Substance A has a density of 4.0 g/mL and substance B has a density of 2.0 g/mL. If we have equal-mass samples of each, which has the greatest volume?
Well, let's do some clown math here! If the density of substance A is 4.0 g/mL and the density of substance B is 2.0 g/mL, we can say that substance A is double the density of substance B. So, it's like substance A is trying to squeeze twice as much mass into the same volume as substance B.
If we have equal-mass samples of each substance, that means they have the same amount of mass. But because substance A is denser, it wants to fit that mass into a smaller volume. So, substance A has a smaller volume than substance B, which means that substance B has the greatest volume.
You can imagine substance A being like a high-maintenance friend who takes up a lot of space but substance B is cool and chill, taking up more room for a good time!
To determine which substance has the greatest volume, we can use the formula for density:
Density = mass/volume
Since the mass is equal for both substances, we can rewrite the formula as:
Volume = mass/density
If we have equal-mass samples of each substance, the volume will be greater for the substance with the lower density.
Let's calculate the volume for each substance:
For substance A:
Density of substance A = 4.0 g/mL
Mass of substance A = Equal to the mass of substance B (let's say it is m grams)
Volume of substance A = mass/density = m/4.0 g/mL = m/4.0 mL
For substance B:
Density of substance B = 2.0 g/mL
Mass of substance B = m grams
Volume of substance B = mass/density = m/2.0 g/mL = m/2.0 mL
Comparing the two volumes, we find that the volume of substance B (m/2.0 mL) is greater than the volume of substance A (m/4.0 mL).
Therefore, substance B has the greatest volume.
To determine which substance has the greatest volume, we can compare their densities and mass. The formula for density is:
Density = Mass / Volume
Given that the density of Substance A is 4.0 g/mL and that of Substance B is 2.0 g/mL, we can deduce that the mass and volume of the equal-mass samples of each substance will be the same.
Let's assume we have 1 gram of Substance A and 1 gram of Substance B. We can calculate the volume of each substance using the given densities and the formula:
Volume = Mass / Density
For Substance A:
Volume A = 1 g / 4.0 g/mL = 0.25 mL
For Substance B:
Volume B = 1 g / 2.0 g/mL = 0.5 mL
Therefore, even though the samples of Substance A and Substance B have the same mass, Substance B has a greater volume.