7.75 litres of radon gas is at 1.55 atm and -19 degrees c what is the volume at stp
Use (P1V1/T1) = (P2V2/T2)
To find the volume of the radon gas at STP (Standard Temperature and Pressure), we need to use the ideal gas law. The ideal gas law equation is:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature
STP conditions are defined as:
Pressure (P) = 1 atmosphere (atm)
Temperature (T) = 273.15 Kelvin (K)
Volume (V) = ?? (what we need to find)
First, we need to convert the given values to the appropriate units.
1 atm = 1.01325 * 10^5 Pascals (Pa)
-19 degrees Celsius = -19 + 273.15 Kelvin (K)
Given:
Initial pressure (P1) = 1.55 atm
Initial volume (V1) = 7.75 L
Initial temperature (T1) = -19 °C = -19 + 273.15 K
Now, let's calculate the number of moles of radon gas using the ideal gas law:
n1 = (P1 * V1) / (R * T1)
The ideal gas constant (R) is 0.0821 L·atm/(K·mol).
Substituting the values:
n1 = (1.55 atm * 7.75 L) / (0.0821 L·atm/(K·mol) * (254.15 K))
n1 ≈ 2.08 moles
Next, we'll use the Avogadro's Law, which states that equal volumes of gases at the same temperature and pressure contain an equal number of molecules.
Since the number of moles remains constant, we can write:
(V1 / n1) = (V2 / n2)
At STP, the pressure (P2) is 1 atm, and we want to find the volume (V2).
Substituting the values:
(7.75 L / 2.08 moles) = (V2 / 1 mole)
V2 = 7.75 L / 2.08
V2 ≈ 3.72 L
Therefore, the volume of the radon gas at STP would be approximately 3.72 liters.