Gas Laws: Pressure, Temperature, and Advanced Numerical Scenarios
Batch 14: Numericals on Pressure and Temperature Effects
Q1: A steel tank of ( 50 , text{liters} ) capacity is filled with oxygen at ( 15 , text{atm} ). If the oxygen is used to fill cylinders of ( 10 , text{liters} ) capacity at ( 3 , text{atm} ), how many cylinders can be filled?
Using Boyle’s Law:
( V_2 = frac{P_1 V_1}{P_2} = frac{15 cdot 50}{3} = 250 , text{liters} )
Each cylinder has a volume of ( 10 , text{liters} ):
( text{Number of cylinders} = frac{250}{10} = 25 )
Answer: ( 25 , text{cylinders} ) can be filled.
Q2: Calculate the volume occupied by ( 10 , text{g} ) of ( text{O}_2 ) at ( 27^circ text{C} ) and ( 2 , text{atm} ).
Using the ideal gas equation:
( PV = nRT )
( V = frac{0.3125 cdot 0.0821 cdot 300}{2} = 3.84 , text{liters} )
Answer: The volume is ( 3.84 , text{liters} ).
Q3: ( 2500 , text{cm}^3 ) of hydrogen at STP is compressed to ( 1000 , text{cm}^3 ). What is the final pressure if temperature remains constant?
Using Boyle’s Law:
( P_2 = frac{2500}{1000} = 2.5 , text{atm} )
Answer: The final pressure is ( 2.5 , text{atm} ).
Batch 15: Advanced Numerical Scenarios
Q1: ( 2 , text{g} ) of hydrogen gas occupies ( 22.4 , text{liters} ) at STP. Calculate the volume of ( 2 , text{g} ) of hydrogen at ( 127^circ text{C} ) and ( 5 , text{atm} ).
Using the combined gas law:
( V_2 = frac{22.4 cdot 400}{5 cdot 273} = 6.56 , text{liters} )
Answer: The volume is ( 6.56 , text{liters} ).
Q2: A gas has a volume of ( 100 , text{cm}^3 ) at ( 27^circ text{C} ). At what temperature will the volume be doubled, pressure remaining constant?
Using Charles’ Law:
( T_2 = frac{200 cdot 300}{100} = 600 , text{K} )
Convert to Celsius:
( t_2 = T_2 – 273 = 327^circ text{C} )
Answer: The temperature is ( 327^circ text{C} ).
Q3: A gas at STP occupies ( 22.4 , text{liters} ). What will be its volume if the pressure is halved and the temperature is doubled?
Using the combined gas law:
( V_2 = frac{1 cdot 22.4 cdot 546}{273 cdot 0.5} = 89.6 , text{liters} )
Answer: The volume is ( 89.6 , text{liters} ).