Animated Solution for Chemistry - Basic Concepts in Chemistry: The mass of ammonia in grams produced when $2.8\text{ kg}$ of dinitrogen quantitatively reacts with $1\text{ kg}$ of dihydrogen is ......... .

Haber's Recipe

Imagine you are a chemical chef, and you are about to cook up a batch of ammonia. The recipe you need is the classic Haber process.

We start by writing down the balanced chemical equation:

This equation is our master blueprint. It tells us that exactly one mole of nitrogen gas reacts with three moles of hydrogen gas to produce two moles of ammonia.

But in the real world, we don't measure things in moles on a weighing scale; we measure them in grams and kilograms. So, let's translate this recipe into masses.

The molar mass of nitrogen ($N_2$) is $28\text{ g/mol}$, and for hydrogen ($H_2$), it is $2\text{ g/mol}$. Since we need three moles of hydrogen, that's $6\text{ g}$ in total.

This means our baseline stoichiometric ratio is: $28\text{ g}$ of nitrogen requires exactly $6\text{ g}$ of hydrogen to produce $34\text{ g}$ of ammonia.

Who Runs Out First?

Now, let's look at the ingredients we actually have in our pantry. The problem gives us $2.8\text{ kg}$ of nitrogen and $1.0\text{ kg}$ of hydrogen.

In chemistry, just like in cooking, you usually run out of one ingredient before the other. The one that runs out first is called the limiting reagent, and it completely dictates how much product you can make.

To find the limiting reagent, let's ask a simple question: How much hydrogen do we actually need to completely react with our $2.8\text{ kg}$ of nitrogen?

Using the unitary method based on our recipe:

Calculating this gives us exactly $0.6\text{ kg}$ of hydrogen.

But wait! We have $1.0\text{ kg}$ of hydrogen available. Since we only need $0.6\text{ kg}$, we have an excess of hydrogen.

This confirms that nitrogen is our limiting reagent. It will be completely consumed, and it will determine the final yield of ammonia.

Grams, Not Kilograms!

Since nitrogen is in the driver's seat, we base our final calculation entirely on it.

Our recipe told us that $28\text{ g}$ of nitrogen yields $34\text{ g}$ of ammonia. Therefore, $2.8\text{ kg}$ of nitrogen will yield:

This beautifully simplifies to $3.4\text{ kg}$ of ammonia.

But here is where many students fall into a classic trap! The examiner specifically asked for the mass of ammonia in grams.

To convert kilograms to grams, we simply multiply by $1000$:

And there we have it! A perfect $3400\text{ g}$ of ammonia produced. Always remember to double-check the units requested in the question to secure your hard-earned marks!