Question

a sample of an unknown compound is vaporized at 140. °c. the gas produced has a volume of 2230. ml at a pressure of 1.00 atm, and it weighs 2.24 g.
assuming the gas behaves as an ideal gas under these conditions, calculate the molar mass of the compound. be sure your answer has the correct number of significant digits.

\\( \square \frac { g } { m o l } \\)

Explanation:

Step1: Convert units

• Convert volume \( V = 2230\,\text{mL}\) to liters: \( V=2230\times10^{- 3}\,\text{L}=2.23\,\text{L}\)
• Convert temperature \(T = 140^{\circ}\text{C}\) to Kelvin: \(T=(140 + 273.15)\,\text{K}=413.15\,\text{K}\)
• Pressure \(P = 1.00\,\text{atm}\), gas constant \(R=0.0821\,\text{L}\cdot\text{atm}\cdot\text{K}^{-1}\cdot\text{mol}^{-1}\)

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

$$n=\frac{PV}{RT}$$

Substitute \(P = 1.00\,\text{atm}\), \(V = 2.23\,\text{L}\), \(R=0.0821\,\text{L}\cdot\text{atm}\cdot\text{K}^{-1}\cdot\text{mol}^{-1}\), \(T = 413.15\,\text{K}\)

$$n=\frac{1.00\times2.23}{0.0821\times413.15}$$

$$n=\frac{2.23}{33.92}$$

$$n\approx0.0657\,\text{mol}$$

Step3: Calculate the molar mass \(M\)

The mass of the sample \(m = 2.24\,\text{g}\), and \(M=\frac{m}{n}\)
Substitute \(m = 2.24\,\text{g}\) and \(n\approx0.0657\,\text{mol}\)

$$M=\frac{2.24}{0.0657}$$

$$M\approx34.1\,\text{g/mol}$$

Answer:

\(34.1\,\text{g/mol}\)