Given:
[tex]$2 LiBr+Ba \rightarrow BaBr_2+2 Li$[/tex]
In this chemical reaction, 325 grams of barium (Ba) react completely. How many moles of lithium (Li) are produced?
A. 1.18 mol
B. 2.37 mol
C. 4.73 mol
D. [tex]$16.4 mol^{\prime}$[/tex]
E. 32.9 mol
Answer (2)
Determine the moles of barium (Ba) using its molar mass: m o l es = 137.33 325 ≈ 2.366 mol.
Use the stoichiometry of the reaction 2 L i B r + B a → B a B r 2 + 2 L i to find the mole ratio between Ba and Li (1:2).
Calculate the moles of lithium (Li) produced: m o l es o f L i = 2.366 × 2 ≈ 4.73 mol.
The number of moles of lithium produced is approximately 4.73 mol.
Explanation
Understanding the Problem We are given the balanced chemical reaction: 2 L i B r + B a → B a B r 2 + 2 L i . We know that 325 grams of barium (Ba) react completely, and we want to find out how many moles of lithium (Li) are produced.
Finding the Molar Mass of Barium First, we need to find the molar mass of barium (Ba). The molar mass of barium (Ba) is approximately 137.33 g/mol.
Calculating Moles of Barium Next, we calculate the number of moles of barium (Ba) that reacted. We use the formula: m o l es = m o l a r ma ss ma ss . Plugging in the values, we get: m o l es o f B a = 137.33 g / m o l 325 g ≈ 2.366 m o l .
Determining the Mole Ratio Now, we use the stoichiometry of the balanced chemical equation to determine the mole ratio between barium (Ba) and lithium (Li). From the equation, 1 mole of Ba produces 2 moles of Li.
Calculating Moles of Lithium Finally, we calculate the number of moles of lithium (Li) produced using the mole ratio: m o l es o f L i = m o l es o f B a × 2 . Plugging in the value, we get: m o l es o f L i = 2.366 m o l × 2 ≈ 4.733 m o l .
Final Answer Therefore, approximately 4.73 moles of lithium (Li) are produced.
Examples
In the manufacturing of batteries, lithium is a crucial component. If a chemical engineer needs to determine the amount of lithium produced from a reaction involving barium, they would use stoichiometry similar to this problem. By knowing the mass of barium reacted, they can calculate the moles of lithium produced, which helps in controlling the production process and ensuring the desired output. This calculation is essential for optimizing the use of resources and meeting production targets.
By using the balanced chemical reaction and the mass of barium, we calculated that approximately 4.73 moles of lithium are produced. This is done by first finding the moles of barium and then applying the stoichiometric ratios from the balanced equation. Hence, the answer is option C: 4.73 mol.
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