Ammonium carbonate decomposes upon heating according to the...

Ammonium carbonate decomposes upon heating according to the balanced equation: $$ \left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}(s) \rightarrow 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ Calculate the total volume of gas produced at $22{ }^{\circ} \mathrm{C}$ and $1.02 \mathrm{~atm}$ by the complete decomposition of $11.83 \mathrm{~g}$ of ammonium carbonate.

Ammonium carbonate decomposes upon heating according to the balanced equation:
$$
\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}(s) \rightarrow 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)
$$
Calculate the total volume of gas produced at $22{ }^{\circ} \mathrm{C}$ and $1.02 \mathrm{~atm}$ by the complete decomposition of $11.83 \mathrm{~g}$ of ammonium carbonate.

Key Concepts

Reaction Stoichiometry

This concept involves using a balanced chemical equation to relate the number of moles of reactants to the number of moles of products. It is essential for determining how much of each product is formed from a given amount of a reactant.

Molar Mass Calculation

Calculating the molar mass of a compound allows one to convert between the mass of a substance and the number of moles. This conversion is critical in quantitative chemistry to bridge the gap between measured mass and chemical quantities.

Ideal Gas Law

The ideal gas law (PV = nRT) links pressure, volume, temperature, and the number of moles of a gas. It is used to predict and calculate the behavior of gases under various conditions, making it a fundamental tool in gas volume calculations.

Temperature Conversion

Converting temperatures from Celsius to Kelvin is necessary when applying the ideal gas law, as the gas law requires absolute temperature measurements to accurately relate the physical properties of gases.

Transcript

00:01 All right, so in this question, we've got the decomposition of ammonium carbonate to produce ammonium gas, carbon dioxide, and water paper.

00:11 All right, so given that we have 11 .83 grams of ammonium carbonate, what's the total volume of gas that can be produced? okay, so first thing we're going to do is convert that to moles, the grams, to moles, because it's always a good thing to deal with these kind of questions in molar quantities.

00:27 So i've got 11 .83 grams.

00:32 I'm just going to multiply that by its molar, or divide that by its molar mass.

00:36 So that's one mole per 96 .094 grams.

00:45 All right, grams cancel, giving me only moles and giving me a grand total of 0 .1231 moles.

00:54 And that's going to be of the solid.

00:57 Okay, so if you look at that, one mole of the solid, if you look at the balanced equation, gives me 2 moles of ammonium, 1 mole of carbon dioxide, and 1 mole of water.

01:07 So for every 1 mole of solid, i actually have 4 moles of gas that's being produced.

01:11 So i can do 4 and then times 0 .123 1 to give me the moles of gas involved, and that's 0 .49 to 4 moles.

01:24 All right, so now it's important to remember that we can, we don't have to break this up to being how much volume does the ammonia produce versus the carbon dioxide versus the water, because these are all particles and we can treat all particles kind of the same using the ideal gas law and its assumptions...

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