A 4.0 L of a gas at a pressure of 205 kPa is allowed to expand to a volume of 16.0 L. Calculate the pressure in atmospheres (atm) in the container at constant temperature.
To solve this problem, we can use the formula for the ideal gas law:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.
Since the temperature is constant, we can simplify the equation to:
P1V1 = P2V2
Where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.
Substituting the given values, we get:
205 kPa x 4.0 L = P2 x 16.0 L
Simplifying the equation, we get:
P2 = (205 kPa x 4.0 L) / 16.0 L
P2 = 51.25 kPa
To convert this to atmospheres, we divide by the standard atmospheric pressure (101.3 kPa):
P2 = 51.25 kPa / 101.3 kPa/atm
P2 = 0.506 atm (rounded to three significant figures)
Therefore, the pressure in the container at constant temperature is 0.506 atm.
To find the pressure in atmospheres (atm), we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature of the gas in Kelvin (K)
Since the temperature is constant, we can rewrite the equation as:
P₁V₁ = P₂V₂
Where:
P₁ and V₁ are the initial pressure and volume
P₂ and V₂ are the final pressure and volume
Given:
P₁ = 205 kPa
V₁ = 4.0 L
V₂ = 16.0 L
Now we can substitute the given values into the equation and solve for P₂:
P₁V₁ = P₂V₂
205 kPa × 4.0 L = P₂ × 16.0 L
820 kPa·L = P₂ × 16.0 L
P₂ = (820 kPa·L) / (16.0 L)
P₂ = 51.25 kPa
To convert kPa to atm, we can use the conversion factor:
1 atm = 101.325 kPa
Therefore, the pressure in the container at constant temperature is 51.25 kPa / 101.325 kPa = 0.506 atm.