Question

The density of ethanol, C 2H 5OH, is 0.789 g/mL. How many milliliters of ethanol are needed to produce 25.0 g of CO 2 according to the following chemical equation?

C 2H 5OH( l) + 3 O 2( g) → 2 CO 2( g) + 3 H 2O( l)

Answer 1

11.1mL

Step-by-step explanation:

The reaction expression is given as:

C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O

Given parameters:

density of ethanol = 0.789g/mL

mass of CO₂ = 25g

Unknown:

Volume of ethanol = ?

Solution:

First find the number of moles of the CO₂ from the given mass;

Number of moles =
`(mass)/(molar mass)`

Molar mass of CO₂ = 12 + 2(16) = 44g/mol

Number of moles =
`(25)/(44)` = 0.57mol

Then;

Find the number of moles of ethanol used;

3 moles of CO₂ is produced from 1 mole of ethanol;

0.57mole of CO₂ will be produced from
`(0.57)/(3)` = 0.19mole of ethanol

Now;

Find the mass of the ethanol from the given mole;

Mass of ethanol = number of moles x molar mass

Molar mass of ethanol = 2(12) + 5(1) + 16 + 1 = 46g/mol

Mass of ethanol = 0.19 x 46 = 8.74g

Then;

Density is the mass per unit volume of a substance;

Density =
`(mass)/(volume)`

Volume =
`(mass)/(density)`

Volume =
`(8.74)/(0.789)` = 11.1mL