Question

In 1783, the French physicist Jacques Charles supervised and took part in the first human flight in a hydrogen balloon. Such balloons rely on the low density of hydrogen relative to air for their buoyancy. In Charles’s balloon ascent, the hydrogen was produced (together with iron(II) sulfate) from the reaction of aqueous sulfuric acid on iron filings. (a) Write a balanced chemical equation for this reaction. (b) What volume of hydrogen is produced at 300 K and a pressure of 1.0 atm when 300 kg sulfuric acid is consumed in this reaction? (c) What would be the radius of a spherical balloon filled by the gas in part (b)?

Answer 1

(a) The balanced chemical equation for the reaction is:

Fe(s) + H₂SO₄(aq) = H₂(g) + FeSO₄(aq)

(c) According to the balanced chemical equation, the mole ratio of H₂SO₄ and H₂ = 1 : 1

Mass of sulfuric acid consumed in the reaction = 300 Kg = 300000 g

Moles of sulfuric acid consumed in the reaction = (300000/ 98.079) mol = 3058.75 mol   

[Since molar mass of sulfuric acid = 98.079 g /mol]

Moles of H₂ gas produced in the reaction = 3058.75 mol [ Since the mole ratio is 1 : 1]

According to the gas equation, PV = nRT

Here, n = moles of the gas produced = 3058.75 mol

P = pressure of the gas = 1.0 atm

T = temperature of the gas = 300 K

R = Universal gas constant = 0.0821 L.atm/ K.mol

Therefore, V = nRT / P

V = (3058.75 mol) (0.0821 L.atm/K.mol) (300 K) / (1.0 atm) = 75337 L = 75337000 cm³

(c) Let the radius of the spherical balloon be R cm.

Volume of the balloon = 4/3 π R³ cm³

Volume of the balloon = volume of the gas inside the balloon

Therefore, 4/3 π R³ = 75337000

R³ = (3/4) (75337000) / π = 17978147.7273

R = 261.96 = 262

The radius of the balloon is 262 cm.