Given that 6.20 x 10^23 ethanol molecules have a mass of 46.04g calculate the number of ethanol molecules in a film of ethanol that is 3.08 mm by 0.0015 mm. Assume the density of ethanol is 0.790 g/mL
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To find the number of ethanol molecules in the given film of ethanol, we can follow these steps:
Step 1: Calculate the volume of the film of ethanol.
The volume of the film can be calculated using the formula:
Volume = Length x Width x Height
Given:
Length = 3.08 mm
Width = 0.0015 mm
Height (considered as thickness) = Density of ethanol = 0.790 g/mL
First, we need to convert the lengths from millimeters to milliliters, as the density is given in grams per milliliter. Since 1 mL is equal to 1 cm³, we can convert the lengths as follows:
Length = 3.08 mm = 3.08 x 0.001 cm = 0.00308 cm
Width = 0.0015 mm = 0.0015 x 0.001 cm = 0.0000015 cm
Now, we can calculate the volume:
Volume = 0.00308 cm x 0.0000015 cm x 0.790 g/mL
Step 2: Convert the volume to milliliters.
Since the density is given in grams per milliliter and the volume we calculated is in cubic centimeters, we need to convert the volume to milliliters:
Volume = Volume × 1 mL/1 cm³
Step 3: Calculate the mass of ethanol in the film.
The mass of ethanol can be calculated using the density and volume of the film:
Mass = Volume x Density
Step 4: Calculate the number of ethanol molecules.
Given that 6.20 x 10^23 ethanol molecules have a mass of 46.04 g, we can calculate the number of ethanol molecules in the film using the mass of ethanol we calculated and the given ratio:
Number of molecules = (Mass / 46.04 g) x (6.20 x 10^23 molecules)
By following these steps, you should be able to calculate the number of ethanol molecules in the given film of ethanol.