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What volume of hydrogen gas (in liters) did he produce for this flight? Assume the...

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What volume of hydrogen gas (in liters) did he produce for this flight?

Assume the pressure is 1 atm and the temperature is 22°C.

Jaques Charles used the reaction of hydrochloric acid on iron to produce the hydrogen for one of his balloons. For one flight in 1783 he used 1,000 lbs. (1 lb. = 454 g) of iron with an excess of acid (this means iron was the limiting reactant).

Fe(s) + 2 HCl(aq) --> FeCl2(aq) + H2(g)

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Since iron is the limiting reagent we can assume that it is completely consumed in the reaction with HCl to produce hydrogen gas.  First we convert the amount of iron from pounds to moles (the MW of iron is 55.845 gram/mole):

1000 lbs iron*(454 grams/1 lb)*(1 mole/55.845 grams)=8129.64 moles of iron.

We can see from the balanced chemical equation above that 1 mole of iron produces 1 mole of hydrogen gas:

8129.64 moles iron = 8129.64 moles H2.

We can now insert this value into the gas law equation PV=nRT.  The value of R using atm for pressure is 0.0821 L atm/mol K and 22 degrees C is equal to 295.15 Kelvin.  Solving for volume:

V=(nRT)/P=[(8129.64 moles)*(0.0821 L atm/mol K)*(295.15 K)]/1 atm=196995.93 liters of hydrogen gas.

The volume of H2 gas produced is 196,995.93 liters.


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