Suppose 2 moles of an ideal gas are enclosed in a container of volume 2.70·10^4 m^3. The container is then placed in a furnace and raised to a temperature of 390 K. What is the final pressure of the gas?
Use the ideal gas law:
P V = n R T
You know what V, n and T are .
R is the molar gas constant, 8.317 J/mole*K
The computed value of P will be in pascals (Pa), which is N/m^2
To find the final pressure of the gas, we can make use of the ideal gas law equation, which states:
PV = nRT
Where:
P is the pressure of the gas,
V is the volume of the container,
n is the number of moles of the gas,
R is the ideal gas constant, and
T is the temperature of the gas.
In this case, we have the following information:
n = 2 moles
V = 2.70·10^4 m^3
T = 390 K
We also need the value of the ideal gas constant, which is R = 8.314 J/(mol·K).
Now, we can rearrange the ideal gas law equation to solve for the pressure, P:
P = (nRT) / V
Plugging in the given values:
P = (2 moles * 8.314 J/(mol·K) * 390 K) / (2.70·10^4 m^3)
Simplifying the equation:
P = 191.14 J / (10^4 m^3)
P = 19.1 Pa
Therefore, the final pressure of the gas in the container is 19.1 Pa.