0.75 mol of argon gas is admitted to an evacuated 40 cm^{3} container at 40 C. The gas then undergoes an isochoric heating to a temperature of 500 C.
Before I forgot to write the question...so the question is What is the final pressure of the gas?
* physics - drwls, Friday, December 11, 2009 at 11:07am
What is the question?
I had to look up "isochoric". It means "contant volume". During that heating process, p will increase such that it remains proportional to (absolute) T. The absolute temperature increases by a factor 773/313 = 2.47. Pressure increases by the same factor. They do not tell you the initial pressure, but you can get the pressure using
P = nRT/V
where R = 82.06 cm^3*atm/mole K
Po = 0.75*82.06*313/40 = 482 atm
I have to get the answer in kPa so I got 4.883865e^4 kPa...but it is wrong
ok...now tired
P=(0.75)*(8.31)*(773-313)/(4*10^-5)=106373
106373/1000=106.37kPa..still wrong
To find the final pressure of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant
T is the temperature in Kelvin
First, we need to convert the temperature from Celsius to Kelvin:
Temperature in Kelvin = 40 C + 273.15 = 313.15 K (initial temperature)
Final temperature = 500 C + 273.15 = 773.15 K
The gas is isochorically heated, which means the volume remains constant throughout the process. Therefore, the initial and final volumes are the same.
Next, we can calculate the initial pressure using the given information:
P_initial = (nRT) / V_initial
Given:
n = 0.75 mol
R = 82.06 cm^3*atm/mol*K
V_initial = 40 cm^3
T_initial = 313.15 K
P_initial = (0.75 mol * 82.06 cm^3*atm/mol*K * 313.15 K) / 40 cm^3
P_initial = 482 atm
Now, we can determine the final pressure using the information that the temperature increases to 500 C:
P_final = P_initial * (T_final / T_initial)
P_final = 482 atm * (773.15 K / 313.15 K)
P_final = 1191.8 atm
To convert the pressure from atm to kPa, we know that 1 atm = 101.325 kPa. Therefore:
P_final in kPa = 1191.8 atm * 101.325 kPa/atm
P_final in kPa = 120,613.5 kPa
So, the final pressure of the gas is approximately 120,613.5 kPa.