To solve this problem, we can use the ideal gas law, which states:
PV = nRT
Where: P = pressure V = volume n = number of moles of gas R = ideal gas constant T = temperature in Kelvin
First, we need to convert the temperatures from Celsius to Kelvin. The conversion formula is:
T(K) = T(°C) + 273.15
Given: Initial pressure, P1 = 2.00 ATM Initial temperature, T1 = 25.0 °C Final temperature, T2 = 50.0 °C
Converting the temperatures to Kelvin: T1(K) = 25.0 °C + 273.15 = 298.15 K T2(K) = 50.0 °C + 273.15 = 323.15 K
Since the container is sealed and rigid, the volume (V) remains constant. Therefore, we can rewrite the ideal gas law as:
P1V = nRT1 P2V = nRT2
Dividing the two equations, we get:
P2/P1 = (T2/T1) * (R/R)
We can cancel out the volume (V) and the number of moles (n) since they remain constant.
Now, let's calculate the pressure (P2):
P2 = P1 * (T2/T1)
Substituting the given values:
P2 = 2.00 ATM * (323.15 K / 298.15 K) P2 = 2.17 ATM
Therefore, the pressure of the gas at 50.0 °C is approximately 2.17 ATM.