# Numerical Problems : Gaseous State

#### Level – 1

1.(a) 3.00 moles of a gas are placed in a 4.55 L container at 245 ° C. What is the pressure in kPa?

(b) 65.85 grams of nitrogen gas are placed in 17.5 L container. The pressure is 1988 mm Hg. What is the temperature, in °C ?

2. (a) A gas is placed in a 2.00 L container at 25 °C and 550.0 mm Hg. The gas is now compressed to a volume of 0.75 L at constant temperature. What is the new pressure ?

(b) (i) A gas is placed in a heavy container. The container is now heated. What happens to the gas and why ?

(ii) A gas is placed in a container with a moveable piston. It is then cooled down at constant pressure. What happens? Explain.

(iii) A gas is placed in a container at a certain temperature and pressure. More gas is added and in order to keep the pressure and volume constant the temperature had to change. Was the container heated or cooled? Explain.

3. (a) A gas is placed in a 3.45 L container at 45 °C and 2.7 atm. It is then compressed to a pressure of 8.25 atm and a volume of 0.550 L. What is the new temperature?

(b) Butane (C4H10) is a fuel used in many lighters. The reaction is as follows:

2 C4H10 (g) + 13 O2 (g) –> 8 CO2 (g) + 10 H2O (g)

(i) If 26.7 L of O2 react at STP, how many liters of butane are needed at STP?

(ii) 24.57 moles of water are formed. How many liters of butane were reacted at STP?

(iii) 13.6 L of butane are reacted at STP, how many grams of carbon dioxide are formed?

4. (a) 5.0 moles of a gas is put into a container of 2.0 L. More gas is added to the flask so that there is now 15 moles of the gas present. What must the new volume be if temperature and pressure are to remain constant?

(b) A 7.0 L container is filled with 10.0 moles of a gas. The pressure is read at 4.00 atm, what is the temperature of the gas, in ° C?

5.(a) 3.0 L of a gas has a pressure of 12.0 atm. What is the new pressure if the gas is expanded to 17.0 L?

(b) A gas is at 135 °C and 455 mm Hg in a 2.00 L container. It is cooled down to a temperature of 25 °C. If it is kept in the same container, what is its new pressure?

6.(a) How large a balloon could you fill with 4.0 g of He gas at 22 °C and 720 mm of Hg ?

(b) Calculate the density of CO2 at 100 °C and 800 mm Hg pressure.

7. (a) A container has 3.2 g of a certain gas at NTP. What would be the mass of the same gas contained in the same vessel at 200°C and 16 atm. Pressure?

(b) A certain quantity of a gas measured 500 mL at a temperature of 15°C and 750 mm Hg. What pressure is required to compress this quantity of gas into a 400 mL vessel at a temperature of 50°C?

8. (a) Three footballs are respectively filled with N2, H2 and He. In what order are these footballs to be reinflated?

(b) The ratio of rates of diffusion of two gases A and B under same pressure is 1:4. If the ratio of their masses present in the mixture is 2:3. What is the ratio of their mole fraction in mixture?

9. (a) Calculate the rms speed in cm/sec at 25°C of a free electron and a molecule of UF6.

(b) The flask (A) and (B) have equal volumes. Flask (A) contains H2 gas at 300K, while (B) contains equal mass of CH4 at 900K. Calculate the ratio of average speed of molecules in flask (A) and (B).

10. (a) Calculate total energy of one mole of an ideal monatomic gas at 27°C?

(b) How much thermal energy should be added to 3.45 g Ne in a 10 litre flask to raise the temperature from 0°C to 100°C. (Atomic weight Ne = 20.18)?