The density of sea water is slightly higher than that of fresh water. The higher density is due to the fact that sea water contains salts such as sodium chloride and magnesium chloride. Suppose you have a container that holds 5.00 kg of fresh water, which has a density of 1.00 g/cm3. If 5.00 kg of sea water with a density of 1.03 g/cm3 is placed in
a container of the same size, what is the volume of the space that is left unfilled?
mass = volume x density
volume sea water = mass/density
volume sea water = 5,000/1.03 = 4854.4 cc.
original container is 5,000 cc.
5,000-4854.4 = 145.6 cc which would round to 146 cc space left (to three significant figures).
To find the volume of the space that is left unfilled in the container, we need to calculate the volume of the sea water and subtract it from the total volume of the container.
Given:
Mass of fresh water = 5.00 kg
Density of fresh water = 1.00 g/cm^3
Mass of sea water = 5.00 kg
Density of sea water = 1.03 g/cm^3
We can use the formula for density:
Density = Mass / Volume
Using this formula, we can rearrange it to solve for volume:
Volume = Mass / Density
First, let's calculate the volume of the sea water:
Volume = Mass / Density = 5.00 kg / 1.03 g/cm^3
But we need to convert the mass of sea water from kg to grams:
1 kg = 1000 g
So, 5.00 kg = 5000 g
Substituting the values into the equation:
Volume = 5000 g / 1.03 g/cm^3
Now, we can calculate the volume of the space left unfilled:
Total volume of the container = Volume of fresh water = 5.00 kg / 1.00 g/cm^3
Converting the mass of fresh water from kg to grams:
5.00 kg = 5000 g
Substituting the values into the equation:
Volume of the space left unfilled = Total volume - Volume of sea water = 5000 g / 1.00 g/cm^3 - 5000 g / 1.03 g/cm^3
Simplifying the equation, we get:
Volume of the space left unfilled = 5000 cm^3 - 4854.37 cm^3
Therefore, the volume of the space that is left unfilled in the container is approximately 145.63 cm^3.
To find the volume of the unfilled space, we can calculate the difference in volume between the container filled with fresh water and the container filled with sea water.
First, let's find the volume of the fresh water in the container:
Mass of fresh water = 5.00 kg
Density of fresh water = 1.00 g/cm³
To find volume, we can use the formula:
Volume = Mass / Density
Volume of fresh water = 5.00 kg / (1.00 g/cm³)
Volume of fresh water = 5.00 L (since 1 kg of water has a volume of 1 L)
Now, let's find the volume of the sea water in the container:
Mass of sea water = 5.00 kg
Density of sea water = 1.03 g/cm³
Volume of sea water = 5.00 kg / (1.03 g/cm³)
Volume of sea water = 4.85 L (rounded to two decimal places)
Now, to find the volume of the unfilled space, subtract the volume of the sea water from the volume of the container:
Volume of unfilled space = Volume of fresh water - Volume of sea water
Volume of unfilled space = 5.00 L - 4.85 L
Volume of unfilled space = 0.15 L
Therefore, the volume of the space that is left unfilled is 0.15 L.