Comprehensive Gas Laws: Numerical Problems, Applications, and Graphs

Batch 9: Numerical Problems on Gas Laws

Q1: A gas occupies ( 800 , text{cm}^3 ) at ( 650 , text{mm Hg} ) pressure. At what pressure will its volume reduce to ( 480 , text{cm}^3 ), temperature being constant?

Using Boyle’s Law:

( P_1 V_1 = P_2 V_2 )

Substitute values:

• ( P_1 = 650 , text{mm Hg}, V_1 = 800 , text{cm}^3, V_2 = 480 , text{cm}^3, P_2 = ? )

( 650 times 800 = P_2 times 480 )

( P_2 = frac{650 times 800}{480} = 1083.33 , text{mm Hg} )

Answer: The pressure is ( 1083.33 , text{mm Hg} ).

Q2: ( 98 , text{cm}^3 ) of nitrogen is at ( 770 , text{mm Hg} ). If the pressure is raised to ( 880 , text{mm Hg} ), find how much the volume will diminish, assuming temperature remains constant.

Using Boyle’s Law:

( P_1 V_1 = P_2 V_2 )

Substitute values:

• ( P_1 = 770 , text{mm Hg}, V_1 = 98 , text{cm}^3, P_2 = 880 , text{mm Hg}, V_2 = ? )

( 770 times 98 = 880 times V_2 )

( V_2 = frac{770 times 98}{880} = 85.75 , text{cm}^3 )

Diminished volume:

( text{Diminished Volume} = V_1 – V_2 = 98 – 85.75 = 12.25 , text{cm}^3 )

Answer: The volume diminishes by 12.25 cm³.

Q3: A gas has a volume of ( 500 , text{cm}^3 ) at STP. At what temperature will the gas occupy ( 1000 , text{cm}^3 ), pressure remaining constant?

Using Charles’ Law:

( frac{V_1}{T_1} = frac{V_2}{T_2} )

Substitute values:

• ( V_1 = 500 , text{cm}^3, T_1 = 273 , text{K}, V_2 = 1000 , text{cm}^3, T_2 = ? )

( frac{500}{273} = frac{1000}{T_2} )

( T_2 = frac{1000 times 273}{500} = 546 , text{K} )

Convert to Celsius:

( t_2 = T_2 – 273 = 273^circ text{C} )

Answer: The gas will occupy ( 1000 , text{cm}^3 ) at 273°C.

Batch 10: Conceptual Applications and Graphs

Q1: What is meant by STP?

Answer: STP stands for Standard Temperature and Pressure, defined as:

• Temperature: ( 0^circ text{C} = 273 , text{K} )
• Pressure: ( 1 , text{atm} = 760 , text{mm Hg} )

These standard conditions are used to compare gas properties.

Q2: Explain why gases are compressible, using kinetic molecular theory.

Answer: According to the kinetic molecular theory, gas molecules are far apart and have large intermolecular spaces. When pressure is applied, the molecules can be brought closer together, making gases highly compressible.

Q3: How does the graph of ( P ) vs ( frac{1}{V} ) verify Boyle’s Law?

Answer: The graph of ( P ) vs ( frac{1}{V} ) produces a straight line through the origin, verifying the inverse proportionality between pressure and volume as stated in Boyle’s Law.

Q4: State one real-life application of Boyle’s Law.

Answer: One real-life application of Boyle’s Law is in syringes. When the plunger of a syringe is pulled, the volume inside the syringe increases, causing the pressure to decrease and drawing liquid into the syringe.