Assuming that all of the carbon dioxide ends up in the balloon, what will be the volume of the balloon at a temperature of 27 ∘C and a pressure of 742 mmHg?

Given:

P = 742 mmHg

= 98925.2 Pa

T = 22 °C

= 295 K

R = 8.3145 J/mol. K

Molar mass of CO2, M = 12 + (16*2)

= 44 g/mol

Number of moles = mass/molar mass

= 28.8/44

= 0.655 mol.

Using ideal gas law,

PV = nRT

V = nRT/P

= 0.655 * 8.3145 * 295/98925.2

= 0.0162 m^3

The volume of the balloon would be (580.12m) cm^3

Explanation:

From the ideal gas equation,

PV = nRT

P is pressure in the balloon = 742 mmHg = 742/760 = 0.976 atm

V is the volume of the balloon

n is the number of moles of carbon dioxide in the balloon. Let the mass of carbon dioxide be m.

n = mass/MW = m/44 = (0.023m) mol

R is gas constant = 82.057 cm^3. atm/mol. K

T is temperature of the balloon = 27 °C = 27 + 273 = 300 K

V = 0.023m * 82.057 * 300/0.976 = (580.12m) cm^3