d) 4.74* 10-4
3) An example of a systematic error is error in measuring temperature because of poor thermal contact between the water and the thermometer. This would cause the data to be incorrect in the same direction. All the results are either too high or too low. An example of random error would be measuring the freezing point of the water several times and getting slightly different results. The results due to random error would be both too high and too low when compared to the accepted value.
4) Error analysis is important because it shows the magnitude of errors that can be expected.
a) 7.38 ± 0.93
b) 101.0 ± 4.5
c) 0.16± 1.5
b) variance: 6.971
d) standard error: 0.9334
e) 95% confidence: 400.0 ± 1.830
The following 2 graphs show the dataset depicted as graphs. The outlier was x=9. Upon removing the outlier, the correlation coefficient became closer to 1, signifying that without the outlier the data has a more linear trend.
In the following experiment the ideal gas law and the van der Waals equation were examined. In Part 1, the gas constant was determined by graphing P vs 1/V for data collected using nitrogen gas. The equation of the line was y= 2.7817x- 0.2592. The gas constant was 0.93 ± 0.014 L*atm/mol*K. In Part II, six different isotherms were graphed assuming ideal gas behavior. In Part III, six different isotherms were graphed using the van der Waals equation. Using the same volume, the pressure under ideal gas behavior was higher than using the van der Waals equation. This lab demonstrated that there is a direct relationship between pressure and 1/volume.
The ideal gas law relates the volume, pressure, and temperature of an ideal gas by the equation:
PV= nRT (1) where P is the pressure of the gas in atmospheres, V is the volume of the container in liters, n is the number of moles of the gas, R is the universal gas constant (0.0821 L-atm/K-mol), and T is the absolute temperature of the gas (1). The ideal gas law cannot be rigorously applied to real gases under some conditions such as high pressures and low temperatures. The van der Waals equation accounts for deviations from the deal gas law. The van der Waals equation is:
(P+ (an2/V2)) (V-nb)= nRT (2) where a and b are van der Waals constants, an2/V2 corrects for intermolecular forces, and nb corrects for volume. The accuracy of the van der Waals equation can be determined by examining experimentally observed isotherms (1).
Part I of the experiment was performed by admitting 0.280 grams of pressurized N2 gas into a piston that is reserved at a constant temperature of 25°C. Over the course of the experiment the volume of the piston was altered, and the pressure was measured. Part II of the experiment was conducted using excel by constructing a graph with six different isotherms, assuming ideal gas conditions. The graph consisted of an ideal gas between 0 and 50 °C, 0 and 0.6 L/mol, and up to 150 atm. Part III was constructed using isotherms calculated using the van der Waals equation and the coefficients for carbon dioxide.
Figure 1: Pressure (atm) vs. 1/Volume (1/L)
Figure 1 shows the graph for P vs 1/V. The graph shows pressure is directly proportional to 1/V. In other words, as the volume increased, the pressure decreased. The equation of the line is y= 2.7817x- 0.2592. The slope of the line is equivalent to nRT. Solving for R, the gas constant is 0.93 ± 0.014 L*atm/mol*K.
Figure 2: Pressure (atm) vs Molar Volume (L/mol) Using Ideal Gas Law Equation
Figure 2 shows six different isotherms of an ideal gas. The graph shows a nonlinear relationship between temperature and…