A sample of 6.022 x 1023 particles of gas has a volume of 22.4 L at 0°C and a pressure of 1.000 atm. Although it may seem silly to contemplate, what volume would 1 particle of gas occupy?

pv=nRT

1 particle of the gas would occupy a volume of 3.718*10⁻²³L

Explanation:

Hello,

1. The sample has a particle of 6.022*10²²particles

2. Volume of the sample = 22.4L

3. Temperature of the sample = 0°C = (0 + 273.15) K = 273.15K

4. Pressure of the sample = 1.0atm

What volume would 1 particle of the gas occupy?

But we remember that 1 mole of any substance = 6.022*10²² molecules or particles or atoms

What would be the number of moles for 1 particule?

1 mole = 6.022*10²² particles

X moles = 1 particle

X = (1 * 1) / 6.022*10²² particles

X = 1.66*10⁻²⁴ moles

Therefore, 1 particle contains 1.66*10⁻²⁴ moles

Since we know our number of moles, we can proceed to use ideal gas equation,

Ideal gas equation holds for all ideal gas and is defined as

PV = nRT

P = pressure of the ideal gas

V = volume the gas occupies

n = number of moles of the gas

R = ideal gas constant = 0.082 L. atm / mol. K

T = temperature of the gas

PV = nRT

Solving for V,

V = nRT / P

We can now plug in our values into the above

equation.

V = (1.66*10⁻²⁴ * 0.082 * 273.15) / 1

V = 3.718*10⁻²³L

Therefore, 1 particule of the gas would occupy a volume of 3.718*10⁻²³L.