RELATIONSHIPS BETWEEN VARIABLES: MASS AND VOLUME OF A LIQUID

 Objectives:

1.     To determine the relationship which exists between the mass and volume of a liquid.

2.     To find a mathematical expression for the relationship.

3.     To use the relationship for prediction.

4.     To practice making graphs.

 

Introduction:

    The study of a particular phenomenon often suggests that two measured properties are related to each other. An experiment can then be designed to determine this relationship by measuring the effect that changing one property (the independent variable) has on the other (the dependent variable). In this experiment we will study the way the mass and the volume of a liquid are related.

 

In searching for relationships between two properties it is frequently useful to make a graph showing how one property varies with the other. Each of the coordinates on the graph represents one of the properties being studied. In an experiment involved with mass and volume we might have the volume values along the x-axis (the bottom) and the mass values along the y-axis (vertical). To make the graph we would put data points for each sample at the proper values of volume and mass. If, for example, we find that a sample containing 2.0 cm³ and mass equals 2.80 grams. By using all the data points we get an idea of how the mass varies with volume. In order to be able to say what the mass of the sample would be for volumes other than those we measured, we draw a line through the data points which best fits the trend shown by those points. Having found the line showing how the properties like mass and volume are related, it is often possible to find a mathematical equation for that line. That equation can then be used to calculate one property when the other one is known. In this experiment we will be doing all of these things, with the ultimate purpose of understanding that property of a liquid called its density.

Our actual experiment is quite simple. We will measure the volume and mass of several different liquid samples, working first with water and then with an unknown liquid. These measurements will furnish us with the data from which we can make and interpret graphs for the mass volume relationships of water and the unknown.

Procedure:

1.   Mass a clean, dry graduated cylinder to the nearest 0.1 grams.

2.   Add water until the level is as close as possible to the 10 mL mark. Read the level and mass again. Make the volume measurement at the bottom of the liquid meniscus.

3.   Add another 10 mL of water. Read the volume and mass the cylinder again. Continue in this way to make the volume and mass measurements for every 10 mL up to 50 mL mark. Record all volumes to the nearest 0.1 mL and all masses to the nearest 0.1 gram.

4.   Empty and dry the graduated cylinder. Repeat procedure steps 2 and 3 with the unknown liquid. Record your values for the unknown liquid.

 

Sample Data Table

  Mass of graduated cylinder  = __________ g

  Total volume of water                          Mass of grad.cyl.                           Total mass of
                                                              and water                                     water

__________________ mL                      _____________ g                          ____________g

__________________                           _____________                             ____________

__________________                           _____________                             ____________

__________________                           _____________                             ____________

__________________                           _____________                             ____________      

 

 

Use   a similar arrangement for the data on the unknown liquid.

  CALCULATIONS AND QUESTIONS

1.     From the data obtained, calculate the total mass of the water in the cylinder for each of the volumes you measured. Carry out similar calculations for the mass of the unknown liquid for each volume.

 

2.     On graph paper plot the data you obtained for the water samples. Plot mass on the y-axis and volume on the x-axis. You should have a point on the graph paper showing the volume and mass for each sample you measured. When you have completed plotting the data, draw a straight line through the data points in such a way as to minimize the distances the points lie off the line. Your line should go through the origin (why?). Repeat the procedure, plotting the data you found for the unknown liquid, and drawing a line through those data points. Label the first line as WATER, and the other line as UNKNOWN LIQUID.

 

3.     The lines on the graph describe how the volume and mass of each of the two liquids are related. For any given volume, we can find the mass that volume of water, or unknown liquid, would have. Using the line for water on the graph, find the mass of water which would have the following volumes: 5 mL, 15 mL, 25 mL, 35 mL. Then using the line for the unknown, find the mass of the unknown liquid which would have each of these volumes.

 

4.     This method works for certain values of the volume, but what about 14.3 mL or 76 mL. At this point I will show you how to find the density of the liquids from our graph using the slope of the line you drew. This will then allow you to find any values needed if this constant (density for that substance) is known or found as you have in this lab.