45 𝐿)(303 𝐾)
P2 =
(3,6000,000 𝑚𝑚𝐻𝑔.𝐿.𝐾)
(1,635 𝐿.𝐾)
P2 = 264.03 mmHg

7. Activity 1.
A 15. 0 L is filled with helium and the pressure is 150 atm at
30°C. How many 5.0 L balloons can be filled when the temperature is
22°C and the atmospheric pressure is 350 mmHg?
Given:
P1 = 150 atm (114, 000 mmHg) P2 = 350 mmHg (0.46 atm)
T1 = 30°C or 303 K T2 = 22°C or 295 K
V1 = 15 L V2 = ?

8. Solution:
V2 =
𝑷𝟏
𝑽𝟏
𝑻𝟐
𝑷𝟐
𝑻𝟏
V2 =
(150 atm)(15 L)(295 K )
(0.46 atm)(303 K)
=
663,750 𝑎𝑡𝑚.𝐿.𝐾
139.38 𝑎𝑡𝑚.𝐾
= 4,762.16L =
4,762.16 𝐿
5 𝐿
= 952. 43
There are 952 of 5 L balloons can be filled.