Question

In 1897 the Swedish explorer Andree tried to reach the North Pole in a balloon. The balloon was filled with hydrogen gas. The hydrogen gas was prepared from iron splints and diluted sulfuric acid. The reaction is given below.Fe(s) + H2SO4(aq) FeSO4(aq) + H2(g)The volume of the balloon was 4870 m3 and the loss of hydrogen gas during filling was estimated at 20.%. What mass of iron splints and 95% (by mass) H2SO4 were needed to ensure the complete filling of the balloon? Assume a temperature of 0°C, a pressure of 1.0 atm during filling, and 100% yield.iron splints = ____kg95% sulfuric acid =_____kg

Answer 1

Answer:

iron = 15000 kg 95% sulfuric acid = 27646.32 kg

Explanation:

The molar volume to a gas is 22.4 L, which means that a mole of a given gas at 0°C and 1 atm will have a volume os 22.4 L.

1 m3 - 1000 L

4870 m3 - x

x = 4870 * 1000 = 4.87 *10^6 L

1 mole - 22.4 L

y mole - 4.87 * 10^6 L

y = $\frac{4.87 * 10^6}{22.4}$ = 2,17 *10^5 moles (if 100% of the H2 is used)

as 20% of it is lost, we need to know how much more we need to use.

80% - 2.17 * 10^5 moles

100% - z

z = $\frac{2.17* 10^7}{80}$ = 2,68*10^5 moles

so we would need 2.68*10^5 moles of iron and sulfuric acid.

1 mole of iron - 56 *10^-3 kg

2.68*10^5 moles - t

t= 2.68*56 *10^2 = 15000 kg

1 mole of sulfuric acid - 98 * 10^-3 kg

2.68*10^5 - u

u = 2.68*98 *10^2 = 26264 kg (if 100%)

95% - 26264 kg

100% - v

v = $\frac{26264 * 100}{95}$ = 27646.32 kg