A sample of helium gas occupies 355ml at 23°c. if the container the he is in is expanded to 1.50 l at constant pressure, what is
the final temperature for the he at this new volume?
2 answers:
Answer: The final temperature would be 1250.7 K.
Explanation: We are given a sample of helium gas, the initial conditions are:
(Conversion factor: 1L = 1000 mL)
(Conversion Factor: 1° C = 273 K)
The same gas is expanded at constant pressure, so the final conditions are:
To calculate the final temperature, we use Charles law, which states that the volume of the gas is directly proportional to the temperature at constant pressure.
Putting the values, in above equation, we get:
<em>The final temperature for the He at this new volume = 1250,704 liters</em>
<h3><em>Further explanation</em></h3>There are several gas equations in various processes:
- 1. The general ideal gas equation
PV = nRT
PV = NkT
N = number of gas particles
n = number of moles
R = gas constant (8,31.10³ J / kmole K)
k = Boltzmann constant (1,38.10⁻²³)
n = = N / No
n = m / M
n = mole
No = Avogadro number (6.02.10²³)
m = mass
M = relative molecular mass
- 2. Avogadro's hypothesis
In the same temperature and pressure, in the same volume conditions, the gas contains the same number of molecules
So it applies: the ratio of gas volume will be equal to the ratio of gas moles
- 3. Boyle's Law
At a fixed temperature, the gas volume is inversely proportional to the pressure applied
- 4. Charles's Law
When the gas pressure is kept constant, the gas volume is proportional to the temperature
- 5. Gay Lussac's Law
When the volume is not changed, the gas pressure in the tube is proportional to its absolute temperature
- 6. Law of Boyle-Gay-Lussac
Combined with Boyle's law and Gay Lussac's law
P1 = initial gas pressure (N / m2 or Pa)
V1 = initial gas volume (m3)
P2 = gas end pressure
V2 = the final volume of gas
T1 = initial gas temperature (K)
T2 = gas end temperature
In the problem, the conditions that are set constant are Pressure, so we use Charles' Law
We first convert the known number
V1 = 355 ml = 355.10-3 liters
T1 = 23 C = 23 + 273 = 296 K
V2 = 1.5 liters
We enter the formula
T2 = 1250, 704 K
<h3><em>Learn more</em></h3>a description of Charles’s law
Charles's law
State Boyle's, Charles's, and Gay-Lussac's laws
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