Density - MCAT Chemical and Physical Foundations of Biological Systems
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What is the specific gravity of a boat that has a mass of 6000kg and a volume of 10m3?
What is the specific gravity of a boat that has a mass of 6000kg and a volume of 10m3?
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Specific gravity is the density of the substance over the density of water.
Density is given by mass over unit volume.
A boat with a mass of 6000kg and a volume of 10m3 will have a density of 600 kg/m3.
Specific gravity is the density of the substance over the density of water.
Density is given by mass over unit volume.
A boat with a mass of 6000kg and a volume of 10m3 will have a density of 600 kg/m3.
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A 200-gram object is placed into a bucket of water and floats so that its top edge is just below the surface of the water. Which best describes the density of this object?
Density of water is 1000kg/m3.
A 200-gram object is placed into a bucket of water and floats so that its top edge is just below the surface of the water. Which best describes the density of this object?
Density of water is 1000kg/m3.
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If the object is at rest, the net force on it must equal 0. At any point in the liquid, the total downwards force is described as the difference between the gravitational force and bouyant force: 
. When the object is not accelerating, this reduces to 
.
Plugging in the equations for these forces respectively yields 
.
Since mass is the product of density and volume, 
.
Note that in this case the object's volume equals the volume of liquid displaced, since the object is completely submerged. So, the volumes on either side cancel, as does gravity, leaving just 
.
If the object is at rest, the net force on it must equal 0. At any point in the liquid, the total downwards force is described as the difference between the gravitational force and bouyant force:
Plugging in the equations for these forces respectively yields
Since mass is the product of density and volume,
Note that in this case the object's volume equals the volume of liquid displaced, since the object is completely submerged. So, the volumes on either side cancel, as does gravity, leaving just
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An ice cube is placed into a glass containing an unknown liquid. If the ice cube sinks to the bottom, which of the following conclusions could be made?
An ice cube is placed into a glass containing an unknown liquid. If the ice cube sinks to the bottom, which of the following conclusions could be made?
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The density of ice is less than that of water (density of ice = 0.92 g/cm3, density of water = 1 g/cm3). Ice will only sink in liquids that are less dense than 0.92 g/cm3. Since ice will only sink in liquids that are less dense than water, the unknown liquid must have a lower density than that of water.
The density of ice is less than that of water (density of ice = 0.92 g/cm3, density of water = 1 g/cm3). Ice will only sink in liquids that are less dense than 0.92 g/cm3. Since ice will only sink in liquids that are less dense than water, the unknown liquid must have a lower density than that of water.
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What is the density of a log that is 25cm long, has a cross sectional area of 5cm2, and weighs 100g?
What is the density of a log that is 25cm long, has a cross sectional area of 5cm2, and weighs 100g?
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The density of an object is equal to mass over volume.
Knowing the length and the cross sectional area of the log, we can find its volume.
Plugging in volume and mass into the equation will enable us to find density.
The density of an object is equal to mass over volume.
Knowing the length and the cross sectional area of the log, we can find its volume.
Plugging in volume and mass into the equation will enable us to find density.
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Phase diagrams are used to depict changes in the properties of a solution at different temperatures and pressures. Below is a phase diagram of a polar solution.
The density of the solution in section 1 is the density of the solution in section 2.
Phase diagrams are used to depict changes in the properties of a solution at different temperatures and pressures. Below is a phase diagram of a polar solution.
The density of the solution in section 1 is the density of the solution in section 2.
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The slope of the solid/liquid phase transition line can predict the comparative density of the solution in each section. A negative slope indicates that the solid phase is less dense than the liquid phase. A positive slope indicates that the solid is more dense. In the above phase diagram, the slope is negative, indicating that the solid is less dense than the liquid.
The slope of the solid/liquid phase transition line can predict the comparative density of the solution in each section. A negative slope indicates that the solid phase is less dense than the liquid phase. A positive slope indicates that the solid is more dense. In the above phase diagram, the slope is negative, indicating that the solid is less dense than the liquid.
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An object is at equilibrium when 
of the total volume is submerged in gasoline. Find the density of the object.
An object is at equilibrium when
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To solve, we can equate the volume of the gasoline displaced to the volume of the portion of the object that is submerged.
We know that 
of the object is submerged, thus 
of the object's total volume will equal the volume of water displaced.
The displaced masses are equal.
To solve, we can equate the volume of the gasoline displaced to the volume of the portion of the object that is submerged.
We know that
The displaced masses are equal.
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Solid A has a volume of 
and a density of 
. Solid B is cube with sides of 
and has a density of 
.
What is the difference in mass between the two solids?
Solid A has a volume of
What is the difference in mass between the two solids?
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The formula for density is:
In the question, we are given the densities of both solids and a means to find their volumes. Using these values, we will be able to determine the mass of each solid.
Now that we know both masses, we can find the difference.
The formula for density is:
In the question, we are given the densities of both solids and a means to find their volumes. Using these values, we will be able to determine the mass of each solid.
Now that we know both masses, we can find the difference.
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Water has a density of 
at a temperature of 
. An certain oil has a specific gravity of 
at this temperature. What is the mass of 
of the oil?
Water has a density of
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The formula for density is:
Specific gravity is the density of a material relative to the density of water.
We are given the specific gravity of the oil and the density of water, allowing us to calculate the density of the oil.
Returning to the equation for density, we can use the density of the oil to find the mass on one liter.
The formula for density is:
Specific gravity is the density of a material relative to the density of water.
We are given the specific gravity of the oil and the density of water, allowing us to calculate the density of the oil.
Returning to the equation for density, we can use the density of the oil to find the mass on one liter.
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A given iceberg floats such that 90% of its volume is below water. Supposing that the iceberg is composed of pure water, what is the density of the saltwater in which the iceberg floats?
A given iceberg floats such that 90% of its volume is below water. Supposing that the iceberg is composed of pure water, what is the density of the saltwater in which the iceberg floats?
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We can solve this question by using a density ratio, given by the equation:
We know the density of ice, and we can find the ratio of the densities by using buoyancy. If the iceberg were completely submerged, then we could conclude that the density of the ice was equal to the density of the salt water. Since the iceberg is 90% submerged, we can conclude that the density of the ice is 90% of the density of the salt water.
Use this ratio and the density of ice to solve for the density of the salt water.
We can solve this question by using a density ratio, given by the equation:
We know the density of ice, and we can find the ratio of the densities by using buoyancy. If the iceberg were completely submerged, then we could conclude that the density of the ice was equal to the density of the salt water. Since the iceberg is 90% submerged, we can conclude that the density of the ice is 90% of the density of the salt water.
Use this ratio and the density of ice to solve for the density of the salt water.
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A researcher performs an elemental analysis on a compound. He finds that the compound is made up of only carbon, hydrogen, and oxygen atoms. He isolates a pure sample of the compound and finds that this sample contains 
of carbon, 
of hydrogen, and 
of oxygen. The researcher wants to perform further analysis on this compound the next day. Before leaving the lab the researcher creates three stock solutions of varying concentrations of this compound: 
(solution A), 
(solution B), and 
(solution C). He stores these solutions overnight at a temperature of 
.
Molecular weight of this compound = 
Which of the following is true regarding the densities of the three stock solutions?
A researcher performs an elemental analysis on a compound. He finds that the compound is made up of only carbon, hydrogen, and oxygen atoms. He isolates a pure sample of the compound and finds that this sample contains
Molecular weight of this compound =
Which of the following is true regarding the densities of the three stock solutions?
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Density is a measure of concentration, defined as mass per unit volume.
Since the stock solutions contain different concentrations, the density of each solution must be different. The solution with the highest concentration will contain the highest density, and the solution with lowest concentration will contain the lowest density. The order of increasing density is solution A, solution B, and solution C. Solution C is the most concentrated and will contain the greatest amount of mass per unit volume, followed by solution B and solution A.
Remember that concentration can be defined in various ways: molarity, molality, mass percent, density, etc. Increasing concentration means you are increasing all of these quantities. Also remember that the density of the compound remains the same in each solution; only the solutions, as a whole, have different densities.
Density is a measure of concentration, defined as mass per unit volume.
Since the stock solutions contain different concentrations, the density of each solution must be different. The solution with the highest concentration will contain the highest density, and the solution with lowest concentration will contain the lowest density. The order of increasing density is solution A, solution B, and solution C. Solution C is the most concentrated and will contain the greatest amount of mass per unit volume, followed by solution B and solution A.
Remember that concentration can be defined in various ways: molarity, molality, mass percent, density, etc. Increasing concentration means you are increasing all of these quantities. Also remember that the density of the compound remains the same in each solution; only the solutions, as a whole, have different densities.
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A researcher performs an elemental analysis on a compound. He finds that the compound is made up of only carbon, hydrogen, and oxygen atoms. He isolates a pure sample of the compound and finds that this sample contains of carbon, of hydrogen, and of oxygen. The researcher wants to perform further analysis on this compound the next day. Before leaving the lab the researcher creates three stock solutions of varying concentrations of this compound: (solution A), (solution B), and (solution C). He stores these solutions overnight at a temperature of 
.
Molecular weight of this compound =
A 
stock solution, solution X, kept at room temperature (
) will have compared to solution A.
A researcher performs an elemental analysis on a compound. He finds that the compound is made up of only carbon, hydrogen, and oxygen atoms. He isolates a pure sample of the compound and finds that this sample contains
Molecular weight of this compound =
A
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Solution A and solution X have the same concentration, therefore, we are only concerned with temperature differences between the two solutions. Density is dependent on temperature: as temperature increases density decreases. Recall the definition of density:
Increasing the temperature will slightly increase the volume of the solution and, subsequently, decrease density. The temperature has no effect on mass. The solution at the higher temperature (solution X) will have a lower density.
Solution A and solution X have the same concentration, therefore, we are only concerned with temperature differences between the two solutions. Density is dependent on temperature: as temperature increases density decreases. Recall the definition of density:
Increasing the temperature will slightly increase the volume of the solution and, subsequently, decrease density. The temperature has no effect on mass. The solution at the higher temperature (solution X) will have a lower density.
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Various sample sizes of a pure, unknown substance are measured for mass (in grams) and volume (in mL). The results are plotted on a graph with grams of the y-axis and milliliters on the x-axis. Which of the following results most likely indicates experimental error?
Various sample sizes of a pure, unknown substance are measured for mass (in grams) and volume (in mL). The results are plotted on a graph with grams of the y-axis and milliliters on the x-axis. Which of the following results most likely indicates experimental error?
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Plotted in this way, the slope of the line is equal to the density of the substance.
We would expect the line to be linear and positive. A slope close to zero could indicate that the data was not graphed optimally or that the density is extremely small, and a density greater than one is possible (anything that sinks in water has a density greater than one). A negative density would indicate that greater masses of this substance have smaller volumes, which, for a pure substance, does not make sense.
Plotted in this way, the slope of the line is equal to the density of the substance.
We would expect the line to be linear and positive. A slope close to zero could indicate that the data was not graphed optimally or that the density is extremely small, and a density greater than one is possible (anything that sinks in water has a density greater than one). A negative density would indicate that greater masses of this substance have smaller volumes, which, for a pure substance, does not make sense.
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Which of these samples, if any, has a volume greater than three liters?
Which of these samples, if any, has a volume greater than three liters?
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Solving this question requires that we use the given densities to convert mass to volume.
We see that only the aluminum sample has a volume over three liters.
Solving this question requires that we use the given densities to convert mass to volume.
We see that only the aluminum sample has a volume over three liters.
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What is the specific gravity of a boat that has a mass of 6000kg and a volume of 10m3?
What is the specific gravity of a boat that has a mass of 6000kg and a volume of 10m3?
Tap to reveal answer
Specific gravity is the density of the substance over the density of water.
Density is given by mass over unit volume.
A boat with a mass of 6000kg and a volume of 10m3 will have a density of 600 kg/m3.
Specific gravity is the density of the substance over the density of water.
Density is given by mass over unit volume.
A boat with a mass of 6000kg and a volume of 10m3 will have a density of 600 kg/m3.
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A 200-gram object is placed into a bucket of water and floats so that its top edge is just below the surface of the water. Which best describes the density of this object?
Density of water is 1000kg/m3.
A 200-gram object is placed into a bucket of water and floats so that its top edge is just below the surface of the water. Which best describes the density of this object?
Density of water is 1000kg/m3.
Tap to reveal answer
If the object is at rest, the net force on it must equal 0. At any point in the liquid, the total downwards force is described as the difference between the gravitational force and bouyant force: . When the object is not accelerating, this reduces to .
Plugging in the equations for these forces respectively yields .
Since mass is the product of density and volume, .
Note that in this case the object's volume equals the volume of liquid displaced, since the object is completely submerged. So, the volumes on either side cancel, as does gravity, leaving just .
If the object is at rest, the net force on it must equal 0. At any point in the liquid, the total downwards force is described as the difference between the gravitational force and bouyant force:
Plugging in the equations for these forces respectively yields
Since mass is the product of density and volume,
Note that in this case the object's volume equals the volume of liquid displaced, since the object is completely submerged. So, the volumes on either side cancel, as does gravity, leaving just
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An ice cube is placed into a glass containing an unknown liquid. If the ice cube sinks to the bottom, which of the following conclusions could be made?
An ice cube is placed into a glass containing an unknown liquid. If the ice cube sinks to the bottom, which of the following conclusions could be made?
Tap to reveal answer
The density of ice is less than that of water (density of ice = 0.92 g/cm3, density of water = 1 g/cm3). Ice will only sink in liquids that are less dense than 0.92 g/cm3. Since ice will only sink in liquids that are less dense than water, the unknown liquid must have a lower density than that of water.
The density of ice is less than that of water (density of ice = 0.92 g/cm3, density of water = 1 g/cm3). Ice will only sink in liquids that are less dense than 0.92 g/cm3. Since ice will only sink in liquids that are less dense than water, the unknown liquid must have a lower density than that of water.
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What is the density of a log that is 25cm long, has a cross sectional area of 5cm2, and weighs 100g?
What is the density of a log that is 25cm long, has a cross sectional area of 5cm2, and weighs 100g?
Tap to reveal answer
The density of an object is equal to mass over volume.
Knowing the length and the cross sectional area of the log, we can find its volume.
Plugging in volume and mass into the equation will enable us to find density.
The density of an object is equal to mass over volume.
Knowing the length and the cross sectional area of the log, we can find its volume.
Plugging in volume and mass into the equation will enable us to find density.
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Phase diagrams are used to depict changes in the properties of a solution at different temperatures and pressures. Below is a phase diagram of a polar solution.
The density of the solution in section 1 is the density of the solution in section 2.
Phase diagrams are used to depict changes in the properties of a solution at different temperatures and pressures. Below is a phase diagram of a polar solution.
The density of the solution in section 1 is the density of the solution in section 2.
Tap to reveal answer
The slope of the solid/liquid phase transition line can predict the comparative density of the solution in each section. A negative slope indicates that the solid phase is less dense than the liquid phase. A positive slope indicates that the solid is more dense. In the above phase diagram, the slope is negative, indicating that the solid is less dense than the liquid.
The slope of the solid/liquid phase transition line can predict the comparative density of the solution in each section. A negative slope indicates that the solid phase is less dense than the liquid phase. A positive slope indicates that the solid is more dense. In the above phase diagram, the slope is negative, indicating that the solid is less dense than the liquid.
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An object is at equilibrium when of the total volume is submerged in gasoline. Find the density of the object.
An object is at equilibrium when
Tap to reveal answer
To solve, we can equate the volume of the gasoline displaced to the volume of the portion of the object that is submerged.
We know that of the object is submerged, thus of the object's total volume will equal the volume of water displaced.
The displaced masses are equal.
To solve, we can equate the volume of the gasoline displaced to the volume of the portion of the object that is submerged.
We know that
The displaced masses are equal.
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Solid A has a volume of and a density of . Solid B is cube with sides of and has a density of .
What is the difference in mass between the two solids?
Solid A has a volume of
What is the difference in mass between the two solids?
Tap to reveal answer
The formula for density is:
In the question, we are given the densities of both solids and a means to find their volumes. Using these values, we will be able to determine the mass of each solid.
Now that we know both masses, we can find the difference.
The formula for density is:
In the question, we are given the densities of both solids and a means to find their volumes. Using these values, we will be able to determine the mass of each solid.
Now that we know both masses, we can find the difference.
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