Ethyl alcohol has been added to 190 {\rm mL} of water in a container that has a mass of 140 {\rm g} when empty. The resulting container and liquid mixture has a mass of 450 {\rm g}.
What volume of alcohol was added to the water?
Express your answer using two significant figures.
330 mL is water and container.
120 mL of ethyl alcohol was added.
Divide that mass by the alcohol density for the volume of alcohol added.
To find the volume of alcohol added to the water, we need to determine the mass of alcohol in the container and then convert it to volume using the density of alcohol.
First, let's calculate the mass of the alcohol by subtracting the mass of the empty container from the mass of the container with the liquid mixture:
Mass of alcohol + water = Mass of container and liquid mixture - Mass of empty container
Mass of alcohol + 190 mL water = 450 g - 140 g
Mass of alcohol + 190 mL water = 310 g
Now, since we know the mass of the alcohol + water mixture, we can find the mass of the alcohol alone by subtracting the mass of the water:
Mass of alcohol = Mass of alcohol + water - Mass of water
Mass of alcohol = 310 g - (190 mL × density of water)
The density of water is approximately 1 g/mL, so the mass of alcohol becomes:
Mass of alcohol = 310 g - (190 mL × 1 g/mL)
Mass of alcohol = 310 g - 190 g
Mass of alcohol = 120 g
Now that we have the mass of the alcohol, we can convert it to volume using the density of ethyl alcohol. The density of ethyl alcohol is approximately 0.79 g/mL:
Volume of alcohol = Mass of alcohol / Density of alcohol
Volume of alcohol = 120 g / 0.79 g/mL
Calculating this division:
Volume of alcohol ≈ 151.9 mL
Therefore, the volume of alcohol added to the water is approximately 151.9 mL, rounded to two significant figures.