Question

1. a 0.465 g sample of an unknown compound occupies 245 ml at 298 k and 1.22 atm. what is the molar mass of the unknown compound? a. 26.3 g/mol b. 33.9 g/mol c. 12.2 g/mol d. 38.0 g/mol e. 81.8 g/mol

Explanation:

Step1: Convert volume to liters

The volume \( V = 245\space mL=245\times10^{- 3}\space L = 0.245\space L\)

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

The ideal gas law is \(PV = nRT\), where \(P = 1.22\space atm\), \(R=0.0821\space L\cdot atm/(mol\cdot K)\), \(T = 298\space K\)

$$n=\frac{PV}{RT}=\frac{1.22\space atm\times0.245\space L}{0.0821\space L\cdot atm/(mol\cdot K)\times298\space K}$$

$$n=\frac{1.22\times0.245}{0.0821\times298}\space mol$$

$$n=\frac{0.2989}{24.4658}\space mol\approx0.0122\space mol$$

Step3: Calculate the molar mass \(M\)

The molar mass \(M=\frac{m}{n}\), where \(m = 0.465\space g\) and \(n\approx0.0122\space mol\)

$$M=\frac{0.465\space g}{0.0122\space mol}\approx38.1\space g/mol$$

Answer:

D. \(38.0\space g/mol\)