Question

a 1.27 - g sample of an unknown gas has a volume of 722 ml and a pressure of 563 mmhg at 39.0°c. calculate the molar mass of this compound.

Explanation:

Step1: Convert units

• Convert volume \( V = 722\space mL=0.722\space L \)
• Convert pressure \( P = 563\space mmHg=\frac{563}{760}\space atm\approx0.741\space atm \)
• Convert temperature \( T = 39.0^{\circ}C=(39.0 + 273.15)\space K = 312.15\space K \)
• The ideal gas constant \( R=0.0821\space L\cdot atm/(mol\cdot K) \)
• Given mass \( m = 1.27\space g \)

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

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

Substitute the values:

$$n=\frac{0.741\space atm\times0.722\space L}{0.0821\space L\cdot atm/(mol\cdot K)\times312.15\space K}$$

$$n=\frac{0.535\space L\cdot atm}{25.63\space L\cdot atm/mol}\approx0.0209\space mol$$

Step3: Calculate molar mass \( M \)

Molar mass \( M=\frac{m}{n} \)
Substitute \( m = 1.27\space g \) and \( n\approx0.0209\space mol \)

$$M=\frac{1.27\space g}{0.0209\space mol}\approx60.8\space g/mol$$

Answer:

\(60.8\space g/mol\)