# Produce Methanol: Calculating Hydrogen Gas Requirement

## How many liters of hydrogen gas are required to produce 50.3 g of methanol at 345 K and a pressure of 0.998 atm?

Final answer: About 70.3 liters of hydrogen gas under the conditions specified is needed to produce 50.3g of methanol.

## Answer:

The calculation for the volume of hydrogen gas required to produce 50.3 g of methanol involves utilizing the ideal gas law, stoichiometry, and molar mass.

In this chemical reaction, the molar ratio between hydrogen gas (H2) and methanol (CH3OH) is 2 moles of H2 to produce 1 mole of CH3OH. Given that 50.3 g of CH3OH corresponds to approximately 1.57 moles, we calculate that 3.14 moles of H2 are needed.

Applying the ideal gas law equation (PV = nRT) with the provided temperature of 345 K, pressure of 0.998 atm, and number of moles of H2 as 3.14, we find that the volume of hydrogen gas required is approximately 70.3 liters.

To produce methanol efficiently, it is crucial to accurately determine the quantity of reactants needed, such as hydrogen gas in this case. By understanding the stoichiometry of the reaction and applying the ideal gas law, we can calculate the required volume of hydrogen gas with precision.

Stoichiometry plays a key role in balancing chemical equations and establishing the molar ratios between reactants and products. In this scenario, knowing that 2 moles of hydrogen gas are necessary to produce 1 mole of methanol enables us to convert the given mass of methanol to moles and subsequently determine the amount of hydrogen gas required.

Utilizing the ideal gas law formula, which relates pressure, volume, temperature, and the number of moles of gas, we can solve for the volume of hydrogen gas under the given conditions. By substituting the known values into the equation and rearranging to isolate the volume variable, we arrive at the calculated volume of approximately 70.3 liters.

Understanding the principles of stoichiometry and gas laws empowers us to make accurate calculations in chemical processes, ensuring efficient utilization of reactants and successful production of desired compounds like methanol.