At 265 K, the pressure of 0.0454 mol of an ideal gas is 1.42×105 Pa. What volume does the gas occupy?
To find the volume that the gas occupies, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure (in Pa)
V is the volume (in m³)
n is the number of moles of the gas
R is the gas constant (8.314 J/(mol·K))
T is the temperature (in Kelvin)
We are given:
P = 1.42×10^5 Pa
n = 0.0454 mol
T = 265 K
First, we need to convert the pressure from Pascal to atm since the gas constant is given in units of J/(mol·K) and atm is a more commonly used unit of pressure.
1 atm = 101325 Pa (approximately)
So, we can convert the given pressure as follows:
P(atm) = P(Pa) / 101325
P(atm) = 1.42×10^5 Pa / 101325
P(atm) ≈ 1.4 atm (approximately)
Now, we can rearrange the ideal gas law equation to solve for the volume (V):
V = (nRT) / P
Substituting the known values into the equation:
V = (0.0454 mol * 8.314 J/(mol·K) * 265 K) / 1.4 atm
Simplifying:
V ≈ 9.67 m³ (approximately)
Therefore, the gas occupies approximately 9.67 m³ of volume at 265 K.