Question

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 3.73 kg of galena with 170. L of oxygen gas at 220°C and 2.00 atm? Lead(II) oxide also forms.

Answer 1

Answer: The volume of sulfur dioxide measured at STP is 125.44 L

Step-by-step explanation:

• For galena:

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

`\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}`

Given mass of galena = 3.73 kg = 3730 g (Conversion factor: 1 kg = 1000 g)

Molar mass of galena = 239.3 g/mol

Putting values in above equation, we get:

`\text{Moles of galena}=(3730g)/(239.3g/mol)=15.59mol`

• For oxygen gas:

To calculate the amount of oxygen gas, we use the equation given by ideal gas which follows:

`PV=nRT`

where,

P = pressure of the gas = 2.00 atm

V = Volume of the gas = 170 L

T = Temperature of the gas =
`220^oC=[220+273]K=493K`

R = Gas constant =
`0.0821\text{ L. atm }mol^(-1)K^(-1)`

n = number of moles of oxygen gas = ?

Putting values in above equation, we get:

`2.00atm* 170L=n* 0.0821\text{ L. atm }mol^(-1)K^(-1)* 493\\\\n=(2.00* 170)/(0.0821* 493)=8.4mol`

The chemical equation for the reaction of lead (II) sulfide and oxygen gas follows:

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

By Stoichiometry of the reaction:

3 moles of oxygen gas reacts with 2 moles of galena

So, 8.4 moles of oxygen gas will react with =
`(2)/(3)* 8.4=5.6mol` of galena

As, given amount of lead (II) sulfide is more than the required amount. So, it is considered as an excess reagent.

Thus, oxygen gas is considered as a limiting reagent because it limits the formation of product.

By Stoichiometry of the reaction:

3 moles of oxygen gas produces 2 moles of sulfur dioxide

So, 8.4 moles of oxygen gas will produce =
`(2)/(3)* 8.4=5.6moles` of sulfur dioxide

At STP:

1 mole of a gas occupies 22.4 L of volume

So, 5.6 moles of sulfur dioxide will occupy =
`(22.4L)/(1mol)* 5.6mol=125.44L` of volume

Hence, the volume of sulfur dioxide measured at STP is 125.44 L