Question

Methanol, CH₃OH, is produced industrially by the following reaction: CO(g) + 2H₂(g) (copper catalyst, 300 °C, 300 atm) → CH₃OH(g). Copper catalyst at 300 deg-C and 300 atm was used. Assuming that the gases behave as ideal gases, find the ratio of the total volume of the reactants to the final volume.

a) 1:1
b) 2:1
c) 3:1
d) 4:1

Answer 1

The ratio of the total volume of reactants to the final volume of the product in the synthesis of methanol is 3:1, as we have 3 moles of gases reacting to form 1 mole of methanol, and volume is proportional to moles for ideal gases.

Step-by-step explanation:

The student's question asks about the volume ratio of reactants to products in the synthesis of methanol from carbon monoxide and hydrogen. According to the balanced chemical equation for the production of methanol, CO(g) + 2H₂(g) → CH₃OH(g), under the assumption that gases behave as ideal gases, we can compare the number of moles of reactants to the number of moles of products.

Given that one mole of CO reacts with two moles of H₂ to form one mole of CH₃OH, we have a total of 3 moles of reactant gases producing 1 mole of product gas. Since we're dealing with gases at the same temperature and pressure, their volumes are proportional to the number of moles according to the ideal gas law.

Therefore, the ratio of the total volume of the reactants to the final volume of the product is 3:1, which corresponds to option (c).