Answer: The equations in column A is matched with gas laws in column B as follows:
21. PV = nRT : (g) Ideal gas law
22. [tex]V_{1}n_{2} = V_{2}n_{1}[/tex] : (f) Avogadro's law
23. [tex]P_{1}V_{1}T_{2} = P_{2}V_{2}T_{1}[/tex] : (e) Combined Gas Law
24. [tex]P_{1}T_{2} = P_{2}T_{1}[/tex] : (d) Gay-Lusaac's law
25. [tex]V_{1}T_{2} = V_{2}T_{1}[/tex] : (c) Charles' law
26. [tex]P_{1}V_{1} = P_{2}V_{2}[/tex] : (b) Boyle's law
27. [tex]\frac{v_{1}}{v_{2}} = \frac{\sqrt{MM_{1}}}{MM_{2}} = \frac{\sqrt{p_{1}}}{p_{2}}[/tex] : (a) Graham's Law of effusion
Explanation:
(A) Ideal gas law: It states that the product of pressure and volume is directly proportional to the product of number of moles and temperature.
So, PV = nRT
where,
P = pressure
V = volume
n = no. of moles
R = gas constant
T = temperature
- Boyle's law: At constant temperature, the pressure of a gas is inversely proportional to volume.
So, [tex]P_{1}V_{1} = P_{2}V_{2}[/tex]
- Charles' law: At constant pressure, the volume of a gas is directly proportional to temperature. So,
[tex]V \propto T\\\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}\\V_{1}T_{2} = V_{2}T_{1}[/tex]
- Gay-Lussac's law: At constant volume, the pressure of a gas is directly proportional to temperature.
So, [tex]P_{1}T_{2} = P_{2}T_{1}[/tex]
- Avogadro's law: At same temperature and pressure, the volume of gas is directly proportional to moles of gas.
So, [tex]V_{1}n_{2} = V_{2}n_{1}[/tex]
- Combined gas law: When Boyle's law, Charles' law, and Gay-lussac's law are combined together then it is called combined gas law. So,
[tex]\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}\\or, P_{1}V_{1}T_{2} = P_{2}V_{2}T_{1}[/tex]
- Graham's law of effusion: It states that the rate of effusion of a gas is inversely proportional to the square root of mass of its particles.
[tex]\frac{v_{1}}{v_{2}} = \frac{\sqrt{MM_{1}}}{MM_{2}} = \frac{\sqrt{p_{1}}}{p_{2}}[/tex]
Thus, we can conclude that equation in column A is matched with gas laws in column B as follows:
21. PV = nRT : (g) Ideal gas law
22. [tex]V_{1}n_{2} = V_{2}n_{1}[/tex] : (f) Avogadro's law
23. [tex]P_{1}V_{1}T_{2} = P_{2}V_{2}T_{1}[/tex] : (e) Combined Gas Law
24. [tex]P_{1}T_{2} = P_{2}T_{1}[/tex] : (d) Gay-Lusaac's law
25. [tex]V_{1}T_{2} = V_{2}T_{1}[/tex] : (c) Charles' law
26. [tex]P_{1}V_{1} = P_{2}V_{2}[/tex] : (b) Boyle's law
27. [tex]\frac{v_{1}}{v_{2}} = \frac{\sqrt{MM_{1}}}{MM_{2}} = \frac{\sqrt{p_{1}}}{p_{2}}[/tex] : (a) Graham's Law of effusion
