The pressure in a constant-volume gas thermometer is 0.700 atm at 100°C and 0.512 atm at 0°C.
(a) What is the temperature when the pressure is 0.0500 atm?
°C
(b) What is the pressure at 405°C?
atm
A 5.0 flask contains 0.60 g O2 at a temperature of 22 celcus. What is the pressure (in atm) inside the flask?
To solve these problems, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P is the pressure,
V is the volume (which is constant in this case),
n is the number of moles,
R is the ideal gas constant, and
T is the temperature in Kelvin.
To convert temperatures from Celsius to Kelvin, we can use the formula:
T(K) = T(°C) + 273.15
(a) To find the temperature when the pressure is 0.0500 atm, we can rearrange the ideal gas law equation to solve for temperature:
T = PV / (nR)
Given:
P1 = 0.700 atm
T1 = 100°C + 273.15 = 373.15 K
P2 = 0.0500 atm
The number of moles and the gas constant will cancel out, as they are the same for all temperatures. Thus, we can rewrite the equation as:
T2 = (P2 * T1) / P1
Substituting the given values:
T2 = (0.0500 atm * 373.15 K) / 0.700 atm
T2 ≈ 26.67 K
Therefore, the temperature is approximately 26.67°C when the pressure is 0.0500 atm.
(b) To find the pressure at 405°C, we can rearrange the ideal gas law equation to solve for pressure:
P = nRT / V
Given:
T3 = 405°C + 273.15 = 678.15 K
T1 = 100°C + 273.15 = 373.15 K
P1 = 0.700 atm
Since the volume is constant, we can find the pressure using:
P3 = (P1 * T3) / T1
Substituting the given values:
P3 = (0.700 atm * 678.15 K) / 373.15 K
P3 ≈ 1.27 atm
Therefore, the pressure at 405°C is approximately 1.27 atm.
To solve these problems, we can use the ideal gas law, which states that the pressure (P) and temperature (T) of a gas are related by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
In this case, we are given the pressure and temperature at two different points and need to find the temperature or pressure at a third point.
(a) To find the temperature T when the pressure is 0.0500 atm, we can use the ratio of the pressures at the two known points and the corresponding temperatures:
(P1/T1) = (P2/T2)
Let's assign the points as follows:
Point 1: Pressure = 0.700 atm, Temperature = 100°C (373K)
Point 2: Pressure = 0.512 atm, Temperature = 0°C (273K)
Point 3: Pressure = 0.0500 atm, Temperature = T
Using the formula, we can write:
(0.700/373) = (0.512/273)
Rearranging the equation to solve for T:
T = (0.0500 * 273 * 373) / 0.512
Calculating the value, T ≈ 95.9°C
Therefore, the temperature when the pressure is 0.0500 atm is approximately 95.9°C.
(b) To find the pressure at 405°C, we can again use the ratio of pressures at the two known points and the corresponding temperatures:
(P1/T1) = (P2/T2)
Using the values:
Point 1: Pressure = 0.512 atm, Temperature = 0°C (273K)
Point 2: Pressure = ?, Temperature = 405°C (678K)
Rewriting the equation:
(0.512/273) = (P2/678)
Solving for P2:
P2 = (0.512 * 678) / 273
Calculating the value, P2 ≈ 1.27 atm
Therefore, the pressure at 405°C is approximately 1.27 atm.