Find the number of "CO"_2 that exert a pressure of "785 torr" at a volume of "32.5 L" and a temperature 32^@"C"?

find the number of co2 that exert a pressure of 785torrs at a volume of 32.5L and a temperature 32c ?

Feb 25, 2016

${\text{1.3 moles CO}}_{2}$

Explanation:

I'm assuming that the question wants you to determine the number of moles of carbon dioxide, ${\text{CO}}_{2}$, that would occupy that volume under those specific conditions for pressure and temperature.

Your tool of choice here will be the ideal gas law equation

$\textcolor{b l u e}{P V = n R T} \text{ }$, where

$P$ - the pressure of the gas
$V$ - the volume it occupies
$n$ - the number of moles of gas
$R$ - the universal gas constant, equal to $0.0821 \left(\text{atm" * "L")/("mol" * "K}\right)$
$T$ - the absolute temperature of the gas

Now, the problem provides you with everything that you need in order to solve for the number of moles of gas. However, notice that some of the units used in the expression of $R$ do not match those given to you.

This means that you're going to have to do a couple of units conversions to get your units to match those used in expression of $R$. The conversion factors you'll need are

$\text{1 atm " = " 760 torr}$

$t \left[\text{K"] = 273.15 + t [""^@"C}\right]$

Rearrange the ideal gas law equation to solve for $n$

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

Plug in your values to get

n = (785/760color(red)(cancel(color(black)("atm"))) * 32.5color(red)(cancel(color(black)("L"))))/(0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 32)color(red)(cancel(color(black)("K")))) = "1.3399 moles"

Rounded to two sig figs, the number of sig figs you have for the temperature of the gas, the answer will be

$n = \textcolor{g r e e n}{{\text{1.3 moles CO}}_{2}}$