Question

In 1897 the Swedish explorer Andreé 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
Fe(s)+ H2SO_4(aq) -----> FeSO4(aq) + H2(g)
The volume of the balloon was 4800 m^3, and the loss of hydrogen gas during filling was estimated at 20.%. What mass of iron splints and 98% (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

Answer 1

Answer:

$m_{Fe}=59.79x10^6gFe\\m_{H_2SO_4}=107.1511x10^6gH_2SO_4$

Explanation:

Hello,

Based on the given data, the corresponding moles of hydrogen to fill the balloon without loss is:

$n_{H_2}=\frac{PV}{RT}=\frac{1.0atm*4.8x10^6L}{0.082\frac{atm*L}{mol*K}*273.15K} =214302.2molH_2$

Now, considering the 20% loss of hydrogen, the amount that ensured the complete filling was:

$n_{H_2}=\frac{214302.2molH_2}{0.2}=1071511molH_2$

Based on that result, we proceed to computed the amounts of both iron and 98% by mass sulfuric acid that were needed to ensure the complete filling of the balloon as follows:

$m_{Fe}=1071511molH_2*\frac{1molFe}{1molH_2} *\frac{55.8gFe}{1molFe} =59.79x10^6gFe\\m_{H_2SO_4}=1071511molH_2*\frac{1molH_2SO_4}{1molH_2} *\frac{98gH_2SO_4}{1molH_2SO_4}*\frac{100gH_2SO_4}{98gH_2SO_4} =107.1511x10^6gH_2SO_4$

Best regards.