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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주요 개념

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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.

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.