Question

How can I find the volume of 3.0 x 10(25) molecules of Neon gas at STP?

Answer 1

The answer is `1100L`.

In order to determine the volume of `Ne` gas at STP, you need to know that at STP (standard temperature and pressure), `1` mole of any ideal gas occupies exactly `22.4L`.

We must however find out how many moles of `Ne` we are dealing with. We do this by using Avogadro's number - `6.022 * 10^(23)` -, which tells us how many molecules are in `1` mole of a substance.

`(3.0 * 10^(25) mol ecu l e s)* (1 mol e)/(6.022 * 10^(23) mol ecu l es) = 49.8`

moles; this means that `3.0 * 10^(25)` molecules make up `49.8` moles of `Ne` gas.

We can now find out the volume by using

`n_(Ne) = V/V_(mol ar) -> V = n_(Ne) * V_(mol ar)`

`V = 49.8 mol es * 22.4 L/( mol e) = 1100L` -> rounded to two sig figs.

Answer 2

You can determine the volume of `"3.0 x 10"^25"` molecules of Neon at STP using the ideal gas law: `"PV"` = `"nRT"`, solving for V. You must convert the molecules of Neon to moles using Avagadro's number, `"6.022 x 10"^23`. STP for gas laws is `"0"^"o""C"` and 1 atm. You will need to convert the Celsius temperature to Kelvins, which is the temperature scale used in the gas laws.

Convert molecules of Neon to moles.

`"3.0 x 10"^25` `"molecules Ne"` x `"1 mol Ne"` `/` `"6.022 x 10"^23 "molecules Ne"` = `"49.82 moles Ne"`
(I'm leaving some guard units to reduce rounding errors.)

Given/Known:
P = 1 atm
n = 49.82 moles
R = `"0.08205746 L atm K"^(-1) "mol"^(-1)`
T = `"0"^"o""C" + "273.15" = "273.15K"`

Unknown:
Volume

Equation:
`"PV"` = `"nRT"`

Solution:
Divide both sides of the equation by P. Solve for V.

`"V"` = `"nRT"/"P"`
`"V"` = `"49.82 moles x 0.08205746 L atm K"^(-1) "mol"^(-1)"` x `"273.15K/1 atm"` = `"1100 L"`
(The answer is rounded to two significant figures because `"3.0 x 10"^25` has two significant figures.)

Answer:
The volume of `"3.0 x 10"^25` `"molecules Ne"` at STP is `"1100 L"`.