Question

Methanol,CH₃OH, is produced industrially by the following reaction:

Assuming that the gases behave as ideal gases, find the ratio of the total volume of the reactants to the final volume.

Short answer

The ratio of the total volume of reactants to the final volume is obtained as 3:1.

Step-by-step solution

Define Gas

One of the four fundamental states of matter, a gas is made up of particles with no definite volume or structure.

 Evaluating the ratio

Using the Avogadro’s law at the constant pressure and the temperature is:

\(\begin{array}{c}{\rm{V \alpha n or V = k \times n or}}\\\frac{{{{\rm{V}}_{\rm{1}}}}}{{{{\rm{n}}_{\rm{1}}}}}{\rm{ = }}\frac{{{{\rm{V}}_{\rm{2}}}}}{{{{\rm{n}}_{\rm{2}}}}}\end{array}\)

The value of \({{\rm{V}}_{\rm{1}}}\) is the total volume of reactants.

The value of \({{\rm{V}}_{\rm{2}}}\) is the final volume.

\(\begin{array}{c}\frac{{{{\rm{V}}_{\rm{1}}}}}{{{{\rm{V}}_{\rm{2}}}}}{\rm{ = }}\frac{{{{\rm{n}}_{\rm{1}}}}}{{{{\rm{n}}_{\rm{2}}}}}\\{\rm{ = }}\frac{{\rm{3}}}{{\rm{1}}}\end{array}\)

Therefore, the ratio is\({\rm{3:1}}\).