In 1783, the French physicist Jacques Charles supervised and took part in the fi
ID: 983722 • Letter: I
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)?
Explanation / Answer
(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 R3 cm3
Volume of the balloon = volume of the gas inside the balloon
Therefore, 4/3 R3 = 75337000
R3 = (3/4) (75337000) / = 17978147.7273
R = 261.96 = 262
The radius of the balloon is 262 cm.