# What is the volume of 1.00 * 10^24 g of CH_4 gas at STP?

May 27, 2016

The volume is 1.42 × 10^15color(white)(l) "km"^3.

We can convert the mass to moles of methane and then use the Ideal Gas Law to calculate the volume at STP.

Moles of ${\text{CH}}_{4}$

${\text{Moles of CH"_4 = 1.00 × 10^24 color(red)(cancel(color(black)("g CH"_4))) × ("1 mol CH"_4)/(16.04 color(red)(cancel(color(black)("g CH"_4)))) = 6.234 × 10^22 color(white)(l)"mol CH}}_{4}$

Volume at STP

The Ideal Gas Law is:

color(blue)(|bar(ul(PV = nRT)|),

where

• $P$ is the pressure
• $V$ is the volume
• $n$ is the number of moles
• $R$ is the gas constant
• $T$ is the temperature

We can rearrange the Ideal Gas Law to get

$V = \frac{n R T}{P}$

STP is 1 bar and 0 °C.

n = 6.234 × 10^22color(white)(l) "mol"
$R = \text{0.083 14 bar·L·K"^"-1""mol"^"-1}$
$T = \text{273.15 K}$
$P = \text{1 bar}$

V = (nRT)/P = (6.234 × 10^22 color(red)(cancel(color(black)("mol"))) × "0.083 14" color(red)(cancel(color(black)("bar")))·"L"· color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 273.15 color(red)(cancel(color(black)("K"))))/(1 color(red)(cancel(color(black)("bar")))) = 1.42 × 10^24 color(white)(l)"L" = 1.42 × 10^21color(white)(l) "m"^3 = 1.42 × 10^15color(white)(l) "km"^3

This is almost exactly the volume of Jupiter.