Question

The density of methane at 2.0 atm pressure and 27 degrees centigrade is

• A. $0.13{\mathrm{gL}}^{-1}$
• B. $0.26{\mathrm{gL}}^{-1}$
• C. $1.30{\mathrm{gL}}^{-1}$
• D. $26.0{\mathrm{gL}}^{-1}$

Answer 1

The correct option is C

$1.30{\mathrm{gL}}^{-1}$

The explanation for the correct answer:-

Option (C) $1.30{\mathrm{gL}}^{-1}$

Step 1: Given data

$\mathrm{T}=27°\mathrm{C}=300\mathrm{K}\mathrm{P}=2\mathrm{atm}$

Step 2: Calculating the mass of carbon

Mass of methane (${\mathrm{CH}}_4$)

[Mass of Carbon= $12\mathrm{g}/\mathrm{mol}$] [Mass of Hydrogen=$1\mathrm{g}/\mathrm{mol}$ ]

Thus,

$$\begin{gathered} \mathrm{M}=12+(4\mathrm{x}1) \\ =16\mathrm{g}/\mathrm{mol} \end{gathered}$$

Step 3: Evaluating density

We also know that

$\mathrm{R}=0.082\mathrm{L}\mathrm{atm}/\mathrm{K}\mathrm{mol}$

On substituting the values, we get;

$$\begin{gathered} d=\frac{PM}{RT} \\ \mathrm{d}=\frac{2X16}{0.0821X300} \end{gathered}$$

Therefore calculated density = $1.299{\mathrm{gL}}^{-1}$

Hence, option (C) is the correct answer.