Certainly! Let's solve the problem step-by-step.
### Given Data:
- We have 0.833 moles of magnesium (Mg).
### Problem Statement:
We need to find how many moles of oxygen (O₂) are required when 0.833 moles of magnesium (Mg) are used.
### Step-by-Step Solution:
1. Understanding the Chemical Reaction:
The balanced chemical equation for the reaction between magnesium and oxygen is:
[tex]\[
2 \text{Mg} + \text{O}_2 \rightarrow 2 \text{MgO}
\][/tex]
This equation tells us that 2 moles of magnesium react with 1 mole of oxygen gas to form 2 moles of magnesium oxide.
2. Mole Ratio:
From the balanced chemical equation, we can see the mole ratio between magnesium (Mg) and oxygen (O₂):
[tex]\[
\text{2 moles of Mg} : \text{1 mole of O}_2
\][/tex]
This can be simplified to:
[tex]\[
\text{1 mole of Mg} : \frac{\text{1}}{\text{2}} \text{ mole of O}_2
\][/tex]
3. Using the Given Data:
We are given that we have 0.833 moles of magnesium (Mg). To find the corresponding moles of oxygen (O₂), we use the ratio derived from the balanced chemical equation.
4. Calculating Moles of O₂:
According to the ratio, for every mole of magnesium, we need 0.5 moles of oxygen. Therefore, for 0.833 moles of magnesium, the moles of oxygen required are:
[tex]\[
\text{Moles of O}_2 = \frac{\text{Moles of Mg}}{2}
\][/tex]
Plugging in the given number of moles of Mg, we get:
[tex]\[
\text{Moles of O}_2 = \frac{0.833}{2} = 0.4165 \text{ mol}
\][/tex]
So, 0.833 moles of magnesium (Mg) will require approximately 0.4165 moles of oxygen (O₂).
