Question

the volume of a sample of gas (2.49 g) is 752 ml at 1.98 atm and 62°c. what is the gas?

Explanation:

Step1: Convert units

Convert volume \( V = 752\space mL=0.752\space L\), temperature \(T=(62 + 273.15)\space K = 335.15\space K\)

Step2: Use ideal gas law \(PV=nRT\)

We know \(P = 1.98\space atm\), \(R=0.0821\space L\cdot atm/(mol\cdot K)\). From \(PV=nRT\), we can find \(n=\frac{PV}{RT}\). Substitute the values: \(n=\frac{1.98\times0.752}{0.0821\times335.15}\)

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Step3: Calculate molar mass \(M\)

Molar mass \(M=\frac{m}{n}\), where \(m = 2.49\space g\), \(n\approx0.0541\space mol\). So \(M=\frac{2.49}{0.0541}\approx46.0\space g/mol\)

Step4: Identify the gas

The molar mass of \(NO_{2}\): \(M=(14 + 2\times16)\space g/mol=46\space g/mol\)

Answer:

\(NO_{2}\)