A density bottle weighs 0.25 and when empty and 0.75 when filled with water and 0.65 and when filled with alcohol. Calculate
1. The volume of the bottle
2. The density of the alcohol
I presume you are using the density of water as 1.00 g/cc. Also I assume those numbers are in grams.
0.75 g = mass empty bottle + H2O
-0.25 g = mass empty bottle
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0.50 g = mass water in the density bottle
volume of density bottle = mass/density = 0.50 g/1.00 g/cc = 0.50 cc
0.65 g = mass empty bottle + alcohol
-0.25 g = mass empty bottle
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0.40 g = mass alcohol
density alcohol = mass alcohol/volume alcohol = 0.40/0.50 = 0.80 g/cc
I don't know what "weighs 0.25" means. I'll assume 0.25kg = 250g, and you can revise the solution as needed to fit your interpretation.
if water has density 1g/cm^3 then the bottle holds 500cm^3
so the alcohol has density (650-250)/500 = 0.8 g/cm^3
To calculate the volume of the bottle, we can use the principle of buoyancy. The weight of the liquid displaced by the bottle when it is filled with water or alcohol is the difference in weight between the filled and empty bottle.
1. Volume of the bottle:
The weight difference between the filled bottle and empty bottle with water is 0.75 - 0.25 = 0.5 grams.
The weight difference between the filled bottle and empty bottle with alcohol is 0.65 - 0.25 = 0.4 grams.
Since density is defined as mass per unit volume, we can calculate the volume using the formula:
Volume = Mass / Density
For water:
Volume = 0.5 grams / 1 g/cm^3 = 0.5 cm^3
For alcohol:
Volume = 0.4 grams / Density of alcohol
2. Density of alcohol:
Density of alcohol = Mass / Volume
Density of alcohol = 0.4 grams / 0.5 cm^3 = 0.8 g/cm^3
Therefore:
1. The volume of the bottle is 0.5 cm^3.
2. The density of the alcohol is 0.8 g/cm^3.
To calculate the volume of the bottle and the density of the alcohol, we can use the formulas for density and volume.
1. Volume of the Bottle:
The volume of the bottle can be determined by finding the difference between its filled and empty weights. The weight of the water and the alcohol can be used to calculate the volume.
Empty Weight: 0.25
Weight filled with water: 0.75
Weight filled with alcohol: 0.65
To find the volume, subtract the empty weight from the weight of the liquid (water or alcohol).
Volume of the bottle filled with water: 0.75 - 0.25 = 0.50 (the units could be any, as long as they are consistent throughout the calculation).
Volume of the bottle filled with alcohol: 0.65 - 0.25 = 0.40
Therefore, the volume of the bottle is 0.50 units when filled with water and 0.40 units when filled with alcohol.
2. Density of the Alcohol:
The density can be calculated by dividing the mass of the substance (alcohol) by its volume. Since we already know the volume and the weight of the alcohol, we can determine its density.
Weight of alcohol: 0.65
Volume of the bottle filled with alcohol: 0.40
Density of alcohol = Weight of alcohol / Volume of alcohol
Density of alcohol = 0.65 / 0.40
Hence, the density of the alcohol is 1.625 (units based on the units used for weight and volume).