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
