Ammonium carbonate decomposes upon heating according to the balanced equation: (NH 4 ) 2 CO 3 (s) → 2 NH 3 (g) + CO 2 (g) + H 2 O(g) Calculate the total volume of gas produced at 22 °C and 1.02 atm by the complete decomposition of 11.83 g of ammonium carbonate.

Hey everyone. So we have the following reaction that shows the decomposition of ammonium carbonate and at 28°C and 1.24 atmosphere test to determine the total volume of gas form 15.26 g of ammonium carbonate. That's completely decomposed total total number of malls. He goes to molds of NH three, that's one more Of c. 0. 2. That's one more Of H 20. And this will give us a total of four moles of gas. So now we need to convert from grams of ammonium carbonate, two moles of gas. We have 15.26 grams of ammonia carbonate. And in one mole that the Mueller mass, it's gonna be too. I'm 14.007 g plus eight Times 1.008g as well. 011 g plus three Times 15.999 gramps. Give us 96.086 g. And in one mole of ammonia carbonate, They're four moles of gas. This will give us 0.63 53 balls of gas. So now we can use the ideal gas out to find the total volume. It's going to be PB It goes N R. T. The pressure is 1.24 atmosphere. The volume is what we're looking for Number of moles. 0.6353. Our constant is 0.08 21. There's some atmosphere about about malls. I'm Calvin And the temperature is 28 degrees Celsius. We need to convert our temperature into Calvin 28°C. We need to add 273.15. This will give us 301 15 kelvin. So now we can put the values into the equation and solve for the volume. It's going to give us 1.24 atmosphere terms of volume Equals 0.63 malls From 0.08 later. Sounds atmosphere. What about moles and kelvin? I'm staying in one 15 kelvin. We get 1.24 times of volume. It was 15.707. So if we divide both sides by 1.24, We get a volume of 12.7 L. Thanks for watching my video and I hope it was helpful.

Ch.6 - Gases

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Problem 115

Chapter 6, Problem 115

Ammonium carbonate decomposes upon heating according to the balanced equation: (NH₄)₂CO₃(s) → 2 NH₃(g) + CO₂(g) + H₂O(g) Calculate the total volume of gas produced at 22 °C and 1.02 atm by the complete decomposition of 11.83 g of ammonium carbonate.

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Determine the molar mass of ammonium carbonate, \((NH_4)_2CO_3\), by adding the atomic masses of its constituent elements.

Calculate the number of moles of ammonium carbonate using the formula: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\).

Use the stoichiometry of the balanced equation to find the total moles of gas produced. According to the equation, 1 mole of \((NH_4)_2CO_3\) produces 2 moles of \(NH_3\), 1 mole of \(CO_2\), and 1 mole of \(H_2O\), totaling 4 moles of gas.

Apply the ideal gas law, \(PV = nRT\), to calculate the total volume of gas. Use \(R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1}\), \(T = 22^\circ C = 295 \text{ K}\), and \(P = 1.02 \text{ atm}\).

Solve for \(V\) in the ideal gas law equation: \(V = \frac{nRT}{P}\), using the total moles of gas calculated in step 3.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on balanced equations. It allows us to determine the amount of substances consumed and produced in a reaction. In this case, it helps to find out how many moles of gas are generated from the decomposition of ammonium carbonate.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the volume of gases produced in a reaction under specific conditions. In this problem, it will be used to find the total volume of gas produced from the moles calculated from stoichiometry.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is crucial for converting between grams of a substance and moles, which is necessary for stoichiometric calculations. For ammonium carbonate, knowing its molar mass allows us to determine how many moles are present in the given mass, facilitating further calculations.

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Molar Mass Concept

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Ammonium carbonate decomposes upon heating according to the balanced equation: (NH4)2CO3(s) → 2 NH3(g) + CO2(g) + H2O(g) Calculate the total volume of gas produced at 22 °C and 1.02 atm by the complete decomposition of 11.83 g of ammonium carbonate.

Verified Solution

Key Concepts

Stoichiometry

Ideal Gas Law

Molar Mass

Ammonium carbonate decomposes upon heating according to the balanced equation: (NH₄)₂CO₃(s) → 2 NH₃(g) + CO₂(g) + H₂O(g) Calculate the total volume of gas produced at 22 °C and 1.02 atm by the complete decomposition of 11.83 g of ammonium carbonate.