3: LAB 3 - EXPLORING DENSITY
- Page ID
- 506131
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The purpose of this experiment is to:
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Determine the density of water.
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Determine the density of an unknown liquid and infer its identity from a table of listed densities.
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Calculate the densities of regularly shaped and irregularly shaped solids.
INTRODUCTION
Density is defined as the amount of material present in a given volume. Every substance has a unique density value at a certain temperature, regardless of the amount of material present. (This is known as an intensive property.) For example, 25.0 mL and 50.0 mL of water should have a density of 1.00 g/mL at room temperature because the mass-to-volume ratio is the same. Due to this nature, density can be used to infer the identity of an unknown substance.
In part of this activity, you will learn to determine water density experimentally. You will repeat the procedure with an unknown liquid and be asked to infer its identity using a table of density values. Procedures to calculate the density of regularly and irregularly shaped solids will also be explored, providing a comprehensive understanding of density.
5.0 mL of water was added to a graduated cylinder with a mass of 20.175 g. The combined mass of the graduated cylinder and water was 25.180 g. Using this information, determine the experimental density of water.
Solution
To find the mass of water, we subtract the mass of the empty graduated cylinder from the combined mass of the graduated cylinder and the water, as shown below:
Mass of water = 25.180 g - 20.175 g = 5.005 g
The density can be found by dividing the mass by the volume:
Density = 
= 
= 1.0 
Note: According to rules for multiplication and division, we round the answer to two significant digits because the measurement with the fewest significant digits (5.0 mL) has two significant digits.
Using different volumes of water, experimental densities were found to be 0.98 , 0.99 , and 0.99 
. Calculate the average density and percent error.
Solution
To find the average, we add up each value and divide the sum by the total number.
Average Density = 
= 0.99
The percent error can be calculated using the following equation:
Percent Error = 
x 100
Where E is the experimental average density and T is the theoretical density value of water. This is an absolute value, meaning that even if the answer is negative, it is recorded as a positive value.
Using the average shown above and the true density of water, which is 1.0 g/mL, and multiplying the answer by 100, the percent error can be calculated as:
Percent Error = 
x 100 = 0.01 x 100 =1%
The smaller the percent error, the closer the experimental value is to the true value.
A rectangular block having a mass of 45.250 g was shown to have a length of 2.75 cm, a width of 3.50 cm, and a height of 1.25 cm. Using this information, determine the density.
Solution
First, we need to find the volume of the rectangular block:
Volume = (2.75 cm) x (3.50 cm) x (1.25 cm) = 12.0 cm3
To find the density, we divide the mass by the volume, as follows:
Density = 
= 3.77 
A rubber stopper weighing 10.130 g was added to 30.0 mL of water in a 100-mL graduated cylinder, raising the cylinder's volume to 36.5 mL. Using this information, calculate the density of the rubber stopper.
Solution
First, find the volume of the rubber stopper.
36.5 mL - 30.0 mL = 6.5 mL
To find the density, we will divide the mass by volume.
Density = 
= 1.6 
(or 1.6 
)