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Boyle's Law Data Anaylsis "For a fixed amount of gas kept at a fixed temperature, P and V are inversely proportional." Wikipedia.com The mathematical equation for Boyle's law is: PV = K where: P is the pressure of the gas,V is the volume of the gas, K is a constant value representative of the pressure and volume of the system. The data for this study is Robert Boyle's original data from 1662 and is taken form the Classic Chemistry Papers at http://web.lemoyne.edu/~GIUNTA/index.html Excel was used to graph Boyle's data as a scatter plot of volume vs. pressure. Excel also calculated the trend line, power regression was choosen for the best fit curve. The exponent on this equation is very close to negative one, this illustrates mathematically an inverse relationship. Anything raised to the power of negative one equals its reciprocal (x-1 = 1/x). Graphing volume vs. the inverse of pressure (1/P) should result in a linear trend line. This illustrates that as the volume approaches zero Boyle's law would predict that the inverse of pressure would approach zero. As is illustrated by the graphs as Pressure increases the volume decreases; the pressure and volume of a gas sample at a given temperature are inversely proportional to each other. The law assumes that the temperature remains constant; so with V1 = original volume, V2 = new volume, P1 = original pressure and P2 = new pressure Boyle's law can also be expressed as:
According to Boyle’s law, the shape of the graph between pressure and reciprocal of volume is _______. According to Boyle’s law, the shape of the graph between pressure and reciprocal of volume is Straight line. Concept: Fundamental Laws of Gases - Pressure and Volume Relationship or Bolye's Law Is there an error in this question or solution? 31st Oct 2019 @ 2 min read The graph of Boyle's law is known as pressure-volume graph or PV curve. It is as follows: As observed from the graph above, pressure increases with a decrease in volume, and vice versa. Thus, pressure is inversely proportional to volume. Other parameters (temperature and amount of gas) are constant in the graph above. Mathematical explanationVolume is on the x-axis and pressure, on the y-axis. The equation of the curve is PV = k, which is the equation of Boyle's law. The curve is hyperbolic in nature having two asymptotes: P = 0 (horizontal) and V = 0 (vertical). Note: An asymptote is a line or curve such that the distance between it and a given curve tends to zero as x and/or y coordinates tends to infinity. As volume tends to positive infinity, pressure tends to zero, and we get the horizontal asymptote, P = 0. When volume approaches zero, pressure approaches infinity, and it results in the vertical asymptote, V = 0. Graphs at different temperaturesGraphs of Boyle's law can be plotted at different temperatures. Each curve in the graphs below is at a constant temperature and such curves are called isotherms. The above graph is a pressure-volume graph plotted at three different temperatures (T1, T2, and T3). As observed from the graph, with an increase in temperature, curves shift upwards. This is because of increase in the value of k. The graph of pressure vs inverse volume is a straight line passing through the origin and having the positive slope, k. The graph above is a straight line parallel to the x-axis. This proves the product of pressure and volume at a constant temperature and amount of gas is constant. The lines in the graph are independent of volume (or pressure). Logarithmic graphsThe equation of Boyle's law is PV = k. Taking the logarithm to both sides. The plots are a straight line with the y-intercept of log k. Associated articles
Copy Article Cite "Graphs of Boyle's Law" ChemistryGod, 31st Oct 2019, https://chemistrygod.com/boyle-law-graphThanks for your response!
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Robert Boyle man what u guys are doing is phenomenal . and P = pressure of the gas So at constant temperature, if the volume of a gas is doubled, its pressure is halved. PV = constant PV = k PiVi = PfVf Pi is the initial (original) pressure (a) Pi and Pf must be in the same units of measurement (eg, both in atmospheres or both in kPa) (b) A Real Gas is one which approaches Boyle's Law behaviour as the temperature is raised or the pressure lowered. Please do not block ads on this website. Graphical Representations of Boyle's LawConsider an experiment in which a known amount of hydrogen gas in a syringe has a volume of 23 mL at atmospheric pressure (760 mm Hg or 1 atm or 101.3 kPa). You then apply an external pressure of 912 mm Hg (1.2 atmospheres or 121.6 kPa) by pressing down on the plunger in the syringe. The volume of hydrogen gas is then recorded as 19.2 mL. You continue to apply external pressure by pushing the plunger down further, recording the volume of hydrogen gas as shown in the table below:
If we plot these points on a graph, the graph looks like the one below:
Note that this is not a linear relationship, the line in the graph is curved, it is not a straight line. But look what happens if we multiply volume and pressure (P × V):
For a given amount of gas at constant temperature we now we can write the equation: P × V = constant If we divide both sides of the equation by P, we get: Recall that the equation for a straight line that runs through the point (0,0) is y = mx where m is the slope (or gradient) of the line Then a graph of V against 1/P, should be a straight line with a slope (or gradient) equal to the value of the constant. The table below shows what happens if we calculate 1/P for each volume, V, in the experiment above and then graph the results:
By plotting these points on a graph, we can see that the relationship is linear:
We now have a simple method for determining the value of the constant: Recall that we can calculate the slope (gradient, m) of a straight line using two points on the line and the equation for this straight line is This equation then allows us to calculate the volume of the gas at any pressure, as long as we use the same amount of gas and keep the temperature the same. Let us say we have a specific amount of gas and keep the temperature constant, then initially at pressure Pi the gas has a volume of Vi and we know that: PiVi = constant If we maintain the same temperature and the same amount of gas, but change the pressure to Pf, then the new gas volume will be Vf, and PfVf = the same constant So, as we long as we use the same amount of gas at the same temperature: PiVi = constant = PfVf This means that if we know the initial conditions (Pi and Vi), and, we know the final pressure (Pf), we can calculate the final volume (Vf): or we can calculate the final pressure (Pf) if we know the final volume (Vf): Similarly, if we know the final conditions (Pf and Vf), and, we know the initial pressure (Pi), we can calculate the initial volume (Vi): or we can calculate the initial pressure (Pi) if we know the initial volume (Vi):
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What is the shape of the graph for volume vs pressure in Boyles law?
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