an empty density bottle weighs 25 gram. when completely filled with water, it weighs 55 gram and when completely filled with a liquid, it weighs 52 gram. calculate volume and density of the bottle.
To calculate the volume and density of the bottle, we need to understand the definitions and formulas involved.
1. Volume: Volume refers to the amount of space occupied by a substance. It can be calculated by using the formula:
Volume = Weight in Air / Density of the Substance
2. Density: Density is a measure of how much mass is contained in a given volume of a substance. It can be calculated by using the formula:
Density = Mass / Volume
Now, let's calculate the volume of the empty density bottle:
Given:
- Weight of the empty bottle = 25 grams
Since the bottle is empty, it does not contain any substance. Therefore, the weight of the bottle in the air is equal to its weight.
Volume of the empty density bottle = Weight in Air / Density of the Substance
= 25 grams / Density of the Substance
To calculate the density of the bottle, we need more information. Let's proceed with the given information about the bottle filled with water:
Given:
- Weight of the bottle when filled with water = 55 grams
Now, subtracting the weight of the empty bottle from the weight of the filled bottle gives us the weight of the water:
Weight of the water = Weight of the filled bottle - Weight of the empty bottle
= 55 grams - 25 grams
= 30 grams
Next, we can calculate the volume of the water using the formula:
Volume of the water = Weight of the water / Density of water
Since the density of water is normally 1 gram/cm³, we can substitute the values:
Volume of the water = 30 grams / 1 gram/cm³
= 30 cm³
Finally, let's calculate the density of the bottle filled with the other liquid:
Given:
- Weight of the bottle when filled with the liquid = 52 grams
As before, we subtract the weight of the empty bottle:
Weight of the liquid = Weight of the filled bottle - Weight of the empty bottle
= 52 grams - 25 grams
= 27 grams
Now, we can calculate the volume of the liquid:
Volume of the liquid = Weight of the liquid / Density of the liquid
Since we don't have the density of the liquid provided, we cannot calculate the exact volume and density without that information.
Therefore, we can calculate the volume of the bottle, but without the density of the liquid, we cannot calculate its density.
To calculate the volume and density of the bottle, we can use the following formulas:
1. Density = Mass / Volume
2. Volume = Mass / Density
Given information:
- Weight of the empty bottle = 25 grams (Mass = 25 g)
- Weight of the bottle filled with water = 55 grams (Mass = 55 g)
- Weight of the bottle filled with liquid = 52 grams (Mass = 52 g)
Step 1: Calculate the volume of the bottle filled with water.
Using the formula Volume = Mass / Density:
Volume of water = Mass of water / Density of water
Since the density of water is known to be 1 g/cm^3:
Volume of water = 55 g / 1 g/cm^3 (The unit of volume will be in cm^3)
So, the volume of the bottle filled with water is 55 cm^3.
Step 2: Calculate the volume of the bottle filled with the liquid.
Using the formula Volume = Mass / Density:
Volume of liquid = Mass of liquid / Density of liquid
Given that the weight of the bottle filled with the liquid is 52 grams (Mass = 52 g), but we need the density of the liquid to calculate its volume.
Unfortunately, we don't have the density of the liquid, so we cannot calculate its exact volume.
Step 3: Calculate the density of the bottle.
Using the formula Density = Mass / Volume:
Density of the bottle = Mass of the bottle / Volume of the bottle
Given that the weight of the empty bottle is 25 grams (Mass = 25 g), and we already calculated the volume of the bottle filled with water as 55 cm^3:
Density of the bottle = 25 g / 55 cm^3
So, the density of the bottle is 0.454 g/cm^3.
mass bottle: 25g
volume bottle: (55-25)/density water=30ml
density bottle= 25g/30ml