Answer:
The correct answer is 1.5 balloons.
Explanation:
Based on the given question, the radius of the spherical balloons is 170 cm. Therefore, the volume of each balloon will be,
= 4/3 × π × (170)³ cm³
= 20.5176 × 10⁶ cm³
= 20.5176 m³
The density of air at 100 degree C s 0.946 Kg m⁻³
The mass of air in each balloon can be calculated by using the formula,
Mass = density × volume
Mass = 0.946 Kg m⁻³ × 20.5176 m³
Mass = 19.410 Kg
The heat energy, that is, required to bring the air from 25 degree C to 100 degree C will be,
= 19.410 × 10³ g × (100 -25) degree C × 1.009 J/g degree C
= 14.68 × 10⁵ J
The concentration of butane given is 1.00 Kg or 1000 g
The molecular weight of butane is 58.12 g per mole
The moles or n can be calculated by using the formula,
n = mass / mol.wt
n = 1000 g/58.12 g/mol = 17.20 mol
The formation of enthalpy of butane at 25 degree C is 125.7 × 10³ J/mol. The evolution of heat energy that take place at the time of burning 17.20 moles of butane is,
= 125.7 × 10³ J/mol × 17.20 mol
= 2.16 × 10⁶ J
The number of balloons that can be inflated with hot air is,
= 2.16 × 10⁶ J / 14.68 × 10⁵ J per each balloon
= 1.5 balloons
Hence, maximum of 1.5 balloons can be inflated.
