To determine the number of moles of gas occupying a given volume, pressure, and temperature, we can use the ideal gas law equation:
PV = nRT
Where: P = Pressure (in Pa) V = Volume (in m^3) n = Number of moles of gas R = Gas constant (8.314 J/(mol·K)) T = Temperature (in Kelvin)
First, let's convert the given values to the appropriate units: Pressure = 600 kPa = 600,000 Pa Volume = 0.6 cm^3 = 0.6 × 10^(-6) m^3 (since 1 cm^3 = 10^(-6) m^3) Temperature = 380°C = 380 + 273.15 K (converted to Kelvin)
Now, we can substitute the values into the ideal gas law equation and solve for n:
(600,000 Pa) × (0.6 × 10^(-6) m^3) = n × (8.314 J/(mol·K)) × (380 + 273.15 K)
Simplifying the equation:
360 = n × (8.314 × 653.15)
Dividing both sides by (8.314 × 653.15):
n = 360 / (8.314 × 653.15)
Calculating the value:
n ≈ 0.0684 moles
Therefore, approximately 0.0684 moles of gas occupy a volume of 0.6 cm^3 at a pressure of 600 kPa and a temperature of 380°C.