Question

boron trifluoride gas is collected at -11.0 °c in an evacuated flask with a measured volume of 15.0 l. when all the gas has been collected, the pressure in the flask is measured to be 0.130 atm.
calculate the mass and number of moles of boron trifluoride gas that were collected. round your answer to 3 significant digits.
mass: g
mole: mol

Explanation:

Step1: Convert temperature to Kelvin

The temperature \(T=- 11.0^{\circ}C\). Using the conversion \(T(K)=T(^{\circ}C)+273.15\), we have \(T = (-11.0 + 273.15)K=262.15K\)

Step2: Use the ideal gas law \(PV = nRT\) to find the number of moles \(n\)

The ideal gas constant \(R = 0.0821L\cdot atm\cdot K^{-1}\cdot mol^{-1}\), \(P = 0.130atm\), \(V = 15.0L\).
From \(PV=nRT\), we can solve for \(n\): \(n=\frac{PV}{RT}\)
Substitute the values: \(n=\frac{0.130atm\times15.0L}{0.0821L\cdot atm\cdot K^{-1}\cdot mol^{-1}\times262.15K}\)

$$n=\frac{1.95}{21.522515}mol\approx0.0906mol$$

Step3: Calculate the molar mass of \(BF_{3}\)

The molar mass of \(B\) is \(M_{B}=10.81g/mol\), and the molar mass of \(F\) is \(M_{F} = 19.00g/mol\).
For \(BF_{3}\), \(M=10.81g/mol+3\times19.00g/mol=(10.81 + 57.00)g/mol=67.81g/mol\)

Step4: Calculate the mass \(m\) using \(m=nM\)

Substitute \(n = 0.0906mol\) and \(M = 67.81g/mol\)
\(m=0.0906mol\times67.81g/mol\approx6.14g\)

Answer:

mass: \(6.14g\)
mole: \(0.0906mol\)