how would the graph of Pressure vs Volume look for a sample of an ideal gas that has a volume of 1 L at 0 degrees Celsius and 1 bar. How would the graph of Pressure versus volume look for sample of gas at the same conditions but at 100 degrees Celsius?
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To understand how the graph of Pressure vs Volume would look for the given conditions, we need to consider the relationship between pressure, volume, and temperature for an ideal gas.
According to the ideal gas law, PV = nRT, where P represents the pressure, V represents the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
Now, let's analyze the first scenario where the gas has a volume of 1 L at 0 degrees Celsius and 1 bar.
To analyze the graph, we need to keep two of the variables constant and observe the relationship between the remaining two. In this case, we are keeping the temperature (T) and the amount of gas (n) constant.
Since the volume is fixed at 1 L, and we are exploring the relationship with pressure, we can rewrite the ideal gas law as P = nRT/V. The temperature (T) is fixed at 0 degrees Celsius, which is equivalent to 273 Kelvin.
Now, let's substitute the values into the equation and calculate the pressure (P). n and R are constant and can be taken as 1 and 0.0831 L bar/mol K respectively.
P = (1 mol)(0.0831 L bar/mol K)(273 K) / 1 L
P = 22.71 bar
So, at 0 degrees Celsius and 1 L volume, the pressure is 22.71 bar.
To plot the graph, we vary the volume and calculate the corresponding pressure using the equation P = (nRT)/V. Since we took n and T as constant, we can rearrange the equation as P/V = nRT.
By substituting the constant values: n = 1 mol, R = 0.0831 L bar/mol K, and T = 273 K; we can rearrange the equation as P = (1 mol)(0.0831 L bar/mol K)(273 K)/V.
Now we can plot the graph with volume on the x-axis and pressure on the y-axis. As the volume increases, the pressure decreases, following an inverse relationship. Therefore, the graph would be a rectangular hyperbola, curving downwards.
Now let's analyze the second scenario, where the conditions remain the same except the temperature is 100 degrees Celsius, which is 373 Kelvin.
Using the same formula P = nRT/V, with T = 373 K, we can calculate the pressure (P) and plot the graph in a similar manner as described above.
P = (1 mol)(0.0831 L bar/mol K)(373 K)/V
Again, as the volume increases, the pressure decreases, but the pressure values will be different due to the change in temperature. The relationship is still inverse, and the graph will be a rectangular hyperbola curving downwards but with different pressure values at each corresponding volume.
Therefore, the graph for the second scenario, where the gas is at the same conditions but at 100 degrees Celsius, will have the same shape as the first graph but with different pressure values at each volume point.