Question

1.) If 41.5 moles of an ideal gas occupies 36.5 liters at 485 K, what is the pressure of the gas?

2.) A flexible container at an initial volume of 5.12 L contains 3.51 mol of gas. More gas is then added to the container until it reaches a final volume of 17.9 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container?      Answer: Number ____________________ mol

3.) A hot air balloon is filled with 1.47 x 10^6L of an ideal gas on a cool morning (11 C). The air is heated to 129 C. What is the volume of the air in rhe balloon after it is heated? Assume that none of the gas escapes ffrom the balloon?       Answer: Number _______________ L

Answer 1

1) Ideal gas equation, PV = nRT

where, P = pressure of the gas

V = volume of the gas

n = number of moles of gas

R = Gas constant

T = Temperature

P = nRT/V

P = (41.5 * 0.0821*485) / 36.5

1652/36.5

P = 45.2atm

2)

PV = nRT

V1/V2 = n1/n2

V1 = 5.12 L

n1 = 3.51 mole

V2 = 17.9 L

n2 = ?

V1/V2 = n1/n2

5.12/17.9=3.51/n2

0.286=3.51/n2

n2 = 3.51 / 0.286 = 12.27 mole

There the number of moles of gas added are 12.27 mole - 3.51 mole = 8.76 mole

Therefore number of moles of gas added = 8.76 mole

3)

given,

initial volume v1 = 1.47 * 10^6 L

initial temperature T1 = 11 degree or 284 K

final temperature T2 = 129 degree or 402 K

V1 / T1 = V2 / T2

(1.47 × 10^6) / 284 = V2 / 402

V2 = 2 * 10^6 L

volume of gas after it is heated = 2 * 10^6 L