(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A pop-up turkey thermometer has 1.0 mL of air trapped beneath the red plastic indicator. When the thermometer was assembled, the temperature was 10 *C, and atmosphereic pressure was 750 mmHg. If the pressure required to break the seal and pop up the syringe is 932 mm Hg, at what temperature in *F will the turkey be done?

2. Relevant equations

PV=nrT

*C x 9/5 + 32 = *F

*C + 273 = *K

P_1V_1=P_2V_2

1 atm = 760 mmHg

P_1V_1/n_1T_1=P_2V_2/n_2T_2 (I'm not sure if I need this one or not)

3. The attempt at a solution

First, I started computing my starting variables.

P_1 = 750/760 = .987 atm

V_1= .001 L

T_1= 283 *K

n_1 = ?

P_2= 932/760 = 1.23 atm

V_2 = ?

T_2 = ?

n_2 = ?

To continue, I need to find n. So I used the Ideal Gas Law (no excessive pressures).

PV=nRT

PV/RT=n

(.987 atm)(.001 L)/(.0821 Lxatm/molxK)(283 *K) = 4.25 x 10^-5 mol air

I assign this value to both n_1 and n_2, because the mols of air shouldn't change.

When writing the combined gas law, I still need to find V_2 to find T_2. So I use Charle's Law.

P_1V_1/P_2 = V_2

(.987 atm)(.001 L)/(1.23 atm) = 8.02 x 10^-4

This is where I'm uncertain. I rearrange the combined gas law to look like this:

P_1V_1n_2/P_2V_2n_1T_1 = T_2

Plug in my numbers, I get 3.54 x 10^-3 *K. That's rediculous, considering the context of the problem. So I try to use the Ideal Gas Law, but only on the second state of gas

PV=nRT

manipulated to PV/nR=T

(1.23 atm)(.001 L)/(4.248 x 10^-5 mol)(.0821 L x atm/mol x K) = 353 *K. A much more reasonable answer. I convert to C, and get 80 *C. I think I've got it. Convert to *F, and I get 176 *F. But the computer says I'm wrong. Where did I mess up? Help please?

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# Homework Help: Ideal/Combined Gas Law equation

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