Suppose you have a household cup as the only available measuring tool for mass or volume. Develop an alternative method to determine the approximate volume of pure water that is needed to fill a cylindrical container that has a height of 14.32 cm and a radius of 4.0 cm. Assume that the pure water, with a density of 1 g/cm3 , is at 4 °C of temperature. Provide necessary computations to support your procedure. (show your solution)
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The density, ρ, of an object is defined as the ratio of its mass to its volume. Density can be useful in identifying substances. It is also a convenient property because it provides a link (or conversion factor) between the mass and the volume of a substance.
( 1 )
ρ = m/V
Mass and volume are extensive (or extrinsic) properties of matter - they depend on amount. Density, an intensive (or intrinsic) property, is a kind of "heaviness" factor. In macroscopic terms, density reflects how much mass is packed into a given three-dimensional space. Typically, densities are reported g/ml or g/cm3 (which are equivalent because 1ml ≡ 1cm3). Experimentally, mass and volume measurements are required to calculate density.
Masses are measured on electronic balances. Pan balances, which are accurate to ±0.01 g, are used for quick measurements where greater precision is not required. Analytical balances (accurate to ±0.0001 g) are used for more precise measurements.
Volume is an amount of space, in three dimensions, that a sample of matter occupies. The number and the phase of the molecules in the sample primarily determine the volume of a substance. Volume will be measured in many ways in this course, but the units are usually milliliters (mL) or cubic centimeters (cm3). Methods for determining or delivering precise volumes include volumetric pipets and pycnometers; less precise methods include burets, graduated cylinders, and graduated pipets.
In this experiment, you will measure masses and volumes to determine density. Four different metal cylinders are investigated.
In parts 1-3, three different methods are used to find volume of two solid metal cylinders (Al and brass). Each method has its own degree of precision.
(i)
volume by geometry
(ii)
volume by water displacement
(iii)
volume by pycnometry (mass-based)
In parts 4-5, one method for volume determination is used to find:
(i)
the volume of a void inside a hollow cylinder; and,
(ii)
the percent composition of a mixed-metal cylinder.
Volume by geometry
A cylinder is a standard geometric form. In this case, you can measure the dimensions of the cylinder and apply the formula to calculate its volume.
( 2a )
V = π
d
2
2
l =
π
4
d 2 l where d = diameter and l = length.
Explanation: