Question

Enter your answer in the provided box. Roasting galena [lead(II) sulfide] is an early step in the industrial isolation of lead. How many liters of sulfur dioxide, measured at STP, are produced by the reaction of 5.05 kg of galena with 123 L of oxygen gas at 220°C and 2.00 atm

Answer 1

Answer : The volume of $SO_2$ produced are 90.7 liters.

Explanation :

The balanced chemical reaction will be:

$2PbS+3O_2\rightarrow 2PbO+2SO_2$

First we have to calculate the moles of PbS.

$\text{Moles of }PbS=\frac{\text{Mass of }PbS}{\text{Molar mass of }PbS}$

Molar mass of PbS = 239.26 g/mole

$\text{Moles of }PbS=\frac{5.05kg}{239.26}=\frac{5.05\times 1000g}{239.26}=21.1mole$

Now we have to calculate the moles of $O_2$ by using ideal gas equation.

Using ideal gas equation :

$PV=nRT$

where,

P = Pressure of $O_2$ gas = 2.00 atm

V = Volume of $O_2$ gas = 123 L

n = number of moles  $O_2$ = ?

R = Gas constant = $0.0821L.atm/mol.K$

T = Temperature of $O_2$ gas = $220^oC=273+220=493K$

Putting values in above equation, we get:

$2.00atm\times 123L=n\times (0.0821L.atm/mol.K)\times 493K$

$n=6.07mole$

The number of moles of $O_2$ is, 6.07 mole

Now we have to calculate the limiting and excess reagent.

From the balanced reaction we conclude that

As, 3 mole of $O_2$ react with 2 mole of $PbS$

So, 6.07 moles of $O_2$ react with $\frac{6.07}{3}\times 2=4.05$ moles of $PbS$

From this we conclude that, $PbS$ is an excess reagent because the given moles are greater than the required moles and $O_2$ is a limiting reagent and it limits the formation of product.

Now we have to calculate the moles of $SO_2$

From the reaction, we conclude that

As, 3 mole of $O_2$ react to give 2 mole of $SO_2$

So, 6.07 moles of $O_2$ react to give $\frac{6.07}{3}\times 2=4.05$ moles of $SO_2$

Now we have to calculate the volume of $SO_2$ produced at STP.

As, 1 mole of $SO_2$ contains 22.4 L volume of $SO_2$

So, 4.05 mole of $SO_2$ contains $4.05\times 22.4=90.7L$ volume of $SO_2$

Therefore, the volume of $SO_2$ produced are 90.7 liters.