Finding Temperature Using Ideal Gas Law

[LezardValeth]

The pressure in a constant-volume gas thermometer is 7.09x10 to the fifth power Pa at 100.0 degrees celsius and 5.19 x 10 to the fourth power Pa at 0.0 degrees celsius. What is the temperature when the pressure is 4.05x10 to the third power Pa?

now I've been told how to do this problem many different ways (those sources arent reliable) then I went to my teacher and she said to find the volume and use PV=nRT

ok so I know what R is and in order to use PV=nRT don't I have to find moles?

Im just completely confuse atm

 

[franznietzsche]

The pressure in a constant-volume gas thermometer is 7.09x10 to the fifth power Pa at 100.0 degrees celsius and 5.19 x 10 to the fourth power Pa at 0.0 degrees celsius. What is the temperature when the pressure is 4.05x10 to the third power Pa?
now I've been told how to do this problem many different ways (those sources arent reliable) then I went to my teacher and she said to find the volume and use PV=nRT
ok so I know what R is and in order to use PV=nRT don't I have to find moles?
Im just completely confuse atm

Yes, and no.

The trick is, there are two states here, both with the same n that are given to you. So make a system of two equations using PV=nRT and the first two states given. Then you have two equations with two unknowns, V and n. Solve for both, then use PV=nRT for the third state to answer the question.

 

[durt]

$$\frac{P}{T} = \frac{n R}{V} = constant$$

$$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$

$$T_2 = \frac{P_2 T_1}{P_1}$$

That clear anything up? Just notice that when some combination of variables is constant, you can equate them during different conditions to solve for an unknown.

 

[LezardValeth]

$$\frac{P}{T} = \frac{n R}{V} = constant$$
$$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$
$$T_2 = \frac{P_2 T_1}{P_1}$$
That clear anything up? Just notice that when some combination of variables is constant, you can equate them during different conditions to solve for an unknown.

Im not quite sure about the first equation (math isn't my strong point sorry >< )

 

[durt]

I just rearranged the ideal gas equation, and since the number of moles and the volume don't change, its constant.

 

[LezardValeth]

so if n and V are constant that formula would become P over T = R ?

 

[franznietzsche]

so if n and V are constant that formula would become P over T = R ?

No. Look at my post. Durt did the same thing, he just showed the equations rather than talking about why it worked so much.

 

[durt]

They're not necessarily 1 (and even if they were, the units would be different from those of R). You can't know what the constant is because you don't know n or V. All you know is that P/T is always constant. If P gets bigger, T gets bigger. If T gets smaller, P gets smaller.

 

[LezardValeth]

thanks a lot guys I appreciate the help

Ill try to figure this out with the info you guys gave me =]