An empty relative density bottle has a mass of 108g when filled with a liquid of relative density of 0.8 it's mass become 180g
1. Calculate the mass of bottle when filled with water
2. Calculate the capacity of the bottle
1. Well, let's put on our thinking caps. If an empty relative density bottle has a mass of 108g and when filled with a liquid of relative density 0.8, it becomes 180g, then we need to determine the mass of just the liquid.
The difference in mass is 180g - 108g = 72g.
This difference represents the mass of the liquid in the bottle.
Since the liquid has a relative density of 0.8, we can say that its mass is 0.8 times the mass of an equal volume of water.
So, if we let W represent the mass of water, we can write the equation:
0.8W = 72g
Solving this equation, we find that the mass of water, when the bottle is filled with it, is W = 72g / 0.8 = 90g.
Therefore, the mass of the bottle when filled with water is 108g + 90g = 198g.
2. Now, let's move on to finding the capacity of the bottle.
The capacity of a container is the volume it can hold.
Since the liquid has a relative density of 0.8, it means that 0.8 times the volume of the liquid is equal to the volume of water that the bottle can hold.
Let's assume the capacity of the bottle is C.
So, we can write the equation:
0.8C = volume of water
But the volume of water is equal to its mass divided by its density. The density of water is approximately 1g/cm^3.
So, we can write the equation:
0.8C = 90g / 1g/cm^3 = 90cm^3
Dividing both sides of the equation by 0.8, we find C = 90cm^3 / 0.8 = 112.5cm^3.
Therefore, the capacity of the bottle is 112.5cm^3.
And there you have it! The mass of the bottle when filled with water is 198g, and the capacity of the bottle is 112.5cm^3.
To calculate the mass of the bottle when filled with water, we need to use the concept of relative density. The relative density of water is 1.
1. Calculate the mass of the water:
The increase in mass of the bottle when filled with the liquid is 180g - 108g = 72g (since the liquid has a relative density of 0.8).
This increase in mass is due to the liquid, so the mass of the liquid is 72g.
Since the relative density of the liquid is 0.8, we can say that the mass of the liquid is 0.8 times the mass of an equal volume of water.
Let's assume the volume of the liquid is V liters.
The mass of the liquid = Relative density of the liquid x mass of an equal volume of water
= 0.8 x mass of V liters of water
Given that the mass of the liquid is 72g, we can set up the equation as follows:
0.8 x mass of V liters of water = 72g
Solving for the mass of V liters of water:
Mass of V liters of water = 72g / 0.8
= 90g
Therefore, the mass of the bottle when filled with water is 108g + 90g = 198g.
2. Calculate the capacity of the bottle:
The capacity of the bottle refers to the volume it can hold. Since the mass of water is given, we can use the density of water to calculate the volume (capacity).
The density of water is approximately 1g/mL, so the volume of water can be calculated as follows:
Volume of water = mass of water / density of water
= 90g / 1g/mL
= 90 mL
Therefore, the capacity of the bottle is 90 mL.
To answer these questions, we need to use the formulas related to relative density and density. Here's how to calculate the answers:
1. Mass of the bottle when filled with water:
The relative density of water is 1.0 (since it's being compared to itself), so we can use this information to calculate the mass of the bottle when filled with water.
Let's assume the mass of the water-filled bottle is M grams.
According to the given information:
Mass of the empty bottle = 108g
Mass of the bottle filled with liquid of relative density 0.8 = 180g
The relative density is defined as the ratio of the density of a substance to the density of a reference substance (usually water). So, we can set up the following equation:
Mass of the liquid / Mass of water = Relative density
Using the given values:
180g / M = 0.8
We can now solve for M, the mass of the water-filled bottle:
180g = 0.8 * M
M = 180g / 0.8
M = 225g
Therefore, the mass of the bottle when filled with water is 225 grams.
2. Capacity of the bottle:
To calculate the capacity of the bottle, we need to determine the volume of water it can hold. Volume is related to mass and density. The formula is:
Volume = Mass / Density
The mass of the water-filled bottle is 225g, and the density of water is approximately 1 g/cm^3.
Using these values, we can calculate the capacity of the bottle:
Volume = 225g / 1g/cm^3
Volume = 225 cm^3
Therefore, the capacity of the bottle is 225 cm^3.