If 14.0 kilograms of Al2O3(s), 57.4 kilograms of NaOh(l), and 57.4 kilograms of HF(g) react completely, how many kilograms of cryolite will be produced?

To find out how many kilograms of cryolite will be produced, we first need to determine the balanced chemical equation for the reaction between Al2O3(s), NaOH(l), and HF(g).

The balanced chemical equation for the formation of cryolite (Na3AlF6) is:

2 Al2O3(s) + 6 NaOH(l) + 12 HF(g) → 2 Na3AlF6(s) + 6 H2O(l)

By comparing the coefficients of the reactants (Al2O3, NaOH, and HF) with the coefficients of the products (Na3AlF6), we can determine the stoichiometry of the reaction.

From the balanced equation, we see that 2 moles of Al2O3 react with 6 moles of NaOH and 12 moles of HF to produce 2 moles of Na3AlF6.

Now, we can calculate the number of moles of each reactant based on their given masses:

Number of moles of Al2O3 = mass of Al2O3 / molar mass of Al2O3
= 14.0 kg / (2 * 26.98 g/mol + 3 * 16.00 g/mol)
= 0.159 mol

Number of moles of NaOH = mass of NaOH / molar mass of NaOH
= 57.4 kg / (22.99 g/mol + 16.00 g/mol + 1.008 g/mol)
= 1.54 mol

Number of moles of HF = mass of HF / molar mass of HF
= 57.4 kg / (19.00 g/mol)
= 3.03 mol

Now, we determine the limiting reactant, which is the reactant that is completely consumed first, and it determines the maximum amount of product that can be produced.

From the balanced equation, we know that the stoichiometry of the reaction is 2:6:12, meaning that the ratio of the number of moles of Al2O3, NaOH, and HF is 2:6:12.

To find the limiting reactant, we compare the number of moles of each reactant to this ratio:

Moles of Al2O3 / 2 = 0.159 / 2 = 0.0795 mol
Moles of NaOH / 6 = 1.54 / 6 = 0.257 mol
Moles of HF / 12 = 3.03 / 12 = 0.2525 mol

The smallest value obtained is 0.0795 mol from Al2O3, so it is the limiting reactant.

Now, we can determine the number of moles of cryolite formed using the stoichiometry of the reaction:

From the balanced equation, we see that 2 moles of Al2O3 will produce 2 moles of Na3AlF6.

Therefore, the number of moles of cryolite formed is 2 * 0.0795 mol = 0.159 mol.

Finally, to find the mass of cryolite formed, we use the following equation:

Mass of cryolite = number of moles of cryolite * molar mass of cryolite
= 0.159 mol * (2 * 22.99 g/mol + 3 * 18.99 g/mol + 6 * 19.00 g/mol)
= 32.39 kg

Therefore, 32.39 kilograms of cryolite will be produced.