# Question 73c3c

Jul 14, 2017

23,5 L

#### Explanation:

50 g of sodium azide $N a {N}_{3}$ (MM= 71g/mol) , correspond to $\frac{50 g}{71 \frac{g}{m o l}} = 0 , 70 m o l .$,

From the balanced reaction you can see that from 2 mol of $N a {N}_{3}$ you obtain 3 mole of ${N}_{2}$ so, making the proportion, from 0,70 mol you can obtain 1,05 mol of nitrogen.

As 1 mol of any gas occupies a volume of 22,4 L in normal condition (P= 1 atm and T= 273K), 1,05 mol occupy $22 , 4 \frac{L}{m o l} \times 1 , 05 m o l = 23 , 5 L$

Jul 15, 2017

The volume of nitrogen is C) ${\text{27.7 dm}}^{3}$

#### Explanation:

The balanced chemical equation is

$\text{2NaN"_3 → "3N"_2 + "2Na}$

Step 1. Calculate the moles of ${\text{NaN}}_{3}$

${\text{Moles of NaN"_3 = 50 color(red)(cancel(color(black)("g NaN"_3))) × "1 mol NaN"_3/(65.01 color(red)(cancel(color(black)("g NaN"_3)))) = "0.769 mol NaN}}_{3}$

Step 2. Calculate the moles of ${\text{N}}_{2}$

${\text{Moles of N"_2 = 0.769 color(red)(cancel(color(black)("mol NaN"_3))) × "3 mol N"_2/(2 color(red)(cancel(color(black)("mol NaN"_3)))) = "1.15 mol N}}_{2}$

Step 3. Calculate the volume of ${\text{N}}_{2}$

We aren't given the volume or the temperature, so we will have to make an assumption.

Let's assume NTP (1 atm and 20 °C).

Then we can use the Ideal Gas Law to calculate the volume:

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} p V = n R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

We can rearrange the Ideal Gas Law to get

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

In this problem,

$n = \text{1.15 mol}$
$R = \text{0.082 06 dm"^3·"atm·K"^"-1""mol"^"-1}$
$T = \text{(20 + 273.15) K = 293.15 K}$
$p = \text{1 atm}$

V = (1.15 color(red)(cancel(color(black)("mol"))) × "0.082 06 dm"^3·color(red)(cancel(color(black)("atm"·"K"^"-1"·"mol"^"-1"))) × 293.15 color(red)(cancel(color(black)("K"))))/(1 color(red)(cancel(color(black)("atm")))) = "27.7 dm"^3#

Note: The answer should have only two significant figures, because that is all you gave for the mass of sodium azide.

However, I calculated to three significant figures, because that is the answer in
Option C.