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QuestionWhen 20.4 g20.4 \mathrm{~g} of carbon reacts with oxygen, 11.6 g11.6 \mathrm{~g} of oxygen remains. Find the mass of carbon dioxide produced.

Studdy Solution

STEP 1

Assumptions1. The initial mass of carbon is 20.4 g20.4 \mathrm{~g} . The initial mass of oxygen is 11.6 g11.6 \mathrm{~g}
3. The reaction is complete, leaving no carbon unreacted4. The reaction is as follows C+O→COC + O \rightarrow CO
5. The molar mass of carbon (C) is 12.01 g/mol12.01 \mathrm{~g/mol}
6. The molar mass of oxygen () is 16.00 g/mol16.00 \mathrm{~g/mol}
7. The molar mass of carbon dioxide (CO) is 44.01 g/mol44.01 \mathrm{~g/mol}

STEP 2

First, we need to find out how much oxygen reacted with the carbon. We do this by subtracting the remaining oxygen from the initial amount.
Reacted O2=Initial O2−Remaining O2Reacted\, O2 = Initial\, O2 - Remaining\, O2

STEP 3

Now, plug in the given values for the initial and remaining oxygen to calculate the reacted oxygen.
Reacted O2=11.6 g−11.6 gReacted\, O2 =11.6 \mathrm{~g} -11.6 \mathrm{~g}

STEP 4

Calculate the mass of the reacted oxygen.
Reacted O2=11.6 g−11.6 g=0 gReacted\, O2 =11.6 \mathrm{~g} -11.6 \mathrm{~g} =0 \mathrm{~g}

STEP 5

Since no oxygen reacted, all the carbon must have reacted with the oxygen already present in the air to form carbon dioxide. Therefore, the mass of carbon dioxide produced is equal to the initial mass of carbon.
Mass of CO2=Initial mass of CMass\, of\, CO2 = Initial\, mass\, of\, C

STEP 6

Plug in the value for the initial mass of carbon to find the mass of carbon dioxide.
Mass of CO2=20.4 gMass\, of\, CO2 =20.4 \mathrm{~g}The mass of carbon dioxide produced is 20.4 g20.4 \mathrm{~g}.

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