A. Volume-Pressure Data for Gases
Prepare a graph using the following data for a gas sample at 50oC, as you adjust the size of the container.
|
Pressure (atm)
|
Volume (L)
|
|
3.21
|
8.24
|
|
3.75
|
7.07
|
|
5.03
|
5.26
|
|
5.86
|
4.52
|
|
7.86
|
3.36
|
|
9.16
|
2.89
|
|
12.28
|
2.15
|
|
14.30
|
1.84
|
|
19.16
|
1.37
|
1. Which is the independent variable?
2. Which is the dependent variable?
3. You will make two graphs on a single side of graph paper. The data above will be graphed on the upper half. Choose the proper scale for each axis. The axis for volume should start at 1 L (or less), and should go up to 8.5 L (or more). The axis for pressure should range from 3 atm to 20 atm. Choose an appropriate value for the scale of each axis so that the data fills most of the upper half of the graph paper.
4. Draw and label each axis, and write the value of each variable every 5 or 10 lines.
5. Locate each data point, and use a pencil to place a small dot in the appropriate place. Circle each data point. Does the data appear to be linear? _____ If curved, use a French curve or a flexicurve to draw a smooth curve through the data points. The line may not go through all of the points. The points may be slightly scattered above and below the line or curve.
6. Put a title on the top of the graph.
The previous data show an inverse relationship between volume and pressure. As the pressure is increased, the volume decreases. Mathematically, this relationship can be expressed as:
P α 1/V ; or P = (constant) 1/V
To determine if the above relationship is correct, and to determine the value of the constant, a second graph will be prepared.
7. Complete the table below by calculating the value of 1 /V for each volume measured.
|
Pressure (atm)
|
Volume (L)
|
V-1(liters-1)
|
|
3.21
|
8.24
|
|
|
3.75
|
7.07
|
|
|
5.03
|
5.26
|
|
|
5.86
|
4.52
|
|
|
7.86
|
3.36
|
|
|
9.16
|
2.89
|
|
|
12.28
|
2.15
|
|
|
14.30
|
1.84
|
|
|
19.16
|
1.37
|
|
8. Construct a graph of inverse volume and pressure on the bottom half of the graph paper. Put the independent variable on the x-axis, and the dependent variable on the y-axis. Start at the origin (0, 0), and choose the proper scale for each axis. The scale should be such that the data fills most of the area of the graph. Label each axis and put a title on the graph.
9. Plot the data points by placing a small pencil dot on each data point. Circle the data points.
10. If the data is linear, use the see-through straight edge so that you can see all of the data points while you draw the best straight line through the data points. Some points may be off of the line. Do not draw several line segments to connect the data points. Draw the single best line to represent the data. If the data is non-linear, use a French curve to make a smooth curve through the data points. Extend the line past the data, using a dotted or broken line, until you reach one of the axes. Does the line go through the origin (0, 0)? _____ If so, it indicates simple inverse proportionality between volume and pressure.
11. If you got a straight line for the graph of inverse volume versus pressure, determine the slope of the line to obtain the proportionality constant. The slope is the (change in y)/(change in x). Choose two points on the line that are on corners of the grid and spaced fairly far apart. Do not choose data points to determine the slope. Indicate the points on the graph used to calculate the slope of the line. Remember that the slope will have units.
12. Show your calculation of the slope below. Indicate the two points used to calculate the slope on our graph.
B. Volume-Temperature Data for Gases
Prepare a graph using the following data for a gas at constant pressure, as temperature increases.
|
Temperature (oC)
|
Volume (mL)
|
|
11
|
95.3
|
|
25
|
100.0
|
|
47
|
107.4
|
|
73
|
116.1
|
|
159
|
145.0
|
|
233
|
169.8
|
|
258
|
178.1
|
1. Which is the independent variable? _____ Plot this along the horizontal (x) axis. Which is the dependent variable? ______ This should be graphed along the vertical (y) axis.
2. For this graph, you will need to determine the intercept. This is the value along the vertical (y) as where the value of the x-axis equals zero. Because you need to determine the intercept, scale the x-axis so that it begins at zero. The vertical (y) axis does not need to start at zero. Scale each axis so that the data fills most of the graph paper. Label each axis and write in the values every 5 or 10 line. Write the title at the top of the graph.
3. Plot the data by making a small dot for each point. Circle the data points.
4. If the data is linear, use a see-through straight edge or ruler to draw the straight line that best represents the data. The line may not go through all the points. Using a dotted line, extend the line past the data to the intercept, where the line intersects with the vertical (y) axis. Determine the value of the intercept and clearly indicate the intercept and its value on the graph.
5. Calculate the slope of the line. Choose two points on the line that are on the corners of the grid, and far apart. Do not use data points to calculate the slope. Note that the slope will have units. Show the calculation of the slope below. Be sure to indicate the points used to calculate the slope on your graph.
Slope = ______
The data should obey the straight-line relationship:
y = mx + b
Where x and y are temperature and volume, m is the slope of the line, and b is the intercept. Write the equation that is represented bur data using V, T, and your slope and intercept. Be sure to include any units for the slope and intercept.
The equation for the line is:
The relationship between the volume of a gas and temperature has significance. Use your equation to calculate the lowest theoretical limit of temperature, absolute zero. This would be the temperature at which the volume of a gas equals zero. A lower temperature would imply a negative volume for the gas, and is meaningless. Of course a real gas would liquefy or solidify at this very low temperature.
Use your equation to calculate the temperature at which the volume of the gas equals zero. Show your work below. [Hint: Set V=0, and solve for T]
Answer: Absolute zero = ________
How does your value compare with the accepted value of -273oC? Calculate the percent error in your value. Show your work below.
% error = (|experimental value - actual value|/ actual value) (100%)
Answer: % Error = _____
C. Vapor Pressure Curves
On page 15 is a table of the vapor pressure of water at various temperatures. You will make two graphs, each on a separate page. The first graph will illustrate the relationship between temperature and the vapor pressure of water. Although the data doesn't include the boiling point of water, you can extend the graph beyond the data points. This is called extrapolation. The line or curve representing the data is extended beyond the data points using a broken or dotted line.
1. The first graph will be of the vapor pressure and temperature data on the table that follows. The independent variable goes along the x-axis, and the dependent variable goes along the y-axis.
2. You will extend the graph to beyond the data points to estimate the boiling point of water, so the scale must extend beyond the data on the following table. Choose a scale for the temperature axis that goes up to 110oC.
3. Choose a scale for the vapor pressure that goes up to 800 mmHg.
4. Label each axis, showing the value every 5 or 10 lines.
5. Plot the data points by making small dots for each point. Circle the data points.
6. Put a title on the graph.
7. Vapor pressure data is usually curved. Use a French curve or a flexicurve to make a smooth line that best represents the data. Extend the line, using a dotted line, past the data points up to a pressure of 800 mmHg.
8. The normal boiling point of a substance is defined as the temperature at which the vapor pressure equals exactly 1 atmosphere, or 760 mmHg. Using the extended line on your graph, determine the temperature at which the vapor pressure would equal one atmosphere. Using a straight edge, draw a thin line across the graph at 1 atm (760 mmHg) pressure. At the point where the extended line and the 1 atmosphere line intersect, use a straight edge to draw a fine line to the temperature axis. This temperature is the estimated boiling point of water. Indicate the value for the boiling point of water on the temperature axis of your graph.
9. Calculate the % error in the boiling point, and show your calculation below,
%error = (|boiling point from graph - actual boiling point|/actual boiling point) x 100%
|
Temp (oC)
|
Vapor (mmHg)
|
Temp (K)
|
Temp-1(K-1)
|
In (vapor pressure)
|
|
0
|
4.6
|
|
|
|
|
5
|
6.5
|
|
|
|
|
10
|
9.2
|
|
|
|
|
15
|
12.8
|
|
|
|
|
20
|
17.5
|
|
|
|
|
25
|
23.8
|
|
|
|
|
30
|
31.8
|
|
|
|
|
35
|
42.2
|
|
|
|
|
40
|
55.3
|
|
|
|
|
45
|
71.9
|
|
|
|
|
50
|
92.5
|
|
|
|
|
55
|
118.0
|
|
|
|
|
60
|
149.4
|
|
|
|
|
65
|
187.5
|
|
|
|
|
70
|
233.7
|
|
|
|
|
75
|
289.1
|
|
|
|
|
80
|
355.1
|
|
|
|
|
85
|
433.6
|
|
|
|
|
90
|
525.8
|
|
|
|
|
95
|
633.9
|
|
|
|
Several relationships involving a measured property versus temperature are curved like the previous graph. Often, if the natural logarithm of the measured property is graphed versus the inverse of temperature (in Kelvins), the graph will be linear. In addition, the slope of the line often has physical significance.
10. Complete the table above. The third column should be the temperature in Kelvins. The fourth column should be the inverse of temperature in K-1, and the last column should be the natural logarithm (In) of the vapor pressure. Note that when the In of a quantity is taken, there are no units.
11. Use another piece of graph paper to make a graph of In of vapor pressure versus inverse temperature. Choose a scale for each axis so that the data fills most of the area of the graph. You do not need to start at the origin (0, 0). Label each axis.
12. Plot each of the data points, and circle each point. The data should be linear. Use a see-thought straight edge to draw a straight line that best fits the data. Put a title on the graph.
13. Calculate the slope of the line. Choose two points on the line that are on the corners of the grid, and far apart. Do not use data points to calculate the slope. Indicate the two points used to calculate the slope on graph. Show the calculation of the slope below. Note that the ln of P has no units, but 1/T has the units of K-1. As a result, the slope will have units.
14. The slope of the line has physical significance. The slope is used to calculate the enthalpy of vaporization, ΔHvap. The enthalpy of vaporization is the energy needed to vaporize a mole of a substance at its normal boiling point.
Slope = - ΔHvap/R, Where R = 8.314 J/mol-K
Show the calculation of the enthalpy of vaporization below. Pay attention to the sign and units.
15. Loop up the value of the enthalpy of vaporization of water in your textbook. Calculate the %error using the value form your graph and the accepted value. Show your calculation below.
%error = (|ΔHvap from graph - actual ΔHvap|/actual ΔHvap) x 100%
You will turn in these pages that include some of your calculations and all of your graphs. Make sure that each graph is properly labeled and has a title. Make sure that your name appears on all graphs and that your entire report is stapled together. Attach the graphs in the following order:
Part A: Pressure-Volume
Pressure-(Volume)-1
Part B: Volume-Temperature
Part C: Temperature (oC)-Vapor Pressure
[Temperature (K)]-1 - In (vapor pressure)
Questions -
1. When obtaining the slope of a line, you should not use data points. Explain why.
2. When obtaining the slope of a line, the two points used should be far apart from each other. Explain why.