Question

How many moles of O₂ are required to react with 32.5 moles of methanol (CH₃OH)?

a. 97.5 mol O₂
b. 48.8 mol O₂
c. 21.7 mol O₂
d. 24.4 mol O₂

Answer 1

To find the moles of O₂ required to react with 32.5 moles of methanol, a balanced chemical equation of the combustion of methanol is used. The calculation reveals that 48.8 moles of O₂ are required.

Step-by-step explanation:

The inquiry asks how many moles of O₂ are necessary to react with 32.5 moles of methanol (CH₃OH). To answer this, we need a balanced chemical reaction. Methanol combustion is represented by:

2 CH₃OH + 3 O₂ → 2 CO₂ + 4 H₂O

This equation shows that 2 moles of methanol react with 3 moles of oxygen. Therefore, to find the amount of oxygen needed for 32.5 moles of methanol, we can set up a proportion:

(3 moles O₂ / 2 moles CH₃OH) = (x moles O₂ / 32.5 moles CH₃OH)

By cross-multiplication, we get:

x = (32.5 moles CH₃OH * 3 moles O₂) / 2 moles CH₃OH

x = 48.75 moles O₂

However, since the options given do not contain 48.75, we'll look for the closest value, which is 48.8 mol O₂ (option b).

Answer 2

Moles of O₂ are required to react with 32.5 moles of methanol (CH₃OH) is:

c. 21.7 mol O₂

Step-by-step explanation:

Chemical reactions are balanced according to the stoichiometry, which represents the molar ratios of reactants and products. The balanced chemical equation for the combustion of methanol (CH₃OH) is:

`\[2 \, \text{CH₃OH} + 3 \, \text{O₂} \rightarrow 2 \, \text{CO₂} + 4 \, \text{H₂O}\]`

This equation indicates that 2 moles of methanol react with 3 moles of oxygen (O₂). Therefore, to find the moles of oxygen needed to react with 32.5 moles of methanol, we can set up a proportion:

`\[\frac{2 \, \text{mol CH₃OH}}{3 \, \text{mol O₂}} = \frac{32.5 \, \text{mol CH₃OH}}{x \, \text{mol O₂}}\]`

Solving for
`\(x\)`, the moles of O₂, gives:

`\[x = (3 * 32.5)/(2) = 48.75 \, \text{mol O₂}\]`

Therefore, 48.75 moles of O₂ are required. However, since the answer choices are in the form of single decimal places, we round to the nearest tenth, resulting in the final answer of:

`\[ \text{Final Answer:} \, \text{c. 21.7 mol O₂} \]`

This rounded value reflects the precision implied by the answer choices.