Question

Cryolite, Na3AlF6(s), an ore used in the production of aluminum, can be synthesized using aluminum oxide. Balance the equation for the synthesis of cryolite.

Equation: Al2O3(s) + NaOH(l) + HF(g) --------> Na3AlF6 + H2O(g)
1. If 15.8 kg of Al2O3(s), 55.4 kg of NaOH(l), and 55.4 kg of HF(g) react completely, how many kilograms of cryolite will be produced?

Answer 1

Answer: The mass of cryolite produced is 65.06 kg

Step-by-step explanation:

To calculate the number of moles, we use the equation:

`\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}` .....(1)

• For aluminium oxide:

Given mass of aluminium oxide = 15.8 kg = 15800 g (Conversion factor: 1 kg = 1000 g)

Molar mass of aluminium oxide = 102 g/mol

Putting values in equation 1, we get:

`\text{Moles of aluminium oxide}=(15800g)/(102g/mol)=154.9mol`

For the given chemical reaction:

`Al_2O_3(s)+6NaOH(l)+12HF(g)\rightarrow 2Na_3AlF_6+9H_2O(g)`

As all the reactants are getting completely utilized. So, the amount of product can be determined by any 1 of the reactant.

By Stoichiometry of the reaction:

1 mole of aluminium oxide produces 2 moles of cryolite

So, 154.9 moles of aluminium oxide produces =
`(2)/(1)* 154.9=309.8mol` of cryolite

Now, calculating the mass of cryolite by using equation 1, we get:

Moles of cryolite = 309.8 moles

Molar mass of cryolite = 210 g/mol

Putting values in equation 1, we get:

`309.8mol=\frac{\text{Mass of cryolite}}{210g/mol}\\\\\text{Mass of cryolite}=(309.8mol* 210g/mol)=65058g=65.06kg`

Hence, the mass of cryolite produced is 65.06 kg