Laws related to gases
All gases can be characteristised by four variables:
1. Pressure
2. Volume
3. Temperature
4. Number of moles of gases
Gas laws
The relationships that expresses the influence of one variable on another with two variable constant are called gas laws.
Boyls law
Boyl's law states that the volume of a fixed amount of a gas at constant temperature is inversly propational to the applied pressure.
Mathmatically,
V @ 1/P
V = constant × 1/P
PV = constant
Thus Boyl's law can also be defined as:
The product of volume and pressure of a given mass of a gas remains constant at constant temperature.
Example 1.
Account for pressure volume changes in ethene gas using Boyl's law. Ethene is used as anesthetic gas. The pressure on 2.5 dm3 of ethene changes from 1.05 to 2.10 atm. The volume of ethene becomes 1.25 dm3 if the temperature remains constant explain the changes using Boyl's law.
Solution.
Note:
Let us calculate the product of PV for any two set of conditions. If product of pressure and volume of any two conditions is same, the Boyl's is obeyed.
Before the change
P1 = 1.05
V1 = 2.5dm3
P1V1 = 1.05 × 2.5 dm3 = 2.625atm.dm3 ......1
After the change
P2 = 2.1 atm
V2 = 1.25 dm3
P2V2 =2.1 atm × 1.25dm3 = 2.625atm.dm3 .....2
Since,
eq. 1 and 2 are equal, so
P1V1 = P2V2
Thus, calculated values agree with Pressure-Volume relationship (Boyl's law).
Charl's law
Charl's law states that the volume of a fixed amount of a gas at constant pressure is directly propational to absolute temperature.
Mathmatically,
V @ T (at constant pressure)
V = constant × T
V/T= constant
Thus Charles's law can also be defined as:
The volum and absolute temperature of a given mass of a gas remains constant at constant pressure.
Example 1.
Account for pressure volume changes in ethene gas using Charlesl's law.
The data of volume of a gas and its temperature for a given mass of a gas at 900 mmHg is given as follows.
Temperature (oC) Volume (cm3)
0 107.9
5 109.7
10 111.7
15 113.6
20 115.5
Solution.
Note:
Let us convert C temperature to Kelvin by adding 273.
Then we calculate the ratio of V and T for each set of conditions.
If ratio of volume and absolute temperature of any two conditions is same, the Charles's is obeyed.
Temperature (oC) Volume (cm3) Temperature (oC) V/T
0 107.9 273 (107.9/273)= 0.3952
5 109.7 278 (109.9/278)= 0.3948
10 111.7 283 (111.7/283)= 0.3947
15 113.6 288 (113.6/288)= 0.3944
20 115.5 293 (115.5/293)= 0.3942
Since,
Ratio of V and T are fairly constant each set of values.
Thus, calculated values agree with volume absolute temperature relationship (Charles's law).
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