To calculate the volume occupied by a gas under given conditions (temperature and pressure) assuming ideal behavior, you can use the ideal gas law, which is given by:
PV = nRT
Where:
P = Pressure (in Pascals)
V = Volume (in cubic meters)
n = Number of moles of the gas
R = Universal gas constant (approximately 8.314 J/(mol·K))
T = Temperature (in Kelvin)
First, you need to find the number of moles (n) of carbon dioxide (CO2) using its molar mass. The molar mass of CO2 is approximately 44.01 g/mol.
Given mass (m) of CO2 = 0.07 kg = 70 g
Molar mass (M) of CO2 = 44.01 g/mol
n = m / M
n = 70 g / 44.01 g/mol
n ≈ 1.590 moles
Now, you can use the ideal gas law to find the volume (V):
PV = nRT
V = (nRT) / P
Where:
P = Pressure = 30500 Pa
T = Temperature = 303 K
R = Universal gas constant = 8.314 J/(mol·K)
V = (1.590 moles * 8.314 J/(mol·K) * 303 K) / 30500 Pa
V ≈ 0.396 cubic meters
So, the volume occupied by 0.07 kg of carbon dioxide gas at a temperature of 303 K and a pressure of 30500 Pa, assuming ideal behavior, is approximately 0.396 cubic meters.