If the density of ethanol, C2H5OH, is 0.789 g/mL. How many milliliters of ethanol are needed to produce 15.0 g of CO2 according to the following chemical equation? C2H5OH (l) + 3 O2 (g) → 2 CO2 (g) + 3 H2O (l)

9.94 mL, the volume of ethanol needed

Explanation:

The reaction is:

C₂H₅OH (l) + 3 O₂ (g) → 2 CO₂ (g) + 3 H₂O (l)

We convert the mass of the formed product to moles:

15 g. 1mol / 44g = 0.341 moles

2 moles of dioxide are produced by 1 mol of ethanol, in order to stoichiometry.

Therefore, 0.341 moles of CO₂ must be produced by (0.341. 1) / 2 = 0.1705 moles of alcohol.

We convert the moles to mass, and then, the mass to volume by the use of density.

0.1705 mol. 46 g / 1 mol = 7.84 g of ethanol

Ethanol density = Ethanol mass / Ethanol volume

Ethanol volume = Ethanol mass / Ethanol density → 7.84 g / 0.789 g/mL =

9.94 mL

We need 9.95 mL of ethanol

Explanation:

Step 1: Data given

Density ethanol = 0.789 g/mL

Mass CO2 produced = 15.0 grams

Step 2: The balanced equation

C2H5OH (l) + 3 O2 (g) → 2 CO2 (g) + 3 H2O (l)

Step 3: Calculate moles CO2

Moles CO2 = mass CO2 / molar mass CO2

Moles CO2 = 15.0 grams / 44.01 g/mol

Moles CO2 = 0.341 moles

Step 4: Calculate moles ethanol

For 1 mol ethanol, 3 moles we need O2 to produce 2 moles CO2 and 3 moles H2O

For 0.341 moles CO2 we need 0.341 / 2 = 0.1705 moles ethanol

Step 5: Calculate mass ethanol

Mass ethanol = moles ethanol * molar mass ethanol

Mass ethanol = 0.1705 moles * 46.07 g/mol

Mass ethanol = 7.85 grams

Step 6: Calculate volume ethanol

Volume ethanol = mass / density

Volume = 7.85 grams / 0.789 g/mL

Volume = 9.95 mL

We need 9.95 mL of ethanol