QuestionA $52.6 \mathrm{~cm}^{3}$ ethanol-water solution has a mass of $50.2 \mathrm{~g}$ . Find the ethanol percentage by mass.

Studdy Solution

STEP 1

Assumptions1. The volume of the ethanol-water solution is $52.6 \mathrm{~cm}^{3}$ . The mass of the ethanol-water solution is $50. \mathrm{~g}$
3. The density of ethanol is $0.789 \mathrm{~g} / \mathrm{cm}^{3}$
4. The density of water is $0.998 \mathrm{~g} / \mathrm{cm}^{3}$
5. There is no change in volume when the pure compounds are mixed

STEP 2

We can find the volume of ethanol in the solution using the total volume and the volume of water. The volume of water can be found by subtracting the mass of ethanol from the total mass of the solution.
$Volume\, of\, water = (Total\, mass - Mass\, of\, ethanol) / Density\, of\, water$

STEP 3

We can find the mass of ethanol by subtracting the mass of water from the total mass of the solution.
$Mass\, of\, ethanol = Total\, mass - Mass\, of\, water$

STEP 4

The mass of water can be found by multiplying its volume by its density.
$Mass\, of\, water = Volume\, of\, water \\times Density\, of\, water$

STEP 5

Substitute the expression for the volume of water from step2 into the equation from step4.
$Mass\, of\, water = ((Total\, mass - Mass\, of\, ethanol) / Density\, of\, water) \\times Density\, of\, water$

STEP 6

implify the equation from step5 to find the mass of water.
$Mass\, of\, water = Total\, mass - Mass\, of\, ethanol$

STEP 7

Substitute the expression for the mass of water from step6 into the equation from step3.
$Mass\, of\, ethanol = Total\, mass - (Total\, mass - Mass\, of\, ethanol)$

STEP 8

implify the equation from step7 to find the mass of ethanol.
$Mass\, of\, ethanol =2 \\times Mass\, of\, ethanol - Total\, mass$

STEP 9

Rearrange the equation from step8 to solve for the mass of ethanol.
$Mass\, of\, ethanol = Total\, mass /2$

STEP 10

Substitute the given values into the equation from step9 to find the mass of ethanol.
$Mass\, of\, ethanol =50.2 \mathrm{~g} /2$

STEP 11

Calculate the mass of ethanol.
$Mass\, of\, ethanol =25. \mathrm{~g}$

STEP 12

The percentage of ethanol by mass can be found by dividing the mass of ethanol by the total mass and multiplying by100.
$Percentage\, of\, ethanol = (Mass\, of\, ethanol / Total\, mass) \\times100\%$

STEP 13

Substitute the given values into the equation from step12 to find the percentage of ethanol.
$Percentage\, of\, ethanol = (25. \mathrm{~g} /50.2 \mathrm{~g}) \\times100\%$

STEP 14

Calculate the percentage of ethanol.
$Percentage\, of\, ethanol =50\%$ The percentage of ethanol in the solution is50%.

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