t 103
◦
C, the pressure of a sample of nitrogen
is 1
.
89 atm. What will the pressure be at
275
◦
C, assuming constant volume?
Answer in units of atm
To answer this question, we can make use of the Ideal Gas Law, which states that the pressure of a gas is directly proportional to its temperature (in Kelvin) when the volume and the amount of gas are kept constant. The equation for the Ideal Gas Law is:
PV = nRT
Where:
P = pressure
V = volume
n = amount of gas (in moles)
R = ideal gas constant
T = temperature (in Kelvin)
First, let's convert the initial temperature from Celsius to Kelvin. We can do this by adding 273.15 to the Celsius temperature:
T1 = 103 + 273.15 = 376.15 K
Next, let's find the pressure at a new temperature of 275 °C, which can also be converted to Kelvin:
T2 = 275 + 273.15 = 548.15 K
Since the volume is assumed to be constant, we can rearrange the Ideal Gas Law equation to solve for the final pressure:
P1/T1 = P2/T2
Now, substitute the known values:
1.89 atm / 376.15 K = P2 / 548.15 K
To solve for P2 (the pressure at 275 °C), cross-multiply and then divide:
P2 = (1.89 atm) * (548.15 K) / 376.15 K
Calculating this expression gives us:
P2 ≈ 2.76 atm
Therefore, assuming constant volume, the pressure of the nitrogen gas at 275 °C would be approximately 2.76 atm.