Relationship between the pressure and volume of helium gas at a constant temperature of 298K. Volume was changed by moving a piston & following data was obtained:
Vol (L) Pressure (atm)
5 10.229
10 4.749
15 3.198
20 2.381
30 1.665
50 0.98
75 0.655
100 0.47
1. what would be the pressure of the helium gas be if the volume of the cylinder would be changed to 40.0L?
I got 0.611 atm, is that right?
2. I have no clue how to begin this one so please help! since you are aware that for an ideal gas P=nRT/V, the relationship of P vs 1/V is expected to be a straight line. Recalculate the data and plot the graph of P vs. 1/V. Fit the best straight line through the points.
I don't get that answer for #1. I calculated k from PV = k for each of the eight points shown in your post. Then I averaged the eight to find an avg number for k. Then PV = k; therefore, P=k/v, substituted the avg for k and 40 into that equation and calculated p. I obtained something like 1.2 or so but you should confirm that.
For #2, use a piece of graph paper, set up a scale for P and 1/V and the x and y axes, plot the data, and draw the best straight line through all the points.
To answer the first question, we can use the given data to determine the relationship between pressure and volume of helium gas. From the data, it is clear that as the volume of the cylinder decreases, the pressure of the gas increases. This suggests an inverse relationship between pressure and volume at constant temperature.
To find the pressure of the helium gas at a volume of 40.0 L, we can use the data points provided. From the data, we see that at a volume of 30 L, the pressure is 1.665 atm, and at a volume of 50 L, the pressure is 0.98 atm.
We can assume that the relationship between pressure and volume is linear, and use a simple linear interpolation to estimate the pressure at 40.0 L. Using the following formula:
(P - P1) / (V - V1) = (P2 - P1) / (V2 - V1)
where P1, V1 represent the data point at 30 L, and P2, V2 represent the data point at 50 L. Plugging in the values:
(P - 1.665) / (40 - 30) = (0.98 - 1.665) / (50 - 30)
Simplifying the equation, we get:
P - 1.665 = -0.1685
P = 1.4965 atm
Thus, the estimated pressure of the helium gas at a volume of 40.0 L is approximately 1.4965 atm. It seems there might have been a calculation error in your answer of 0.611 atm.
For the second question, we are asked to plot the graph of P vs. 1/V and fit the best straight line through the points. To do this, we need to rearrange the ideal gas law equation, P = nRT/V, to isolate 1/V. The rearranged equation would be:
1/V = P / (nRT)
Now let's recalculate the data points based on 1/V:
Vol (L) 1/V (1/L) Pressure (atm)
5 0.2 10.229
10 0.1 4.749
15 0.067 3.198
20 0.05 2.381
30 0.033 1.665
50 0.02 0.98
75 0.0133 0.655
100 0.01 0.47
Now, plot the graph of P vs. 1/V using the recalculated data points. Each data point will be represented by a point on the graph.
By looking at the graph, we can try to fit the best straight line through the points. We want to find a line that passes through the majority of the points, minimizing the distance between the line and the data points.
You can use a graphing software or a spreadsheet program to plot the graph and observe the line that most closely fits the data points.