# A gas sitting in a 5L container at 12 degrees celcius at 3atm, how many moles do you have?

Jul 9, 2018

A bit over half a mole....

#### Explanation:

We simply solve the Ideal Gas equation...

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

$= \frac{3 \cdot a t m \times 5.0 \cdot L}{0.0821 \cdot \frac{L \cdot a t m}{K \cdot m o l} \cdot \left(12 + 273.15\right) \cdot K}$

=??*mol...

Jul 9, 2018

$0.641435498778218 \setminus \approx 0.641 \setminus \setminus \textrm{m o \le s}$

#### Explanation:

From ideal gas equation

$P V = n R T$

where:

• $P$ is absolute pressure of gas

• $V$ is volume of gas

• $n$ is number of moles of gas

• $R = 8.314 \setminus \setminus \textrm{\frac{J}{m} o \le K}$ is universal gas constant.

• $T$ is absolute temperature of gas

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

Setting the values

• $P = 3 \setminus \text{atm"=3 xx 101325\ "Pa}$,

• $V = 5 \setminus {\text{L"=5 xx 10^{-3}\ "m}}^{3}$

• $R = 8.314 \setminus \setminus \textrm{\frac{J}{m} o \le K}$

• $T = {12}^{0} \text{C"=12+273=285\ "K}$

we get, the number of moles

$n = \setminus \frac{3 \setminus \times 101325 \setminus \times 5 \setminus \times {10}^{- 3}}{8.314 \setminus \times 285}$

$= 0.641435498778218 \setminus \setminus \textrm{m o \le s}$

$\setminus \approx 0.641 \setminus \setminus \textrm{m o \le s}$

Jul 10, 2018

You have $\text{0.6 mol}$ of gas.

#### Explanation:

Use the ideal gas law equation:

$P V = n R T$,

where:

$P$ is pressure, $V$ is volume, $n$ is moles, $R$ is the gas constant, and $T$ is the temperature in Kelvins.

Known

$P = \text{3 atm}$

$V = \text{5 L}$

$R = {\text{0.08206 L atm K"^(-1) "mol}}^{- 1}$

$T = \text{12"^@"C + 273.15"="285 K}$

Unknown

$n$

Solution

Rearrange the equation to isolate moles. Plug in the known values and solve.

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

n=(3color(red)cancel(color(black)("atm"))xx5color(red)cancel(color(black)("L")))/(0.08206color(red)cancel(color(black)("L")) color(red)cancel(color(black)("atm")) color(red)cancel(color(black)("K"))^(-1) "mol"^(-1)xx285color(red)cancel(color(black)("K")))="0.6 mol"
(rounded to one significant figure)