A sample of gas in a closed container at a
temperature of 83�C and a pressure of 9 atm
is heated to 259�C. What pressure does the
gas exert at the higher temperature?
Answer in units of atm
(P1/T1) = (P2/T2)
Remember T must be in kelvin.
i got 6.023
I don't think so.
273 + 83 = 356K
273 + 259 = 532K
(9/56) = (P2/532)
P2 = not 6.023. More like 13.44 atm rounded to the correct number of significant figures.
To understand how to find the pressure of the gas at the higher temperature, 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 of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
However, before proceeding, we need to convert the given temperatures from Celsius to Kelvin since the ideal gas law requires temperature in Kelvin. To convert Celsius to Kelvin, we add 273.15 to the Celsius temperature.
Given:
Initial temperature (Ti) = 83°C
Final temperature (Tf) = 259°C
Initial pressure (Pi) = 9 atm
Converting the temperatures:
Initial temperature in Kelvin (Ti) = 83°C + 273.15 = 356.15 K
Final temperature in Kelvin (Tf) = 259°C + 273.15 = 532.15 K
Now, let's assume the volume (V), the number of moles (n), and the ideal gas constant (R) remain constant. We can rewrite the ideal gas law equation in the following form, assuming initial and final conditions:
(Pi * Vi) / Ti = (Pf * Vf) / Tf
Since Vi = Vf, n = n, and R = R remain constant, we can simplify the equation as:
Pi / Ti = Pf / Tf
Now, let's substitute the given values and solve for Pf:
Pi = 9 atm
Ti = 356.15 K
Tf = 532.15 K
9 atm / 356.15 K = Pf / 532.15 K
Cross-multiplying to solve for Pf:
Pf = (9 atm * 532.15 K) / 356.15 K
Pf = 13.457 atm
Therefore, the gas exerts a pressure of approximately 13.457 atm at the higher temperature of 259°C.