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Chapter 1: Problem 61

The following procedure was used to determine the volume of a flask. The flask was weighed dry and then filled with water. If the masses of the empty flask and filled flask were \(56.12 \mathrm{~g}\) and \(87.39 \mathrm{~g},\) respectively, and the density of water is \(0.9976 \mathrm{~g} / \mathrm{cm}^{3}\), calculate the volume of the flask in \(\mathrm{cm}^{3}\).

Short Answer

Expert verified
The volume of the flask is 31.34 cm鲁.

Step by step solution

01

Calculate the mass of the water

Subtract the mass of the empty flask from the mass of the filled flask. This gives the mass of the water. \(Mass_{water} = Mass_{filled flask} - Mass_{empty flask} = 87.39g - 56.12g = 31.27g\).
02

Use the density formula to calculate the volume

The density formula is \(density = mass / volume\). This can be rearranged to find the volume: \(volume = mass / density\). The mass is 31.27g and the density of water is 0.9976g/cm鲁. Substituting these values in gives: \(volume = 31.27g / 0.9976g/cm鲁 = 31.34 cm鲁\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Density Formula
Understanding the concept of density is essential in volume calculations, especially when dealing with substances like water. The density formula is expressed as \( \text{density} = \frac{\text{mass}}{\text{volume}} \). This means that density is the measure of mass per unit volume. For water, the density is often given in grams per cubic centimeter (g/cm鲁), which tells you how much 1 cm鲁 of water weighs.
  • The density of water is typically around 1 g/cm鲁, but it can vary slightly based on temperature and pressure.
  • In this exercise, the density of water is 0.9976 g/cm鲁, which is very close to the standard density of water at room temperature.
To find the volume using density, the formula can be rearranged: \( \text{volume} = \frac{\text{mass}}{\text{density}} \). This rearranged formula allows us to solve for volume if the mass and density are known.
Mass of Water
Calculating the mass of water is a necessary step before determining the volume of a flask. In this context, mass refers to the amount of matter present in water within the flask. To find this, we use the masses of the empty and filled flask.
  • Mass of the empty flask = 56.12 g
  • Mass of the filled flask = 87.39 g
  • Mass of water = Mass of filled flask - Mass of empty flask = 87.39 g - 56.12 g = 31.27 g
This calculated mass, 31.27 grams, represents how much water is added to the flask. It's crucial to get an accurate measure of the water mass for further calculations, especially when using the density formula to find volume.
Volume of a Flask
The volume of the flask can be determined using the mass of the water and the density of water. Once we know these values, we apply the rearranged density formula to find the volume. First, we already calculated:
  • Mass of water = 31.27 g
  • Density of water = 0.9976 g/cm鲁
Now we substitute these into the rearranged density formula: \[\text{volume} = \frac{\text{mass}}{\text{density}} = \frac{31.27\, \text{g}}{0.9976\, \text{g/cm}^3}\]Doing the calculation gives us:\[\text{volume} \approx 31.34\, \text{cm}^3\]This value of 31.34 cubic centimeters represents the volume of the flask, showing us how much space the water occupies within it.

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