Question

Iron was used to produce hydrogen to fill weather balloons. Find the mass of iron and volume of 5.0 M sulfuric acid required to produce enough hydrogen to fill a balloon of diameter 2.5 m at pressure 780 mm Hg and room temperature. Remember to write down reaction between iron and sulfuric acid. (Hint: recall that the volume of sphere is 4/3*Pi*r^3 , where r   is the radius of the sphere.)

Answer 1

first calculate volume of baloon

diameter of baloon = 2.5 m then redius = 2.5/2 = 1.25 m

volume of baloon = 4/3 r³  

substitue value

4/3 X 3.14159 X 1.25³ = 8.18 m³

1m³ = 1000 liter then 8.18 m³ = 8180 liter  

room tempreure = 25⁰C = 298 K

caluculate no. of mole of hydrogen required to fill baloon by using ideal gas equation

PV = nRT             where, P = atm pressure= 780 mmhg = 1.0263 atm,

V = volume in Liter = 8180 L

n = number of mole = ?

R = 0.08205L atm mol^-1 K^-1 =Proportionality constant = gas constant,

T = Temperature in K = 298 K

We can write ideal gas equation

n = PV/RT

Substitute the value

n = (1.0263 X 8180)/(0.08205 X 298) = 340.744 mole

to fill baloon 340.744 mole of H₂ required

Balanced chemical reaction is

Fe + H₂SO₄ FeSO₄ + H₂

According to reaction 1 mole of Fe produce 1 mole of H₂ therefore to produce 340.744 mole of H₂ required Fe = 340.744 mole

molar mass of Fe = 55.845 gm/mole then 340.744 mole of Fe = 340.744 X 55.845 = 19028.8 gm

19028.8 gm = 19.029 kg

19.029 Kg of Fe required

According to reaction 1 mole of H₂SO₄ produce 1 mole of H₂ therefore to produce 340.744 mole of H₂ required H₂SO₄ = 340.744 mole

volume of solution in liter = no.of mole / molarity

volume of sulfuric acid required = 340.744 / 5 = 68.15 liter

68.15 liter 5.0 M H₂SO₄ required