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QuestionHow many grams of calcium carbonate are required to produce 2.2 grams of carbon dioxide from the reaction?

Studdy Solution

STEP 1

Assumptions1. The reaction is balanced and proceeds to completion. . The molar mass of calcium carbonate (CaCO3) is approximately100.09 g/mol.
3. The molar mass of carbon dioxide (CO) is approximately44.01 g/mol.
4. The mass of carbon dioxide produced is22. g.

STEP 2

First, we need to find the number of moles of carbon dioxide produced. We can do this by dividing the mass of carbon dioxide by its molar mass.
Moles of CO2=Mass of CO2Molar mass of CO2Moles\, of\, CO2 = \frac{Mass\, of\, CO2}{Molar\, mass\, of\, CO2}

STEP 3

Now, plug in the given values for the mass of carbon dioxide and the molar mass of carbon dioxide to calculate the moles of carbon dioxide.
Moles of CO2=22.2 g44.01 g/molMoles\, of\, CO2 = \frac{22.2\, g}{44.01\, g/mol}

STEP 4

Calculate the number of moles of carbon dioxide.
Moles of CO2=22.2 g44.01 g/mol=0.504 molMoles\, of\, CO2 = \frac{22.2\, g}{44.01\, g/mol} =0.504\, mol

STEP 5

According to the balanced chemical equation, one mole of calcium carbonate produces one mole of carbon dioxide. Therefore, the number of moles of calcium carbonate needed is the same as the number of moles of carbon dioxide produced.
Moles of CaCO3=Moles of CO2Moles\, of\, CaCO3 = Moles\, of\, CO2

STEP 6

Plug in the calculated number of moles of carbon dioxide to find the number of moles of calcium carbonate needed.
Moles of CaCO3=0.504 molMoles\, of\, CaCO3 =0.504\, mol

STEP 7

Now, we can find the mass of calcium carbonate needed by multiplying the number of moles of calcium carbonate by its molar mass.
Mass of CaCO3=Moles of CaCO3timesMolar mass of CaCO3Mass\, of\, CaCO3 = Moles\, of\, CaCO3 \\times Molar\, mass\, of\, CaCO3

STEP 8

Plug in the values for the number of moles of calcium carbonate and the molar mass of calcium carbonate to calculate the mass of calcium carbonate.
Mass of CaCO3=0.504 moltimes100.09 g/molMass\, of\, CaCO3 =0.504\, mol \\times100.09\, g/mol

STEP 9

Calculate the mass of calcium carbonate needed.
Mass of CaCO3=.504 moltimes100.09 g/mol=50.44 gMass\, of\, CaCO3 =.504\, mol \\times100.09\, g/mol =50.44\, gApproximately50.44 grams of calcium carbonate are needed to form22.2 grams of carbon dioxide.

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