# How many atoms or molecules are there in 200.0 mL of sulfur dioxide gas?

Jun 27, 2014

There are 5.373 × 10²¹ molecules of SO₂ and 1.620 × 10²² atoms in 200.0 mL of the gas.

You don't give the temperature and pressure, so I will assume that the gas is at STP — 0 °C and 1 atm.

You use the Ideal Gas Law to calculate the number of moles of SO₂.

$P V = n R T$

$T$ = (0 + 273.15) K = 273.15 K

$n = \frac{P V}{R T} = \left(1 \text{atm" × 0.2000"L")/(0.082 06"L·atm·K⁻¹mol⁻¹" × 273.15"K}\right)$ = 8.922 72 × 10⁻³ mol

(4 significant figures + 2 guard digits)

The number of molecules is

8.922 72 × 10⁻³ mol × (6.022 × 10²³"molecules")/(1"mol") = "5.373 26 × 10²¹" molecules = 5.373 × 10²¹ molecules (4 significant figures)

Each molecule contains 3 atoms — 1 S atom and 2 O atoms.

The number of atoms is

5.373 26 ×10²¹ molecules × $\left(3 \text{atoms")/(1"molecule}\right)$ = "1.619 88 × 10²²" atoms = 1.620 × 10²² atoms

Hope this helps.