# How many molecules are in 30 liters of methane CH_4 at STP?

Feb 22, 2017

Moles x Avogadro's number.

#### Explanation:

Pv=nrt is the equation to use, and as we have the excercise already giving us STP we can calculate it as we know that temperature is 273 Kelvin and Pressure is 100000 Pa. We want to find n so let's make it the subject of our formula.

$n = \frac{p v}{r t}$ where p is pressure in pa, v is volume in m cubed, R is the gas constant =(8.31) and T is temperature in kelvin.
The calculation becomes= $\frac{100000 \cdot 0.03}{8.31 \cdot 273} = 1.322383994$

0.03 Is our volume because 30 liters is the same as $30 {\mathrm{dm}}^{3}$ and in the equation we must have it in ${m}^{3}$ so we need to divide by 1000 to get to the correct unit.

So then the amount of molecules is equal to that number times Avogadro's number.

$1.322383994 \cdot \left(6.022 \cdot {10}^{23}\right) = 7.964 \cdot {10}^{23}$ molecules in the sample.