# Question #6dd9c

Mar 1, 2015

You will produce $2.28 \cdot {10}^{19}$ molecules of ammonia from that much hydrogen gas.

Start with the balanced chemical reaction for the synthesis reaction of ammonia from nitrogen gas and hydrogen gas

${N}_{2} + 3 {H}_{2} \to 2 N {H}_{3}$

Now, it's much easier to first determine how many moles of ammonia are produced, and then convert the moles into molecules.

Notice that you have a $\text{3:2}$ mole ratio between hydrogen gas and ammonia; what this means is that every 3 moles of hydrogen will produce 2 moles of ammonia.

The number of moles of hydrogen that react is

$1.15 \cdot {10}^{- 4} \text{g" * "1 mole hydrogen"/"2.02 g" = 5.69 * 10^(-5)"moles hydrogen}$

Using the aforementioned mole ratio, we know that this many moles of hydrogen will produce

$5.69 \cdot {10}^{- 5} \text{moles hydrogen" * "2 moles ammonia"/"3 moles hydrogen" = 3.79 * 10^(-5)"moles ammonia}$

Now to express the number of moles as number of molecules. By definition, 1 mole of any substance or element contains exactly $6.022 \cdot {10}^{23}$ molecules or atoms of that substance or element.

If you look at the number of moles of ammonia, you'll notice that it's much smaller than 1, which means that you'll get fewer than $6.022 \cdot {10}^{23}$ molecules of ammonia produced.

$3.79 \cdot {10}^{- 5} \text{moles" * (6.022 * 10^(23)"molecules")/"1 mole" = 2.28 * 10^(19)"molecules ammonia}$

So, to summarize

1. Write the balanced chemical equation;
2. Establish the mole ratio that exists between hydrogen and ammonia;
3. Calculate the number of moles of hydrogen given;
4. Calculate the number of moles of ammonia produced;
5. Convert the moles into number of molecules by using Avogadro's number, $6.022 \cdot {10}^{23}$ molecules per mole.