Calculate the mass of CuCO3 that decomposed to provide 11.0grams of CO2
how many moles of CO2 in 11g?
Convert that to grams of CuCO3.
To calculate the mass of CuCO3 that decomposed to provide 11.0 grams of CO2, we need to use the molar masses and stoichiometry of the reaction.
The balanced equation for the decomposition of CuCO3 is:
CuCO3 → CuO + CO2
From the equation, we can see that the molar ratio between CuCO3 and CO2 is 1:1. This means that 1 mole of CuCO3 produces 1 mole of CO2.
Step 1: Calculate the molar mass of CO2
The molar mass of CO2 is approximately 44.01 grams/mol.
Step 2: Calculate the moles of CO2
To calculate the moles of CO2, we divide the given mass (11.0 grams) by the molar mass of CO2:
moles of CO2 = mass of CO2 / molar mass of CO2
= 11.0 g / 44.01 g/mol
= 0.250 mol
Step 3: Calculate the moles of CuCO3
Since the stoichiometry of the reaction is 1:1 between CuCO3 and CO2, the moles of CuCO3 will be the same as the moles of CO2:
moles of CuCO3 = moles of CO2
= 0.250 mol
Step 4: Calculate the mass of CuCO3
To calculate the mass of CuCO3, we use the molar mass of CuCO3, which is approximately 123.55 grams/mol:
mass of CuCO3 = moles of CuCO3 * molar mass of CuCO3
= 0.250 mol * 123.55 g/mol
= 30.89 grams
Therefore, the mass of CuCO3 that decomposed to provide 11.0 grams of CO2 is approximately 30.89 grams.
To determine the mass of CuCO3 that decomposed to provide 11.0 grams of CO2, we need to understand the stoichiometry of the reaction involved. The balanced chemical equation for the thermal decomposition of CuCO3 is:
2CuCO3(s) → 2CuO(s) + CO2(g) + O2(g)
From the balanced equation, we can see that 2 moles of CuCO3 produce 1 mole of CO2.
To calculate the mass of CuCO3, we need to convert the mass of CO2 to moles, and then use the mole ratio between CuCO3 and CO2 to find the mass of CuCO3.
Here are the steps to calculate the mass of CuCO3:
1. Determine the molar mass of CO2. Carbon (C) has a molar mass of 12.01 g/mol, and oxygen (O) has a molar mass of 16.00 g/mol. Since CO2 has one carbon atom and two oxygen atoms, the molar mass of CO2 is:
Molar mass of CO2 = (1 * Molar mass of C) + (2 * Molar mass of O)
= (1 * 12.01 g/mol) + (2 * 16.00 g/mol)
= 44.01 g/mol
So, the molar mass of CO2 is 44.01 g/mol.
2. Calculate the number of moles of CO2. We can use the formula:
Number of moles = Mass / Molar mass
Given that the mass of CO2 is 11.0 grams, we can substitute these values into the formula to find the number of moles:
Number of moles of CO2 = 11.0 g / 44.01 g/mol
≈ 0.250 moles (rounded to three decimal places)
3. Use the mole ratio from the balanced equation to find the number of moles of CuCO3 that decomposed. From the balanced equation, we know that 2 moles of CuCO3 produce 1 mole of CO2. Therefore, the number of moles of CuCO3 can be calculated as:
Number of moles of CuCO3 = 0.250 moles of CO2 * (2 moles of CuCO3 / 1 mole of CO2)
= 0.500 moles
4. Finally, calculate the mass of CuCO3 using its molar mass. The molar mass of CuCO3 can be calculated by adding up the atomic masses of copper (Cu), carbon (C), and three oxygen (O) atoms:
Molar mass of CuCO3 = (1 * Atomic mass of Cu) + (1 * Atomic mass of C) + (3 * Atomic mass of O)
Substituting the atomic masses into the equation:
Molar mass of CuCO3 = (1 * 63.55 g/mol) + (1 * 12.01 g/mol) + (3 * 16.00 g/mol)
= 123.55 g/mol
Now, we can calculate the mass of CuCO3:
Mass of CuCO3 = Number of moles * Molar mass
= 0.500 moles * 123.55 g/mol
= 61.78 grams (rounded to two decimal places)
Therefore, the mass of CuCO3 that decomposed to provide 11.0 grams of CO2 is approximately 61.78 grams.