# Numerical Problems | Gaseous State

### Numerical Problems : LEVEL-I

Question : 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 ?

Ans: (a) 2840 kPa ; (b) -36 °C

Question: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.

Ans: (a) 1500 mm Hg

Question :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?

Ans: (a) -120 °C ; (b) (i) 4.1 L (ii) 110.1 L (iii) 107 g

Question :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?

Ans: (a) 6.0 L ; (b) -240 °C

Question :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?

Ans: (a) 2.1 atm ; (b) 332 mm Hg

Question :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.

Ans: (a) 25.65 litre ; (b) 1.5124 g/litre

Question :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?

Ans: (a) 1.3184 g ; (b) 1051 mm

Question :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?

Ans: (a) H2 > He > N2
(b) 1:24

Question :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).

Ans: (a) 1.16 × 107 cm/sec
(b) 1.632

Question :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)?

Ans:( a) 900 cals
(b) 51.29 cal

### Numerical Problems : LEVEL-II

Question :1.(a) 0 grams of oxygen gas are put in a 4.50 L container at 35 °C. What is the pressure, in kPa ?

(b) A gas in a piston is heated up. If the pressure remains the same, what will happen to the volume ? Why ?

Ans: (a) 2750 kPa

Question :2. You went on a road trip to Mumbai (sea level) from New Delhi and made sure to check out your car before leaving. The tire pressures were at the recommended levels and your oil was full. You are driving fast through Jaipur (but not above the speed limit of course) and need to stop for petrol. You decide to check your car’s tire pressure while stopped. The driver’s manual suggests a pressure between 30 and 32 pa.

(a) Knowing that the tires heat up during driving, do you expect your reading to be high, low or the same as the recommended tire pressures? Why?

(b) You arrive in Mumbai that night. The next morning you check your tire pressure. Since you plan on staying in Mumbai a while to see the sights, what adjustments, if any, should be made to your tires ?

Question : 3. In a certain experiment a sample of helium in a vacuum system was compressed at 25 °C from a volume of 200.0 mL to a volume of 0.240 mL where its pressure was found to be 30.0 mm Hg. What was the original pressure of the helium ?

Ans: 0.0360 mm Hg

Question : 4. A hydrogen gas volume thermometer has a volume of 100.0 cm3 when immersed in an ice-water bath at 0 °C. When immersed in boiling liquid chlorine, the volume of the hydrogen at the same pressure is 87.2 cm3. Find the temperature of the boiling point of chlorine in °C.

Ans: -35 °C

Question :5.  2.50 grams of XeF4 is introduced into an evacuated 3.00 liter container at  80.0 °C. Find the pressure in atmospheres in the container.

Ans: 0.117 atm

Question :6. (a) Two flasks of equal volume connected by a narrow tube (of negligible volume) are at 27°C and contain 0.7 moles of H2 at 0.5 atm. One of the flask is then immersed into a bath kept at 127°C, while the other remains at 27°C. Calculate the final pressure and the number of moles of H2 is each flask.

(b) 1 gm of an alloy of Al and Mg reacts with excess HCl to form AlCl3, MgCl2 and H2. The evolved H2 collected over mercury at 0°C occupied 1200 ml at 699 mm Hg. What is the composition of alloy ?

Ans: (a) 0.571 atm , 0.3 and 0.4 moles
(b) 45.25% Mg , 54.75% Al

Question :7. (a) Ladenburg found that a sample of ozonised oxygen containing 86.16% of O3 by weight required 430 secs to diffuse under conditions where pure O2 required 369.5 secs. Determine the vapour density of O3.

(b) The normal density of PH3 at 0°C and at different pressure are

P (atm)            1                      3/4                   1/2                   1/4

d/P (gm/lit)      1.5307             1.5272             1.5238             1.5205

Calculate the molecular weight of PH3 and atomic weight of P

Ans: (a) 23.3
(b) 30.98

Question :8. Assuming O2  molecule spherical in shape and occupying the radius 150 pm. Calculate

(i) the volume of single molecule of gas

(ii) the percentage of empty space in one mole of O2 at NTP

Ans: 1.41 × 1023 cc/molecule , 99.96%

Question :9.  9 volumes of gaseous mixture consisting of gaseous organic compound A and just sufficient amount of O2 required for complete combustion yielded on burning 4 volumes of CO2, 6 volumes of water vapour and 2 volumes of N2 all volumes measured at the same temperature and pressure. If the compound A contained only C, H and N

(i) how many volumes of O2 required for complete combustion?

(ii) What is the molecular formula of the compound A ?