Question

1. if you insert 32.75 grams of h₂, how many moles of ch₃oh are produced?

Explanation:

To solve this problem, we assume the reaction for the production of $\ce{CH3OH}$ (methanol) from $\ce{H2}$ (hydrogen gas) is the synthesis reaction: $\ce{CO + 2H2 -> CH3OH}$. We will follow these steps:

Step 1: Calculate the moles of $\ce{H2}$

The molar mass of $\ce{H2}$ is approximately $2\ \text{g/mol}$ (since the atomic mass of hydrogen, $H$, is approximately $1\ \text{g/mol}$, and $\ce{H2}$ has 2 hydrogen atoms).

The formula to calculate moles is:
$$\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}$$

Given the mass of $\ce{H2}$ is $32.75\ \text{g}$, we substitute the values:
$$\text{Moles of } \ce{H2} = \frac{32.75\ \text{g}}{2\ \text{g/mol}} = 16.375\ \text{mol}$$

Step 2: Use the stoichiometry of the reaction

From the balanced chemical equation $\ce{CO + 2H2 -> CH3OH}$, we see that 2 moles of $\ce{H2}$ produce 1 mole of $\ce{CH3OH}$.

We set up a mole ratio:
$$\text{Moles of } \ce{CH3OH} = \text{Moles of } \ce{H2} \times \frac{1\ \text{mol of } \ce{CH3OH}}{2\ \text{mol of } \ce{H2}}$$

Substituting the moles of $\ce{H2}$ we calculated:
$$\text{Moles of } \ce{CH3OH} = 16.375\ \text{mol} \times \frac{1}{2} = 8.1875\ \text{mol}$$

Answer:

The number of moles of $\ce{CH3OH}$ produced is $\boxed{8.19}$ moles (rounded to two decimal places) or $\boxed{8.1875}$ moles (exact value).