A calibrated flask was filled to the 25.00 mL mark with ethyl alcohol. By weighing the flask before and after add-ing the alcohol, it was determined that the flask contained 19.7325 g of alcohol. In a second experiment, 25.0920 g of metal beads were added to the flask, and the flask was again filled to the 25.00 mL mark with ethyl alcohol. The total mass of the metal plus alcohol in the flask was determined to be 38.4704 g. What is the density of the metal in g/mL?
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Calculate the density of ethyl alcohol using the mass and volume from the first experiment: \( \text{Density} = \frac{\text{mass}}{\text{volume}} = \frac{19.7325\, \text{g}}{25.00\, \text{mL}} \).
Determine the mass of ethyl alcohol in the second experiment by subtracting the mass of the metal beads from the total mass: \( \text{Mass of alcohol} = 38.4704\, \text{g} - 25.0920\, \text{g} \).
Calculate the volume of ethyl alcohol in the second experiment using its density: \( \text{Volume} = \frac{\text{mass of alcohol}}{\text{density of alcohol}} \).
Find the volume occupied by the metal beads by subtracting the volume of ethyl alcohol from the total volume of the flask: \( \text{Volume of metal} = 25.00\, \text{mL} - \text{Volume of alcohol} \).
Calculate the density of the metal using its mass and volume: \( \text{Density of metal} = \frac{25.0920\, \text{g}}{\text{Volume of metal}} \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Density
Density is defined as the mass of a substance divided by its volume, typically expressed in grams per milliliter (g/mL). It is a crucial property that helps identify materials and understand their behavior in different contexts. In this problem, calculating the density of the metal requires knowing both its mass and the volume it occupies, which can be inferred from the changes in mass and volume of the alcohol.
The relationship between mass and volume is fundamental in chemistry, particularly in determining the density of substances. In this scenario, the mass of the metal beads and the volume of ethyl alcohol they displace when added to the flask are key to finding the density. Understanding how to manipulate these measurements is essential for solving the problem accurately.
The displacement method involves measuring the change in volume when an object is submerged in a liquid, which can be used to determine the volume of the object. In this case, the volume of the metal beads can be deduced from the difference in mass of the flask before and after adding the beads, allowing for the calculation of density. This method is particularly useful for irregularly shaped objects.
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