Uranium metal can be produced by the reaction of uranium tetrafluoride
(UF4) with magnesium (Mg) in a sealed reactor heated to 700oC. The by-product is
magnesium fluoride (MgF2). To ensure that all the magnesium is consumed in the
reaction, the reactor is charged with excess UF4, specifically 10% more than the
stoichiometric requirement of the reaction. To produce 222 kg of U, how much UF4
must be introduced into the reactor? Assume complete conversion of Mg. Express
your answer in kg.
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You want 222 Kg U so you will need 222 x (atomic mass U/molar mass UF4) = ? to start.
Then a 10% excess of that will be
? + 0.1*? = ??
To determine the amount of UF4 needed to produce 222 kg of uranium (U), we need to calculate the stoichiometric requirement of the reaction.
First, we need to find the molar mass of uranium (U) and uranium tetrafluoride (UF4):
- The molar mass of uranium (U) is approximately 238 g/mol.
- The molar mass of uranium tetrafluoride (UF4) can be calculated as follows:
- The molar mass of one uranium atom is approximately 238 g/mol.
- The molar mass of four fluorine atoms is 4 * 19 g/mol = 76 g/mol.
- Therefore, the molar mass of UF4 is 238 g/mol + 76 g/mol = 314 g/mol.
Next, we need to determine the ratio of moles between uranium (U) and UF4 in the reaction. From the balanced equation:
UF4 + 2Mg → U + 2MgF2
The ratio from the reaction is 1:1, so one mole of UF4 will produce one mole of uranium (U).
Now, we can calculate the moles of uranium (U) needed to produce 222 kg:
- The molar mass of uranium (U) is 238 g/mol.
- To convert kg to grams, we multiply by 1000.
- Therefore, the mass of uranium (U) needed is (222 kg * 1000 g/kg) / (238 g/mol) = 933.61 mol.
Since we know that the stoichiometric ratio is 1:1, we need the same number of moles of UF4:
- The moles of UF4 needed is also 933.61 mol.
Finally, we can calculate the mass of UF4 needed:
- The molar mass of UF4 is 314 g/mol.
- Therefore, the mass of UF4 needed is (933.61 mol) * (314 g/mol) = 293,010.54 g.
To express the answer in kg, we divide by 1000:
- The mass of UF4 needed is 293.01 kg.
Therefore, to produce 222 kg of uranium, approximately 293.01 kg of UF4 must be introduced into the reactor.