# Ammonia and oxygen produce nitrogen dioxide and water. What volume of nitrogen dioxide gas will be produced if 30.5 grams of ammonia is reacted with excess oxygen?

Apr 1, 2016

40.7 L of ${\text{NO}}_{2}$ will be produced at STP.

#### Explanation:

There are four steps involved in this stoichiometry problem:

Step 1. Write the balanced chemical equation.

$\text{4NH"_3 + "7O"_2 → "4NO"_2 + "6H"_2"O}$

2. Convert grams of ${\text{NH}}_{3}$ to moles of ${\text{NH}}_{3}$

The molar mass of ${\text{NH}}_{3}$ is 17.03 g/mol.

${\text{moles of NH"_3 = 30.5 color(red)(cancel(color(black)("g NH"_3))) × ("1 mol NH"_3)/(17.03 color(red)(cancel(color(black)("g NH_3"_3)))) = "1.791 mol NH}}_{3}$

Step 3. Convert moles of ${\text{NH}}_{3}$ to moles of ${\text{NO}}_{2}$**

The molar ratio of ${\text{NO}}_{2}$ to ${\text{NH}}_{3}$ is ${\text{4 mol NO"_2:"4 mol NH}}_{3}$.

1.791 color(red)(cancel(color(black)("mol NH"_3))) × ("4 mol NO"_2)/(4 color(red)(cancel(color(black)("mol NH"_3)))) = "1.791 mol NO"_2

4. Use the Ideal Gas Law to calculate the volume of ${\text{NO}}_{2}$.

The Ideal Gas Law is

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

• $P$ = the pressure of the gas,
• $V$ = the volume of the gas,
• $n$ = the number of moles of the gas,
• $R$ = the universal gas constant
• $T$ = the temperature of the gas

You don't give the pressure or temperature of the gas, so I will assume STP (100 kPa and 0 °C).

We can rearrange the Ideal Gas Law to get

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

V = (1.791 color(red)(cancel(color(black)("mol"))) ×8.314 color(red)(cancel(color(black)("kPa")))"·L·"color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 273.15 color(red)(cancel(color(black)("K"))))/(100 color(red)(cancel(color(black)("kPa")))) = "40.7 L"

The volume of ${\text{NO}}_{2}$ is 40.7 L.

Here's a useful video on mass-volume calculations.