Question

When coal is burned, the sulfur present in coal is converted to sulfur dioxide (SO2), which is responsible for the acid rain phenomenon. S(s) + O2(g) → SO2(g) If 4.10 kg of S are reacted with oxygen, calculate the volume of SO2 gas (in mL) formed at 30°C and 1.16 atm.

Answer 1

Answer : The volume of $SO_2$ gas is, $2.75\times 10^6mL$

Explanation : Given,

Mass of S = 4.10 kg = 4100 g      (1 kg = 1000 g)

Molar mass of S = 32 g/mol

First we have to calculate the moles of S.

$\text{Moles of }S=\frac{\text{Given mass }S}{\text{Molar mass }S}=\frac{4100g}{32g/mol}=128.125mol$

Now we have to calculate the moles of $SO_2$

The balanced chemical reaction is:

$S(s)+O_2(g)\rightarrow SO_2(g)$

From the balanced reaction, we conclude that

As, 1 mole of $S$ react to give 1 mole of $SO_2$

So, 128.125 mole of $S$ react to give 128.125 mole of $SO_2$

Now we have to calculate the volume of $SO_2$ by using ideal gas equation.

$PV=nRT$

where,

P = Pressure of $SO_2$ gas = 1.16 atm

V = Volume of $SO_2$ gas = ?

n = number of moles $SO_2$ = 128.125 mole

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

T = Temperature of $SO_2$ gas = $30^oC=273+30=303K$

Putting values in above equation, we get:

$1.16atm\times V=128.125mole\times (0.0821L.atm/mol.K)\times 303K$

$V=2747.65L=2.75\times 10^6mL$     (1 L = 1000 mL)

Therefore, the volume of $SO_2$ gas is, $2.75\times 10^6mL$