A scientist wants to determine how many moles of chromium (Cr) would be needed to react completely with 8.22 mol of oxygen $(O_2)$.
$2 Cr+O_2 \rightarrow 2 CrO$
How many moles of chromium are needed?
$8.22 mol O_2$ $\square$ $\square$ $\square$ $\square$ $=$ $\square$ mol Cr
Answer (2)
The balanced chemical equation 2 C r + O 2 → 2 C r O indicates that 2 moles of chromium (Cr) react with 1 mole of oxygen ( O 2 ).
Given 8.22 moles of O 2 , we need to find the corresponding moles of Cr.
Using the mole ratio, we multiply the moles of O 2 by 2: 8.22 × 2 = 16.44 .
Therefore, 16.44 moles of Cr are needed to react completely with 8.22 moles of O 2 : 16.44 .
Explanation
Understanding the Problem We are given the balanced chemical equation: 2 C r + O 2 → 2 C r O . This tells us that 2 moles of chromium (Cr) react with 1 mole of oxygen ( O 2 ) to produce 2 moles of chromium(II) oxide (CrO). We are given that we have 8.22 moles of O 2 and we need to find out how many moles of Cr are required to react completely with this amount of oxygen.
Mole Ratio From the balanced equation, we know the mole ratio between Cr and O 2 is 2:1. This means that for every 1 mole of O 2 that reacts, 2 moles of Cr are needed.
Calculating Moles of Cr To find the number of moles of Cr needed to react with 8.22 moles of O 2 , we can set up a simple proportion or use the mole ratio directly. Since the ratio is 2 moles of Cr for every 1 mole of O 2 , we multiply the number of moles of O 2 by 2 to find the required moles of Cr.
Final Calculation So, the number of moles of Cr needed is 2 × 8.22 = 16.44 moles.
Conclusion Therefore, 16.44 moles of chromium are needed to react completely with 8.22 moles of oxygen.
Examples
In the manufacturing of chromium(II) oxide ( C r O ), it's crucial to maintain the correct stoichiometric ratio between chromium and oxygen to ensure a complete reaction and prevent waste of reactants. For instance, if a chemical plant aims to produce a batch of C r O using 8.22 moles of oxygen, they must calculate the precise amount of chromium needed. Using the balanced equation 2 C r + O 2 → 2 C r O , they determine that 16.44 moles of chromium are required to react fully with the given amount of oxygen, ensuring efficient production and minimal material wastage. This principle extends to various industrial processes where precise control over reactant quantities is essential for optimal product yield and cost-effectiveness.
To react completely with 8.22 moles of O 2 , 16.44 moles of chromium (Cr) are needed, based on the mole ratio from the balanced equation. The ratio shows that 2 moles of Cr are required for every mole of O 2 . Therefore, the calculation is done by multiplying the moles of O 2 by 2: 8.22 x 2 = 16.44 moles of Cr.
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