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. Consider 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: Decreasing the applied pressure increases the volume of the gas. 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):
Do you know this? Join AUS-e-TUTE! Play the game now! Question : A certain mass of gas occupies a volume of 2.5 L at 90 kPa pressure. Solution: (Based on the StoPGoPS approach to problem solving.)
Do you understand this? Join AUS-e-TUTE! Take the test now! Question : 4.5 L of gas at 125 kPa is expanded at constant temperature until the pressure is 75 kPa. Solution: (Based on the StoPGoPS approach to problem solving.)
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