A student finds a rock on the way to school. In the laboratory he determined the volume of the rock by placing the rock in a graduated cylinder with 50 mL of water and watched the water rise to 72.7 mL. The student determined the mass is 39.943 g through the use of a triple beam balance. What is the density of the rock? ( hint: for volume find the difference between the two volumes)
To find the volume of the rock, we need to find the difference between the initial volume of water in the graduated cylinder (50 mL) and the final volume after the rock was added (72.7 mL):
Volume of rock = 72.7 mL - 50 mL = 22.7 mL
Next, we need to convert the volume from milliliters to cubic centimeters (cm³), since density is typically measured in g/cm³:
1 mL = 1 cm³
Therefore, the volume of the rock is 22.7 cm³.
To find the density, we divide the mass of the rock (39.943 g) by its volume:
Density = Mass / Volume
Density = 39.943 g / 22.7 cm³
Calculating this expression, we find the density of the rock is approximately 1.76 g/cm³.
To find the density of the rock, we can use the formula:
Density = Mass / Volume
Step 1: Find the volume of the rock.
Given that the water in the graduated cylinder rose from 50 mL to 72.7 mL, we can find the volume of the rock by subtracting the initial volume from the final volume.
Volume = Final Volume - Initial Volume
Volume = 72.7 mL - 50 mL
Volume = 22.7 mL
Step 2: Convert the volume to the appropriate units.
Density is usually measured in grams per milliliter (g/mL), so we need to convert the volume from milliliters (mL) to grams (g). Since 1 mL of water is equal to 1 gram, we can assume the same for the rock.
Volume = 22.7 g
Step 3: Use the given mass and volume to calculate the density.
Given mass = 39.943 g, and volume = 22.7 g, we can substitute these values into the density formula:
Density = Mass / Volume
Density = 39.943 g / 22.7 g
Density ≈ 1.76 g/mL
Therefore, the density of the rock is approximately 1.76 g/mL.