JSS 3: GENERAL GAS EQUATION

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The General Gas Equation states that for a given mass of gas, the ratio of the product of pressure and volume to the absolute temperature remains constant, provided no gas is added or removed.

Formula
P₁ V₁ /T₁ = P₂ V₂ /T₂

Where:
P₁ = Initial pressure
V₁ = Initial volume
T₁ = Initial absolute temperature (Kelvin)
P₂ = Final pressure
V₂ = Final volume
T₂ = Final absolute temperature (Kelvin)

 Note
Temperature must be converted to Kelvin (K) before using the formula.
K = °C + 273

Worked Example

A gas occupies 4.0 dm³ at a pressure of 100 kPa and a temperature of 27°C. If the pressure is increased to 200 kPa and the temperature becomes 127°C, calculate the new volume.

Solution

P₁ = 100 kPa
V₁ = 4.0 dm³
T₁ = 27 + 273 = 300 K
P₂ = 200 kPa
T₂ = 127 + 273 = 400 K
P₁ V₁ /T₁ = P₂ V₂ /T₂
100 × 4/300 = 200 ×  V₂/400
V₂= (100 × 4 ×400)/(300×200)
 V₂= 2.67 dm³

Class activities 
1. The General Gas Equation is obtained by combining: (a) Boyle's law and Charles's law (b) Dalton's law and Graham's law (c) Avogadro's law and Gay-Lussac's law (d) Ideal gas law and Dalton's law

2. The General Gas Equation is: (a) P₁ V₁ /T₁ = P₂ V₂ /T₂ (b) PV=nRT(c) P₁ V₁  = P₂ V₂ (d)   V₁ /T₁ = V₂ /T₂ 

3. In the General Gas Equation, temperature must be measured in: (a) Celsius (b) Fahrenheit (c) Kelvin (d) Henry

4. Which of the following quantities must remain constant when using the General Gas Equation? (a) Pressure (b) Volume (c) Temperature (d) Mass of the gas

5. If the pressure of a gas increases while the temperature remains constant, the volume will: (a) Increase (b) Decrease (c) Remain the same (d) Double

6. A gas occupies 2.0 dm³ at 300 K. If the temperature increases to 600 K at constant pressure, the new volume is: (a) 1.0 dm³ (b) 2.0 dm³ (c) 4.0 dm³ (d) 6.0 dm³

7. Which law states that the pressure of a fixed mass of gas is inversely proportional to its volume at constant temperature? (a) Charles's law (b) Boyle's law (c) Graham's law (d) Avogadro's law

8. Which law states that the volume of a fixed mass of gas is directly proportional to its absolute temperature at constant pressure? (a) Boyle's law (b) Graham's law (c) Charles's law (d) Dalton's law

9. The SI unit of pressure commonly used in gas laws is: (a) Newton (b) Joule (c) Pascal (Pa) (d) Watt

10. Before solving problems involving the General Gas Equation, temperatures given in degrees Celsius should first be: (a) Divided by 100 (b) Multiplied by 273 (c) Left unchanged (d) Converted to Kelvin

                       Assignment 
 1. A gas has a pressure of 150 kPa, a volume of 6 dm³, and a temperature of 300 K. If the pressure becomes 300 kPa and the temperature becomes 400 K, calculate the new volume.

2. A gas occupies 5 dm³ at 120 kPa and 27°C. If the gas is compressed to 240 kPa and heated to 87°C, calculate the new volume using the General Gas Equation.

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