A chemical engineer must calculate the maximum safe operating temperature of a high-pressure gas reaction vessel. The vessel is a stainless-steel cylinder that measures 13.0cm wide and 15.6cm high. The maximum safe pressure inside the vessel has been measured to be 2.70MPa. For a certain reaction the vessel may contain up to 0.0985kg of boron trifluoride gas. Calculate the maximum safe operating temperature the engineer should recommend for this reaction. Write your answer in degrees Celsius.
Question
Answer:
1577 °C
Explanation:
Step 1: Calculate the volume of the cylinder
The diameter of the base (d) is 13.0 cm and the height (h) is 15.6 cm. We will use the following expression.
V = h × π × (d/2)²
V = 15.6 cm × π × (13.0 cm/2)² = 8.28 × 10³ cm³ = 8.28 × 10³ mL = 8.28 L
Step 2: Calculate the moles of BF₃
We have 0.0985 kg (98.5 g) of BF₃, whose molar mass is 67.81 g/mol.
98.5 g × 1 mol/67.81 g = 1.45 mol
Step 3: Convert 2.70 MPa to atm
We will use the conversion factor 1 MPa = 9.86923 atm.
2.70 MPa × 9.86923 atm/1 MPa = 26.6 atm
Step 4: Calculate the maximum safe operating temperature
We will use the ideal gas equation.
P × V = n × R × T
T = P × V / n × R
T = 26.6 atm × 8.28 L / 1.45 mol × (0.0821 atm.L/mol.K) = 1850 K
We can convert 1850 K to Celsius using the following expression.
°C = K – 273.15 = 1850 K – 273.15 = 1577 °C