Question

A student used a sealed glass jar, whose volume could be adjusted by a moving piston, to set the gas volume and then measure the pressure of 1.00 mol of an ideal gas. The temperature was kept constant at 3.00x10^2K.

Answer 1

I have the equation \[P=nRT \frac{ 1 }{ V }\] and I've figured out was nRT is (it's roughly 2.707). This is primarily a graphing excercise. However the aim is to find R. How do I do this?

Answer 2

I tried to calculate R and came up with 110.823, but it says the accepted value for R is that \[R=8.314JK ^{-1}mol ^{-1}\] What does this mean? I'm seriously stuck!

Answer 3

You're doing this right.
You've arranged the ideal gas law in terms of V.
You know n, R and T are constants.
So you can draw a simple inverse proportion function curve.
Is the value of P given? Is it in Pa? If not, you have to convert.

Answer 4

Yes, P is given, I have a table of them. But what is an invense proportion function curve? I've drawn a graph and it's defintely a straight line (with P as y, nRT as m, etc). I also calculated R again and got 0.83 with the three repeating, which looks similar to 8.314JK−1mol−1.

Answer 5

The -V diagramme should look like below.

However, it may look like a straight line depending on the scale on the graph.
0.83 doesn't look too bad. Try again and see if you can get the accepted value.

Answer 6

The graph is actually P vs. 1/V, which is a straight line. It looks a bit like this.

Answer 7

Oh, okay. I thought you were to draw a P-V diagramme.
Since it is against 1/V, a straight line is correct.
Have you managed to get the gas constant, R?

Answer 8

So far it's just 0.83. I'm not sure how to get it into the form above. We haven't gone over what this equation means exactly in class, we're just supposed to work on graphing and figuring out different values through graphs.

Answer 9

What the ideal gas law, PV = nRT, tells is the following.
(a) When T = constant, P = nRT / V. All the variables you have is pressure, P, and temperature, T. So it just tells you the higher the pressure, the smaller the volume. Vice versa, the larger the volume, the lower the pressure.
Likewise, you can also think what the ideal gas law means when
(b) P = constant
and
(c) V = constant

Answer 10

Just think what you have to do to squash a pillow into a small space.

Answer 11

when you graph P vs. 1/V you get the straight line shown above. THe slope of the line isn't R, it's n*R*T. You have the values of n and T, so take the numerical value of slope and solve for R\[slope = n*R*T\]so \[R = \frac{slope}{n*T}\]

Answer 12

Yes, I've already got that, I entered all the values and the value of R is what I got from it. What I'm wondering is what the JK−1mol−1 means.

Answer 13

The meaning of \[JK^{-1}mol^{-1}\]is exactly the same as what the ideal gas law means.
J is equivalent to the unit of pressure times volume.

Answer 14

Ok, I've got it figured out. Thanks!