# Question #fc002

Dec 14, 2017

$P = 4.70 a t m$

#### Explanation:

Alright, so we are going to use the ideal gas law to solve this one. That law simply states that

$P V = n R T$

In this equation, $P$ is pressure in atm
$V$ is volume in liters
$n$ is the amount of gas in moles
$R$ is a constant equal to $\frac{0.08206 L \cdot a t m}{K \cdot m o l}$
And finally, $T$ is temperature in kelvin

So we are trying to solve for $P$, so we need that on one side of the equation. We can do that by just dividing by $V$

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

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

Ok, at this point lets start plugging variables in.

$V = 10.0 L$

$P = \frac{n R T}{10.0 L}$

To convert ${C}^{o} \to K$ we just add 273

$K = {C}^{o} + 273$

$K = {200}^{o} C + 273$

$T = 473 K$

$P = \frac{n \cdot R \cdot 473 K}{10.0 L}$

Now for the tricky part. We need to convert 32g of ${C}_{2} {H}_{6}$ into moles. To do this we must first find the molar mass of ${C}_{2} {H}_{6}$, then convert 32g to moles.

The molar mass is going to equal $\frac{30.07 g}{m o l}$ because we simply add the atomic mass of both elements:

$C = 12.0107 \cdot 2$
$H = 1.00794 \cdot 6$
....................................
$\frac{30.07 g}{m o l}$

So now we need to find out how much moles 32g is

$n = \frac{m o l}{30.07 g} \cdot 32 g$

$n = \frac{m o l}{30.07 \cancel{g}} \cdot 32 \cancel{g}$

$n = \frac{32 m o l}{30.07}$

$n = 1.1 m o l$

Ok, lets plug that in and the constant $\left(R\right)$. I'd like to note that I like to put the constant outside the equations as it makes it a lot easier.

$P = \frac{n \cdot R \cdot 473 K}{10.0 L}$

$P = \frac{1.1 m o l \cdot 473 K}{10.0 L} \frac{0.08206 L \cdot a t m}{K \cdot m o l}$

This is the fun part, were you cancel out all the conversion names. NOTE: since you are looking to $P$, we should have $a t m$ left over at the end

$P = \frac{1.1 \cancel{m o l} \cdot 473 \cancel{K}}{10.0 \cancel{L}} \frac{0.08206 \cancel{L} \cdot a t m}{\cancel{K} \cdot \cancel{m o l}}$

Now, finally, we just solve! Notice that atm is all that left....

$P = \frac{1.1 \cdot 473 \cdot 0.08206 \cdot a t m}{10.0}$

$P = 4.70 a t m$

Hope this helped! If you have any more questions feel free to ask them!

~Chandler Dowd