Question

The first step in the process used to recover zinc metal from zinc sulfide ore is the reaction of zinc sulfide with oxygen gas to produce zinc oxide and sulfur dioxide. 2ZnS(s) 3O2(g)⟶2ZnO(s) 2SO2(g) When the external pressure is 1.523×105 Pa and the temperature is 675 K, the amount of work performed is 850.1 J. Calculate how many grams of oxygen are consumed in the reaction.

Answer 1

Answer : The mass of oxygen consumed in the reaction is 14.6 grams.

Explanation :

First we have to calculate the change in moles of oxygen.

Formula used :

$w=\Delta nRT$

or,

$\Delta n=\frac{w}{RT}$

where,

w = work done = 850.1 J

$\Delta n$ = change in moles of gas = ?

R = gas constant = 8.314 J/mol.K

T = temperature = 675 K

Now put all the given values in the above formula, we get:

$\Delta n=\frac{850.1J}{(8.314J/mol.K)\times (675K)}=0.152mol$

Now we have to calculate the mass of oxygen consumed.

The balanced chemical reaction is,

$2ZnS(s)+3O_2(g)\rightarrow 2ZnO(s)+2SO_2(g)$

Here, the volume changes of solids can be ignored.

From the balanced chemical reaction, we conclude that

The number of moles oxygen required for the complete reaction = 3

Change in mole of oxygen = 0.152 mol

Molar mass of $O_2$ = 32 g/mol

So,

The mass of oxygen consumed = 3 x 0.152 mol x 32 g/mol = 14.6 g

Therefore, the mass of oxygen consumed in the reaction is 14.6 grams.