How many liters is 3.81 x 10e24 molecules of SO2 gas at STP

V = 141.64 L

Explanation:

Data Given:

No. of Particles = 3.81 * 10²⁴ Molecules

M. Mass of SO₂ = 64.066 g/mol

Standard Pressure = 1 atm

Standard Temperature = 273.15 K

Gas constant = 0.08205 L. atm. K⁻¹. mol⁻¹

Volume = ?

Step 1: Calculate Moles of SO₂ as;

We know that one mole is equal to 6.022 * 10²³ particles. It means,

6.022 * 10²³ molecules are contained in = 1 mole of SO₂

So,

3.81 * 10²⁴ molecules will be in = X moles of SO₂

Solving for X,

X = 3.81 * 10²⁴ molecules * 1 mol / 6.022 * 10²³ molecules

X = 6.32 moles

Step 2: Calculate Volume as;

Assuming that the gas is acting ideally we will apply ideal gas equation.

P V = n R T

Solving for V,

V = n R T / P

Putting values,

V = (6.32 mol * 0.08205 L. atm. K⁻¹. mol⁻¹ * 273.15 K) / (1 atm)

V = 141.64 L