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__Questions Answers Set of Ideal Gas:__

__Questions Answers Set of Ideal Gas:__
1.Calculate the number of molecules present per ml of an ideal gas maintained the pressure of 7.6 × 10⁻³ mm of Hg at 0°C.

__Ans:__**2.69**×**10¹⁴ molecules per ml.**__Solution:____The Solution of this Problem Find in Two different Units.__

We are given that, V = 1 ml = 10⁻³ lit and T = 273 K.

Again, P = (7.6 × 10⁻³)/760 atm = 10⁻⁵ atm.

The Ideal Gas Equation,

**PV = nRT**
or,

**n = PV/RT**
Putting the value in this equation we have,

n = (10⁻⁵ atm × 10⁻³ lit)/(0.082 lit atm mol⁻¹ K⁻¹ × 273 K)

= 0.0447 × 10⁻⁸ mol

Hence, number of molecule per ml, N = n × NðŸ‡¦

Where, NðŸ‡¦ = 6.023 × 10²³

Thus, N = 0.0447 × 10⁻⁸ × 6.023 × 10²³

= 0.269 × 10¹⁵ Molecules

= 2.69 × 10¹⁴ Molecules

Where, NðŸ‡¦ = 6.023 × 10²³

Thus, N = 0.0447 × 10⁻⁸ × 6.023 × 10²³

= 0.269 × 10¹⁵ Molecules

= 2.69 × 10¹⁴ Molecules

__Number of Molecules Present Per ml = = 2.69 × 10¹⁴ Molecules__
We are given that, V = 1 ml = 10⁻⁶ dm³ and T = 273 K.

Again, P = 7.6 × 10⁻³mm Hg

= (7.6 × 10⁻³mm Hg) × (101325 N m⁻²/760 mm Hg)

= 101325 × 10⁻⁵ N m⁻²

= (7.6 × 10⁻³mm Hg) × (101325 N m⁻²/760 mm Hg)

= 101325 × 10⁻⁵ N m⁻²

The Ideal Gas Equation,

**PV = nRT**
or,

**n = PV/RT**
Putting the value in this equation we have,

n = (101325 × 10⁻⁵ N m⁻² × 10⁻⁶ dm³)/(8.314 J mol⁻¹ K⁻¹ × 273 K)

= 44.64 × 10⁻¹¹ mol

Hence, number of molecule per ml,

**N = n****× NðŸ‡¦**
Where, NðŸ‡¦ = 6.023 × 10²³

Thus, N = 44.64 × 10⁻¹¹ × 6.023 × 10²³

= 269 × 10¹² Molecules

= 2.69 × 10¹⁴ Molecules

2. Determine the value of gas constant R when pressure is expressed in Torr and volume in dm³.

3. Derive the value of R when, (a) pressure is expressed in

4.Estimate the number of gaseous molecules left in a volume of 1 m

5. Find the density of ammonia gas at 100°C, Confined by a pressure 1600 mm Hg.

6. When 2 gm gaseous substance A is introduced into an initially evacuated flask kept at 25°C, the pressure is found to be 106 Pa. The flask is evacuated and 3 gm of B is induced. The pressure is found to be 53 Pa at 25°C , Calculate MA/MB.

7. A certain mixture of Helium and Argon weighing 5 gm occupied of 10 d

8. A flask of 2 d

9. The specific heat at constant pressure and volume are 0.125 and 0.75 cal gm⁻¹ K⁻¹ respectively. Calculate the molecular weight and atomicity of the gas.

10. The specific heat of gas at constant volume and at constant pressure are 0.015 and 0.025 calories respectively. What is the molecular weight of the gas.

11. calculate the total kinetic energy of 0.5 mol of an ideal gas at 273 K.

12. Two vessels separately contains two ideal gases A and B at the same temperature, the pressure of A being twice that of B. Under these conditions density of A is found to be one and a half times the density of B. Find the ratio between molecular weight of A and B.

__Ans:__62.36 Torr dm³ K⁻¹ mol⁻¹3. Derive the value of R when, (a) pressure is expressed in

**atom**, and volume in**cm³**and (b) Pressure in**dyne m⁻²**and volume**mm³**.**Ans**:**(a) 82.06 atm****cm³**K⁻¹ mol⁻¹ and**(b) 8.314 × 10¹⁴****dyne m⁻²****mm³****K⁻¹ mol⁻¹**4.Estimate the number of gaseous molecules left in a volume of 1 m

**m³**if it is pumped out to give a vacuum of 10⁻⁶ mm Hg at 298 K.__Ans__:**3.240×10⁷**5. Find the density of ammonia gas at 100°C, Confined by a pressure 1600 mm Hg.

__Ans:__0.00117 gm/cc6. When 2 gm gaseous substance A is introduced into an initially evacuated flask kept at 25°C, the pressure is found to be 106 Pa. The flask is evacuated and 3 gm of B is induced. The pressure is found to be 53 Pa at 25°C , Calculate MA/MB.

__Ans:__1/37. A certain mixture of Helium and Argon weighing 5 gm occupied of 10 d

**m³**at 25°C and 101.325 pa,what is the composition of the mixture in mass percentage?__Ans:__25.24 and 74.76%8. A flask of 2 d

**m³**capacity contains oxygen at 100 Pa and 300K. The gas pressure is reduced to 0.10 pa by attaching the flask to a pump. Assuming ideal behavior, answer the following,(a)What will be the volume of the gas which is left behind?(b)What amount of oxygen and the corresponding number of molecules are left behind in the flask?(c) If now 2 gm of nitrogen is induced, what will be the pressure of the flask?__Ans:__**(a) Here we used same gas container , thus the volume of oxygen left behind will be the same that is 2 dm³.****(b) 8.019 × 10⁻⁸ mol****(c) 89.08 kPa**9. The specific heat at constant pressure and volume are 0.125 and 0.75 cal gm⁻¹ K⁻¹ respectively. Calculate the molecular weight and atomicity of the gas.

**Ans: M=40 and 1.66 mono atomic argon**10. The specific heat of gas at constant volume and at constant pressure are 0.015 and 0.025 calories respectively. What is the molecular weight of the gas.

**Ans: 198.7**11. calculate the total kinetic energy of 0.5 mol of an ideal gas at 273 K.

**Ans: 1702 J**12. Two vessels separately contains two ideal gases A and B at the same temperature, the pressure of A being twice that of B. Under these conditions density of A is found to be one and a half times the density of B. Find the ratio between molecular weight of A and B.

**Ans: 3:4**