Question

what is the mass of bismuth carbonate (597.99 g/mol) that decomposes to release 50.0ml of carbon dioxide gas at stp?

Answer 1

To find the mass of bismuth carbonate that decomposed to release 50.0 ml of CO₂ at STP, the volume of CO₂ is first converted to moles and then used to calculate the mass based on stoichiometry, yielding approximately 0.445 grams.

Step-by-step explanation:

To calculate the mass of bismuth carbonate that decomposes to release 50.0 ml of carbon dioxide gas at STP, we first need to convert the volume of CO₂ to moles. At STP (standard temperature and pressure), 1 mole of any gas occupies 22.414 liters. Therefore, we can calculate the moles of CO₂ by dividing the volume of CO₂ by the molar volume of a gas at STP:

1. Convert 50.0 ml to liters: 50.0 ml × (1 L / 1000 ml) = 0.0500 L
2. Calculate moles of CO₂: 0.0500 L / 22.414 L/mol = 0.00223 mol CO₂

The decomposition reaction for bismuth carbonate (Bi₂(CO₃)₃) to carbon dioxide is as follows:

Bi₂(CO₃)₃ (s) → Bi₂O₃ (s) + 3CO₂ (g)

From the stoichiometry of the reaction, we can see that 1 mole of bismuth carbonate produces 3 moles of CO₂. Therefore, we can determine the moles of bismuth carbonate:

1. Moles of Bi₂(CO₃)₃ = 0.00223 mol CO₂ / 3 = 0.000744 mol Bi₂(CO₃)₃
2. Calculate mass of Bi₂(CO₃)₃: 0.000744 mol × 597.99 g/mol = 0.445 g

The mass of bismuth carbonate that decomposed is therefore approximately 0.445 grams.

Answer 2

To find the mass of bismuth carbonate that decomposes to produce 50.0 mL of CO₂ at STP, first calculate the moles of CO₂, then use stoichiometry to find moles and finally mass of bismuth carbonate. The calculated mass is 0.445 g.

Step-by-step explanation:

To determine the mass of bismuth carbonate that decomposes to release 50.0 mL of carbon dioxide gas at STP, we must first convert the volume of CO₂ to moles using the molar volume of a gas at STP, which is 22.414 L/mol. Since 50.0 mL is 0.0500 L, we calculate the moles of CO₂ released:

Moles CO₂ = 0.0500 L / 22.414 L/mol = 0.002232 mol CO₂

The stoichiometry of the decomposition reaction of bismuth carbonate (Bi₂(CO₃)₃) to bismuth oxide (Bi₂O₃), carbon dioxide (CO₂), and water (H₂O) is:

Bi₂(CO₃)₃(s) → Bi₂O₃(s) + 3CO₂(g) + H₂O(g)

From the stoichiometry, for every mole of bismuth carbonate that decomposes, 3 moles of CO₂ are released. We can solve for the moles of Bi₂(CO₃)₃:

Moles Bi₂(CO₃)₃ = 0.002232 mol CO₂ × (1 mol Bi₂(CO₃)₃ / 3 mol CO₂) = 0.000744 mol Bi₂(CO₃)₃

The molar mass of Bi₂(CO₃)₃ is given as 597.99 g/mol. So, we can calculate the mass:

Mass of Bi₂(CO₃)₃ = 0.000744 mol × 597.99 g/mol = 0.445 g